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Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives
Abstract
This article examines the adequacy of the “rules of thumb” conventional cutoff criteria and several new alternatives for various fit indexes used to evaluate model fit in practice. Using a 2‐index presentation strategy, which includes using the maximum likelihood (ML)‐based standardized root mean squared residual (SRMR) and supplementing it with either Tucker‐Lewis Index (TLI), Bollen's (1989) Fit Index (BL89), Relative Noncentrality Index (RNI), Comparative Fit Index (CFI), Gamma Hat, McDonald's Centrality Index (Mc), or root mean squared error of approximation (RMSEA), various combinations of cutoff values from selected ranges of cutoff criteria for the ML‐based SRMR and a given supplemental fit index were used to calculate rejection rates for various types of true‐population and misspecified models; that is, models with misspecified factor covariance(s) and models with misspecified factor loading(s). The results suggest that, for the ML method, a cutoff value close to .95 for TLI, BL89, CFI, RNI, and Gamma Hat; a cutoff value close to .90 for Mc; a cutoff value close to .08 for SRMR; and a cutoff value close to .06 for RMSEA are needed before we can conclude that there is a relatively good fit between the hypothesized model and the observed data. Furthermore, the 2‐index presentation strategy is required to reject reasonable proportions of various types of true‐population and misspecified models. Finally, using the proposed cutoff criteria, the ML‐based TLI, Mc, and RMSEA tend to overreject true‐population models at small sample size and thus are less preferable when sample size is small.
... Con respecto a la evaluación de las es- (Hu y Bentler, 1998, 1999. En el contexto mexicano Jaimes et al. (2010) realizaron la traducción y adaptación al español del BRIEF-A para identificar sus propiedades psicométricas en una muestra de estudiantes universitarios. ...
... Se realizó primero un AFC de segundo orden para investigar si la estructura factorial original de 9 escalas del BRIEF-A y dos factores del ítem, se confirmaba mediante un análisis de Modelamiento de Ecuaciones Estructurales (SEM por sus siglas en inglés). Los valores considerados como aceptables de TLI y el CFI fueron ≥0.90 (Byrne, Baron, Larsson y Melin, 1995) y ≥0.95 (Hu y Bentler, 1998, 1999; para el RMSEA ≤.0.06 y para el SRMR ≤.08 (Hu y Bentler, 1998, 1999 lo que indica un buen ajuste del modelo. ...
... Se realizó primero un AFC de segundo orden para investigar si la estructura factorial original de 9 escalas del BRIEF-A y dos factores del ítem, se confirmaba mediante un análisis de Modelamiento de Ecuaciones Estructurales (SEM por sus siglas en inglés). Los valores considerados como aceptables de TLI y el CFI fueron ≥0.90 (Byrne, Baron, Larsson y Melin, 1995) y ≥0.95 (Hu y Bentler, 1998, 1999; para el RMSEA ≤.0.06 y para el SRMR ≤.08 (Hu y Bentler, 1998, 1999 lo que indica un buen ajuste del modelo. ...
El Inventario para la Evaluación Conductual de la Función Ejecutiva-Adultos (BRIEF-A) es uno de los autoreportes más utilizados internacionalmente para evaluar la percepción de funciones ejecutivas en adultos, tanto en muestras sanas como clínicas. Estudios previos han reportado diversidad en la estructura factorial interna del inventario, pero pocos han analizado la estructura factorial a nivel de ítem. El objetivo del estudio fue analizar la validez de la estructura factorial a nivel de ítem y las propiedades psicométricas del BRIEF-A en 352 estudiantes universitarios mexicanos. Se adaptó una versión mexicana del BRIEF-A, se evaluó la estructura factorial a nivel de ítems mediante análisis factoriales confirmatorios (AFC) y exploratorios (AFE) cuyos resultados no confirmaron la estructura factorial original de 9 factores. Se propone una versión reducida de 47 ítems organizados en 6 fac-tores con índices aceptables de ajuste (CFI= 0.886, TLI= 0.879, RMSEA= 0.056 y SRMR= 0.054), buenos índices de consistencia interna para los 6 factores (ω=0.77-0.95) y excelente para la escala total (ω=0.97). Se recomienda el uso de esta versión reducida del BRIEF-A en muestras semejan-tes.
... Model fit parameters were root-mean-square error of approximation (RMSEA), comparative fit index (CFI), Tucker-Lewis index (TLI), and standardized root-mean-square residual (SRMR). Values of RMSEA near or below 0.08 represent acceptable model fit, and values lower than 0.06 represent good-to-excellent model fit (Hu & Bentler, 1999;Kline, 2015). CFI and TLI values near or above 0.90 represent acceptable model fit, while values higher than 0.95 represent a good-to-excellent model fit (Hu & Bentler, 1999;Kline, 2015). ...
... Values of RMSEA near or below 0.08 represent acceptable model fit, and values lower than 0.06 represent good-to-excellent model fit (Hu & Bentler, 1999;Kline, 2015). CFI and TLI values near or above 0.90 represent acceptable model fit, while values higher than 0.95 represent a good-to-excellent model fit (Hu & Bentler, 1999;Kline, 2015). SRMR values lower or equal than 0.10 indicate adequate fit and lower than 0.06 in combination with previous indices indicate good fit (Hu & Bentler, 1999;Kline, 2015). ...
... CFI and TLI values near or above 0.90 represent acceptable model fit, while values higher than 0.95 represent a good-to-excellent model fit (Hu & Bentler, 1999;Kline, 2015). SRMR values lower or equal than 0.10 indicate adequate fit and lower than 0.06 in combination with previous indices indicate good fit (Hu & Bentler, 1999;Kline, 2015). ...
Assessment tools for depression and anxiety usually inquire about the frequency of symptoms. However, evidence suggests that different question framings might trigger different responses. Our aim is to test if asking about symptom’s context, ability, duration, and botherment adds validity to Patient Health Questionnaire–9, General Anxiety Disorder–7, and Patient-Related Outcome Measurement Information Systems depression and anxiety. Participants came from two cross-sectional convenience-sampled surveys (N = 1,871) of adults (66% females, aged 33.4 ± 13.2), weighted to approximate with the state-level population. We examined measurement invariance across the different question frames, estimated whether framing affected mean scores, and tested their independent validity using covariate-adjusted and sample-weighted structural equation models. Validity was tested using tools assessing general disability, alcohol use, loneliness, well-being, grit, and frequency-based questions from depression and anxiety questionnaires. A bifactor model was applied to test the internal consistency of the question frames under the presence of a general factor (i.e., depression or anxiety). Measurement invariance was supported across the different frames. Framing questions as ability (i.e., “How easily …”) produced a higher score, compared with framing by context (i.e., “In which daily situations …”). Construct and criterion validity analysis demonstrate that variance explained using multiple question frames was similar to using only one. We detected a strong overarching factor for each instrument, with little variances left to be explained by the question frame. Therefore, it is unlikely that using different adverbial phrasings can help clinicians and researchers to improve their ability to detect depression or anxiety.
... The CR of variable transcendental Leadership was 0.965, an affective commitment was 0.918, intrinsic motivation was 0.891, and altruistic mind-set was 0.889. The findings revealed that each construct's composite reliability (CR) surpassed the threshold values suggested by Hu and Bentler (1999), indicating a stronger significance. Using the AMOS plugin from the master validity tool developed by Gaskin and Lim (2016), we could assess the convergent and discriminant validity of the study variables. ...
... Specifically, the CFI value surpasses the recommended threshold of 0.95, while the SRMR value remains below the preferred threshold of 0.08, highlighting the favorable fit of the model. Moreover, to reinforce the evidence, it is noteworthy that the RMSEA value is below the critical threshold of 0.06, as suggested by Hu and Bentler (1999). Notably, the values obtained from the hypothesized specified model further support its excellent fit. ...
... The PClose value of 0.422 also indicates a favorable fit. Importantly, all the obtained values meet the threshold criteria Hu and Bentler (1999) suggested, further validating the proposed model. ...
... To evaluate the quality of the adjustments of the models, we used the Comparative Fit Index-CFI (Bentler, 1990), the Tucker-Lewis Index-TLI (Tucker & Lewis, 1973), the mean square error of approximation-RMSEA (Sörbom & Jöreskog, 1981;Steiger, 1990), and the residual standardized mean square root-SRMR (Hu & Bentler, 1999;Sörbom & Jöreskog, 1981). An adequate adjustment was considered when CFI and TLI values were >0.90, while values of >0.95 indicated a good (Bentler, 1990;Hu & Bentler, 1999). ...
... To evaluate the quality of the adjustments of the models, we used the Comparative Fit Index-CFI (Bentler, 1990), the Tucker-Lewis Index-TLI (Tucker & Lewis, 1973), the mean square error of approximation-RMSEA (Sörbom & Jöreskog, 1981;Steiger, 1990), and the residual standardized mean square root-SRMR (Hu & Bentler, 1999;Sörbom & Jöreskog, 1981). An adequate adjustment was considered when CFI and TLI values were >0.90, while values of >0.95 indicated a good (Bentler, 1990;Hu & Bentler, 1999). RMSEA and SRMR values between 0.05 and 0.08 indicated an acceptable fit, while values <0.05 indicated a good fit (Hu & Bentler, 1999). ...
... An adequate adjustment was considered when CFI and TLI values were >0.90, while values of >0.95 indicated a good (Bentler, 1990;Hu & Bentler, 1999). RMSEA and SRMR values between 0.05 and 0.08 indicated an acceptable fit, while values <0.05 indicated a good fit (Hu & Bentler, 1999). ...
Poor early childhood self‐regulation is related to many mental health problems and antisocial behaviours, so it is important to use psychometrically sound instruments to assess children's self‐regulation and behavioural development. The aim of this study is to report the translation, adaptation, as well as explore the construct validity of the child self‐regulation & behaviour questionnaire (CSBQ) for the Brazilian context. The process consisted of different steps, such as transcultural translation, item intelligibility analysis, and psychometric analysis based on classical and contemporary theories. The validation process was carried out on a sample of 277 parents/caregivers (35.00 ± 6.72 years old) of 281 children (4.92 ± 1.45 years old; 156 females). The final Brazilian version showed adequate values of semantic, idiomatic, and conceptual equivalence. The validation process resulted in a seven‐dimensional model with 33 items. The validation of Brazilian CSBQ is promising for investigating early self‐regulation and behaviour problems in low‐middle income contexts.
... To assess the CFA model's goodness-of-fit, various goodness-of-fit indices including chi-square test (χ 2 ) and χ 2 /df, Root Mean Square Error of Approximation (RMSEA) with 95% confidence interval (CI), Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), and Standardised Root Mean Square Residual (SRMR) were used. The CFA model was deemed to be a good fit for the data when the χ 2 result was non-significant (Marsh & Hocevar, 1985) and the χ 2 /df < 2 (Hu & Bentler, 1999;Schreiber et al., 2006). The adequacy of the other fit indices was assessed by comparing them to the threshold values recommended in prior research studies (Hu & Bentler, 1999;Ross & Bauldry, 2022;Schreiber et al., 2006); RMSEA ≤ 0.05, CFI ≥ 0.95, and SRMR < 0.08 indicate the model's good fit to the observed data. ...
... The CFA model was deemed to be a good fit for the data when the χ 2 result was non-significant (Marsh & Hocevar, 1985) and the χ 2 /df < 2 (Hu & Bentler, 1999;Schreiber et al., 2006). The adequacy of the other fit indices was assessed by comparing them to the threshold values recommended in prior research studies (Hu & Bentler, 1999;Ross & Bauldry, 2022;Schreiber et al., 2006); RMSEA ≤ 0.05, CFI ≥ 0.95, and SRMR < 0.08 indicate the model's good fit to the observed data. Due to the χ 2 statistic's sensitivity to the sample size (Marsh & Hocevar, 1985) and departures from multivariate normality in the data (Ross & Bauldry, 2022), more importance is placed on these fit indices, because the χ 2 statistic tends to reject the null hypothesis in samples larger than 100 (Lebowitz et al., 2019;Ross & Bauldry, 2022). ...
... CFI = 0.997, TLI = 0.997, RMSEA = 0.021 (90% CI [0.000, 0.035], p = 1.00), and SRMR = 0.056) with standardised factor loadings ranging from 0.452 to 0.722. All of the goodness-of-fit indices of the model comfortably met the threshold values recommended in prior works (Hu & Bentler, 1999;Ross & Bauldry, 2022), indicating a good fit between the model and the data. Hence, no further modification to the model was deemed necessary. ...
This study employed a non-equivalent quasi-experimental pre-test/post-test control-group design to study the effect of the PhET simulation intervention on students’ engagement, satisfaction, and academic achievement in the learning of direct current electric circuit concepts among Bhutanese students. We analysed the pre- and post-test scores and perceptions of 57 ninth-grade students, divided into experimental group (EG, n = 29) and control group (CG, n = 28), from one high school in Paro District, Bhutan. The EG students were taught with the PhET simulation intervention, while the CG students were taught with the traditional chalk-talk method. The pre- and post-test scores were collected with the Electric Circuits Conceptual Evaluation (ECEE) inventory. Mean, standard deviation, a two-sample t-test, and multiple linear regression (MLR) were computed using R and RStudio. The t-test revealed a statistically significant difference in the mean post-test scores of CG and EG students. MLR analysis further confirmed that this difference was due to the PhET simulation intervention, ruling out the influence of other confounding variables. Additionally, an instrument called the PhET Engagement-Satisfaction Questionnaire was developed to assess EG students’ engagement level and satisfaction with the PhET simulation intervention. Confirmatory factor analysis and Cronbach’s alpha calculation confirmed its validity and reliability. Data from the PhET Engagement-Satisfaction Questionnaire unveiled significant impact of the PhET simulation intervention on students’ engagement level and their overall satisfaction, reinforcing prior research. However, further research with a larger sample size, incorporating lesson observations, interviews, and our measurement tool, is necessary to ascertain whether the findings it yields align with the present study’s findings.
... Studies of the factor structure of the LPFS-BF 2.0 have demonstrated a highly correlated two-factor structure in adults Natoli et al., 2022;Weekers et al., 2019), as well as a unidimensional factor structure (Weekers et al., 2023) and a bifactor structure with one general factor and two specific factors (Paap et al., 2024). Regarding prior research on the factor structure of the English translation specifically (Le , although a unidimensional factor structure was not supported according to Hu and Bentley's criteria (Hu & Bentler, 1999), it met fit criteria outlined by Chen (2007). Given empirical support for its unidimensional factor structure and the theoretical basis of the LPF as a unidimensional severity criterion, we expected that the LPFS-BF 2.0 data would fit a unidimensional confirmatory factor analysis (CFA) model. ...
... .95-1.00 = excellent fit, .90-.95 = acceptable fit), Tucker-Lewis index (TLI; .95-1.00 = excellent fit, .90-.95 = acceptable fit), the root-mean-square error of approximation (RMSEA; ,.08 = reasonable fit, ..10 = poor fit), and the standardized root-mean-square residual (SRMR; ,.08 = acceptable fit) (Browne & Cudeck, 1992;Hu & Bentler, 1999;Kline, 2016). Chi-square tests were also conducted, although results were not given much weight due to the test's sensitivity to sample size (Fan et al., 1999). ...
Reflecting the recent consensus that challenges in personality functioning often onsets in adolescence, and the move toward dimensional models of personality pathology such as the level of personality functioning (LPF) of the alternative model for personality disorders, it is important to have validated measures that can assess LPF in young people. The Level of Personality Functioning Scale—Brief Form 2.0 (LPFS-BF 2.0) is the briefest measure of LPF and may be particularly well suited for assessing LPF in youth; however, it has yet to be formally validated in youth. Therefore, the current investigation evaluated the psychometric properties of the LPFS-BF 2.0 in adolescents drawn from a community sample of ethnically diverse North American youth (N = 194, age 12–18; 58% female). Factor structure, gender invariance, reliability, convergent validity, incremental validity, and criterion validity were evaluated. Results demonstrated support for the LPFS-BF 2.0’s unidimensional factor structure, as well as high internal consistency. Configural, metric, and scalar measurement invariance was supported across male and female genders, as well as convergent validity. Relative to the Personality Inventory for the DSM-5 Brief Form and Levels of Personality Functioning Questionnaire 12–18, the LPFS-BF 2.0 demonstrated additional variance in predicting borderline personality features, and internalizing and externalizing problems. Study findings support the English version of the LPFS-BF 2.0 as a brief and psychometrically sound instrument for assessing LPF in youth and adolescents.
... We adjusted for non-normality through the robust maximum likelihood estimator (MLR) for standard errors (Yuan & Bentler, 2000;Brown, 2015;Kline, 2016). To assess the overall model fit of the three models, we evaluated different goodness-of-fit indices based on the cutoff values suggested by Hu and Bentler (1999) and Beauducel and Wittmann (2005). Chi-square (χ²) and the χ 2 ratio (χ 2 /degrees of freedom) was used. ...
... According to Hu and Bentler (1999), good model fit is inferred when values of CFI and TLI are higher than 0.90, and RMSEA is close to 0.06. However, some authors (Cangur & Ercan, 2015) consider that an RMSEA value between 0.05 and 0.08 indicates an adaptation close to good. ...
The main objective of this study is to examine the psychometric properties of the PERMA-Profiler in a Spanish context. The PERMA-Profiler, developed by Butler & Kern (Int J Wellbeing 6(3):1-48, 2016) to measure Seligman’s (Flourish: A visionary new understanding of happiness and well-being, 2011) PERMA model of flourishing, consists of five domains that assess well-being: Positive Emotion (P), Engagement (E), Relationships (R), Meaning (M), and Accomplishment (A). We translated and adapted the PERMA-Profiler, analyzed the instrument’s reliability, its validity based on an internal structure through three confirmatory factor analyses, gender and age invariance, and its convergent and discriminant validity. A total of 2525 participants completed all measures. The results of the analyses to confirm the internal consistency are very acceptable in all the domains and in Overall Well-being (PERMA), except for the Engagement domain. The results of three confirmatory factor analyses show that the model of five independent interrelated factors (domains) presents the best fit. The analysis shows the invariance across gender and age groups. The analyses of the convergent validity show that are positively and significantly related to satisfaction with life (SWLS), to the six evaluated dimensions of psychological well-being (PWB), to positive affect (PANAS) and dispositional optimism (LOT-R) and the general physical and mental health status (SF-36). The discriminant validity analyses show that are related negatively and significantly to negative affect (PANAS), the total score of depression (BDI-II) and the Cognitive-Affective and Somatic-Motivational factors. The findings of this study indicate that the PERMA-Profiler is transferable to the Spanish context, and the Spanish version is a reliable and valid measure of well-being.
... Proposed residual covariances between the items belonging to the same factor were added to the model since items of a defense category are theoretically associated with each other besides statistical recommendations on their covariances (Cole et al., 2007). For the Comparative Fit Index (CFI), literature proposes ≥0.95 as an excellent fit and ≥ 0.90 as an acceptable fit (Hu and Bentler, 1999;McDonald and Ho, 2002;Kline, 2005). The indices of the Root Mean Square Error of Approximation (RMSEA) ≤ 0.06 and the Standardized Root Mean Square Residual (SRMR) ≤ 0.09 were suggested to indicate good fit (Hu and Bentler, 1999;Hooper et al., 2008). ...
... For the Comparative Fit Index (CFI), literature proposes ≥0.95 as an excellent fit and ≥ 0.90 as an acceptable fit (Hu and Bentler, 1999;McDonald and Ho, 2002;Kline, 2005). The indices of the Root Mean Square Error of Approximation (RMSEA) ≤ 0.06 and the Standardized Root Mean Square Residual (SRMR) ≤ 0.09 were suggested to indicate good fit (Hu and Bentler, 1999;Hooper et al., 2008). ...
The Defense Mechanisms Rating Scales-Self Report-30 (DMRS-SR-30) was recently developed to add a self-report alternative to the assessment of defenses, reflecting their generally accepted hierarchical organization. In this study, we aimed to examine psychometric properties and factor structure of the Turkish language version of the DMRS-SR-30. The sample consisted of 1.002 participants who filled out a survey comprising the DMRS-SR-30, the Brief Symptom Inventory, and the Inventory of Personality Organization through Qualtrics. Confirmatory Factor Analysis indicated a three-factor structure (CFI = 0.89, RMSEA = 0.05) that confirms the DMRS theoretical frame with a relatively acceptable fit. Defensive categories and total scale scores showed good to excellent reliability (α values ranging from 0.64 to 0.89). Correlations between defenses, symptoms, and personality functioning demonstrated good convergent and discriminant validity. The individuals with clinically significant BSI scores (T-score ≥ 63) differed on the DMRS-SR-30 scores from the individuals in the non-clinical range. The Turkish version of the DMRS-SR-30 is a reliable and valid instrument to self-assess the hierarchy of defense mechanisms and overall defensive functioning. Moreover, the current study supports the validity of the tripartite model of defenses in a language and culture different from the origins of the DMRS and DMRS-SR-30.
... The factor structure of the models was evaluated based on CFA, using the Comparative Fit Index (CFI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR), as recommended by Brown (2015) for CFA models. The model fit is considered acceptable if SRMR values are close to 0.08 or below, RMSEA values are close to 0.06 or below, and CFI is close to 0.95 or greater (Hu & Bentler, 1999). Raykov`s reliability coefficient (RRC) was calculated for each survey year. ...
... Table 1 showed that the CFA yielded an overall good model fit in the different survey years. Structural validity was established as the model fit was acceptable (SRMR 0.08 or below, RMSEA 0.06 or below, and CFI 0.95 or greater) (Hu & Bentler, 1999). ...
This study assessed the applicability of the Family Affluence Scale II (FASII) for conducting time trend analysis within Norway's “Health Behaviour in School-Aged Children Study” (HBSC), spanning from 2002 to 2018. A dataset comprising 27,470 valid questionnaires was employed to assess the psychometric properties of the FASII with respect to validity and reliability for use at single- and multiple times points. The analytical approach encompassed a range of statistical techniques, including confirmatory factor analysis (CFA), multi-group CFA, polychoric correlation testing between FASII scores and perceived family wealth, a subjective measure of socioeconomic position (SEP), and an assessment of perceived family wealth and FASII scores across time. The results of the study revealed an overall good model fit in CFA and a positive correlation between FASII scores and perceived family wealth. However, the analysis uncovered measurement non-invariance across survey years, sex, and age groups. Measurement non-invariance hampers direct time-to-time comparisons of FASII scores, impeding the assessment of affluence development over time. Despite this limitation, FASII maintains its utility for ranking affluence and measuring health outcomes at single time points. As such, this study offers valuable insight into the suitability of FASII for time trend analysis within the Norwegian HBSC data and broader research on social inequality.
... Regarding the other three measures, the CFI should be larger than 0.9 [35], the RMSEA point estimate and the upper bound of the 95 percent confidence interval should be smaller than 0.05 [36,37], and the SRMR should be smaller than 0.08 [35]. The fit measures and their interpretation can be obtained with the following command: The hypothesis of perfect fit *is* rejected according to the Chi-Square test statistics because the p-value is smaller than 0.05 ...
... Regarding the other three measures, the CFI should be larger than 0.9 [35], the RMSEA point estimate and the upper bound of the 95 percent confidence interval should be smaller than 0.05 [36,37], and the SRMR should be smaller than 0.08 [35]. The fit measures and their interpretation can be obtained with the following command: The hypothesis of perfect fit *is* rejected according to the Chi-Square test statistics because the p-value is smaller than 0.05 ...
Factor analysis is a method commonly employed to reduce a large number of variables into fewer numbers of factors. The method is often used to identify which observable indicators are representative of latent, not directly-observed constructs. This is a key step in developing valid instruments to assess latent constructs in educational research (e.g., student engagement or motivation). The chapter describes the two main approaches for conducting factor analysis (and how to combine them in an integrated factor analysis strategy) and provides a tutorial on implementing both techniques in the R programming language. The first is confirmatory factor analysis (CFA), a more theory-driven approach, in which a researcher actively specifies the number of underlying constructs as well as the pattern of relations between these dimensions and observed variables. The second is exploratory factor analysis (EFA), a more data-driven approach, in which the number of underlying constructs is inferred from the data, and all underlying constructs are assumed to influence all observed variables (at least to some degree).
... The study's path analysis yielded a satisfactory model fit, χ 2 5 31.98, df 5 10, normed χ 2 5 3.20, p < 0.001 and CFI 5 0.92 (Hu and Bentler, 1999;Klein, 1998). ...
... However, these controlling effects did not change the patterns of the original model regarding each path's magnitude and statistical significance. Furthermore, including team identification resulted in the model's unacceptable fit indices, χ 2 5 66.84, df 5 15, normed χ 2 5 4.46, p < 0.001 and CFI 5 0.84 (Hu and Bentler, 1999). Table 4 shows the models' comparisons regarding path coefficients and model fit. ...
Purpose
With the advance of Web 3.0 and the range of sensory experiences offered by virtual reality (VR) to sport fans, this study examines how VR spectators’ sensory experiences affect their intentions to consume VR products and services. For this purpose, the study puts forth an expanded stimulus-organism-response (S-O-R) model. In this framework, the stimuli are the sensory imagery and stimuli, the organism factors are presence and arousal and the response is the consumption intention. This model adeptly encapsulates the comprehensive process of stimuli while spectating a sporting event in a virtual environment.
Design/methodology/approach
For a VR stimulus, researchers developed a 3-min collegiate women’s volleyball game. Watching the game in VR were 131 collegiate students, who were then questioned about their visual and aural imagination of the game stimuli, perceived visual and aural stimuli, sense of presence, arousal and VR consumption intentions. To ensure the validity and reliability of the measurement model, confirmatory factor analysis was first conducted. Subsequently, the model was subjected to path analysis.
Findings
The measurement model demonstrated both validity and reliability. The subsequent path analysis yielded the model’s satisfactory fit. In particular, the mental visualization of VR spectators significantly influenced their perception of visual stimuli, while their imaginative engagement with auditory aspects impacted their perception of aural stimuli. The observed visual stimuli positively impacted the degree of presence experienced and the level of arousal induced. Similarly, the auditory stimuli exerted comparable effects on presence and arousal. The sense of arousal exhibited a considerable influence on the sense of presence. Furthermore, arousal emerged as a substantial determinant of individuals' VR consumption intentions.
Originality/value
The study highlights that the affective status of VR sport spectators is dominant in determining their consumption intentions. Also, the study finds the decisive role of presence in processing sensory stimuli in virtual sport spectating. It also provides managerial insight into designing and customizing VR sport experiences to be more enjoyable and impactful.
... According to Brown [39], the following four common indices to assess fit of the overall model and to calculate the model adjustment were used: Comparative Fit Index (CFI), Tucker-Lewis Index (TLI), Root Mean Square Error of Approximation (RMSEA), and Standardized Root Mean Square Residual (SRMR). In accordance with the recommendations of Hu and Bentler [40], the following criteria were used: TLI/ CFI > 0.90 (accepted fit), RMSEA < 0.08 (accepted fit) and SRMR < 0.08 (good fit). The best fitness of the overall model was represented by higher TLI/CFI values and lower RMSA/SRMR values [40]. ...
... In accordance with the recommendations of Hu and Bentler [40], the following criteria were used: TLI/ CFI > 0.90 (accepted fit), RMSEA < 0.08 (accepted fit) and SRMR < 0.08 (good fit). The best fitness of the overall model was represented by higher TLI/CFI values and lower RMSA/SRMR values [40]. Moreover, we calculated the Akaike Information Criterion (AIC), a parsimony correction index to identify the most parsimonious model which fitted the data. ...
Disorganization is a nuclear dimension of psychosis, especially in schizophrenia. Despite its relevant association with poor prognosis and negative outcomes, it is still under-investigated compared to positive and negative symptoms, in particular at the onset of illness. This study explored disorganization in youth at Clinical High Risk for Psychosis (CHR-P) over a 2-year period. A sample of 180 CHR-P participants (50% males; 51.1% with baseline second-generation antipsychotic medication) recruited within a specialized CHR-P service completed the Positive and Negative Syndrome Scale (PANSS) and the Global Assessment of Functioning (GAF) scale. Across the follow-up, we examined key associations of disorganization with other domains of psychopathology, functioning, and treatment response using Spearman’s rank correlation coefficients and linear regression analyses. Our results showed a significant longitudinal reduction in disorganization severity levels across the follow-up. This decrease was significantly associated with improvements in negative symptoms and daily functioning, with a shorter duration of untreated psychiatric symptoms, and with baseline equivalent dose of antipsychotic medication. No significant longitudinal associations with other treatment component of the PARMS program were found. Our findings suggest a longitudinal improvement in disorganization dimension in CHR-P individuals, especially in the context of early interventions targeting reduction in the duration of untreated psychiatric symptoms and favoring a prompt antipsychotic therapy.
... study variables, evaluating the first hypothesis. The mediation model employing structural equation modeling was developed to evaluate the second hypothesis and the model fit being evaluated using the following criteria recommended by Hu and Bentler (1999) ...
The impact of dysfunctional attitudes and unhelpful thinking upon clients presenting with personality-related psychological distress is an important clinical area of investigation as it informs psychological interventions. Despite this, there is limited research in this area. Thus, this study had two main aims: (1) examine the interrelationships between maladaptive personality traits, dysfunctional attitudes, unhelpful thinking, and psychological distress; and (2) explore the potential mediating roles of dysfunctional attitudes and unhelpful thinking on the relationship between maladaptive personality traits and psychological distress. A convenience sample of 728 undergraduate psychology students (mean age: 31.57 years; 76% female) completed an online questionnaire for course credit. The results supported the first hypothesis that after controlling for gender and age, there would be significant positive correlations among maladaptive personality traits, dysfunctional attitudes, and psychological distress. A structural equation model with an excellent fit (CMIN/df = 2.23, p = .063, TLI = 0.98, CFI = 0.99, SRMR, = 0.01, and RMSEA = 0.04) provided partial support for the second hypothesis in that dysfunctional attitudes and unhelpful thoughts mediated the relationship between maladaptive personality traits and psychological distress. Specifically, negative affectivity and detachment’s relationship with psychological distress were partially mediated via dysfunction attitudes and unhelpful thoughts, and dysfunctional attitudes respectively. These findings suggest that while dysfunctional attitudes and unhelpful thinking contribute to the relationship between personality traits and psychological distress, identification of other factors are required to improve theoretical understanding and subsequently psychological interventions.
... Model fit was assessed with the following benchmarks: comparative fit index (CFI) of 0.95 or greater, non-normed fit index (NNFI) of 0.95 or greater, root mean square error of approximation (RMSEA) less than or equal to 0.05, and standardized root mean square residual (SRMR) being less than or equal to 0.08. These cut-offs were based on established recommendations (Bentler & Bonett, 1980;Hu & Bentler, 1999;Schumacker & Lomax, 2004). ...
Despite the post-COVID return to face-to-face teaching and learning, many higher educational institutions continue to utilize videoconferencing due to its numerous benefits. Along with this increased adoption, reports have surfaced regarding videoconference fatigue (VF), a phenomenon characterized by exhaustion from using videoconference platforms. Despite this, there is a substantial gap in our understanding of the antecedent factors contributing to VF. Our study aims to develop and validate a research instrument for the study of the antecedents to VF in the context of whole-class teaching in higher education, which we term the AVFS-HE. We developed and tested this scale across three studies: first with 21 undergraduates in the substantive validity phase, and a further 508 undergraduates in the structural validity and external validity phases. The final 17-item AVFS-HE encompassed five key antecedents to VF: psychological, technical, social, productivity (engagement), and productivity (distraction) antecedents. The measure was shown to demonstrate good validity both internally and in relation to VF constructs. Recommendations for future research and practical recommendations for educators are discussed.
... Amos version 24 was used to perform CFA to verify the validity of the BALLI factor structure hypothesized by Horwitz (1988) and the one extracted by Nikitina and Furuoka (2006). According to Hu and Bentler (1999), an appropriate fit is one in which 2 is not significant and the 2 difference ( 2 /df) is less than 3. The root mean square error of approximation (RMSEA) and its 90% confidence interval (CI) should be less than .1. ...
Different studies have analyzed the factor structure of the Beliefs about Language Learning Inventory (BALLI) (Horwitz, 1987, 1988) through exploratory factor analysis, and the obtained results were partially or not confirmed by confirmatory factor analysis. Hence, this study examined the subcategories of Horwitz's (1988) BALLI using confirmatory factor analysis and explored the differences in students' language beliefs according to their gender, language proficiency, and major. 423 Moroccan university and high school students were randomly selected and administered a French version of BALLI to examine their beliefs about learning French as a foreign language. The obtained data were analyzed using MANOVA tests in SPSS version 25. The results of the confirmatory factor analysis confirmed the factor structure of Nikitina and Furuoka's (2006) factor structure. Also, the MANOVA tests revealed that the students' beliefs were affected by individual differences, such as their gender, language proficiency, and major. Our results provide further justification for the validity of BALLI and indicate that Nikitina and Furuoka's (2006) refined instrument is more reliable in conducting inferential statistics. Furthermore, our findings imply that research findings about learners' beliefs about language learning cannot be overgeneralized since these beliefs are shaped by learners' individual characteristics.
... The 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 F o r P e e r R e v i e w measurement models generally exhibited a good fit. The study's findings supported the reliability and validity of the scales used, despite minor issues with some items (AVE value of Sensation Seeking) and discriminant validity concerns (HTMT criterions of Identified Regulation and Experience Stimulation) (Bagozzi & Yi, 1988;Fornell & Larcker, 1981;Hair et al., 2010;Henseler et al., 2015;Hu & Bentler, 1999;Nunnally & Bernstein, 1994;Voorhees et al., 2016). Accordingly, the scales demonstrated acceptable to excellent internal consistency and reliability, ensuring robust measurement. ...
Hobby-based leisure activities, such as volleyball, plays a crucial role in promoting psychological well-being through mechanisms like sensation seeking and flow experience. These pathways are key to enhancing mental health via leisure activities. The primary aim of this study is to investigate how sensation seeking and flow experience mediate the relationship between leisure motivation and psychological well-being in young adults who engage in volleyball as a hobby. Data were gathered from 244 young adults (aged between 18-24) in Turkey, who regularly participate in volleyball. Participants completed validated questionnaires measuring leisure motivation (LA), sensation seeking (SS), flow experience (FE), and psychological well-being (PWB). The data were analyzed using confirmatory factor analysis(CFA), cronbach's alpha, composite reliability (CR), and regression analysis to test the proposed relationships. The results revealed that LA significantly predicts PWB, both directly and indirectly, through SS and FE. SS and FE were found to be significant mediators in this relationship. The serial mediation model was supported, highlighting the intricate interplay between these variables. In conclusion, the study showed that LA enhances PWB through the sequential mediation of SS and FE. These findings highlighted the importance of designing leisure activities that foster SS and facilitate FE to improve mental health outcomes. Future research should examine additional mediators and longitudinal effects to provide a more comprehensive understanding of these relationships.
... Bartlett's sphericity test and the Kaiser-Meyer-Olkin (KMO) confirmed the suitability of the EFA [27,28]. Building on the initial exploration of the factor structure using EFA (two-factor loading was selected), CFA was used to assess the validity of the identified factor structure [27,29]. Notably, several fit indices (root mean square error of approximation (RMSEA), goodness-of-fit index (GFI), comparative fit index (CFI), and adjusted goodness-of-fit index (AGFI)) indicated good model fit (p < 0.001). ...
Introduction
The COmprehensive Score for Financial Toxicity (COST) has proven to be a reliable tool for quantifying the impact of financial toxicity (FT) in patients with cancer in clinical and public health settings. However, the COST has not yet been validated in Vietnam. Therefore, we aimed to evaluate its reliability and validity among Vietnamese patients with cancer.
Methods
A cross-sectional study was conducted in a sample of 300 patients with cancer aged 27–95 years (mean: 58.5±11.2) in a tertiary hospital. The COST was translated into Vietnamese and English and adjusted to suit the local culture. Reliability was evaluated using Cronbach’s alpha and McDonald’s omega coefficients. The construct and convergent validities were also assessed.
Results
The COST demonstrated good internal consistency and reliability (Cronbach’s alpha = 0.913; McDonald’s omega = 0.915). The exploratory factor analysis revealed two factors that explained 64.9% of the variance. The adjusted fit indices indicated a good fit of the model (χ² (39) = 67.78, p = 0.003; standardized root mean squared residual = 0.042; Tucker–Lewis index = 0.971; comparative fit index = 0.979; root mean square error of approximation = 0.061, 90% confidence interval = 0.035–0084). Higher COST scores were significantly correlated with higher health-related quality of life (EQ-5D-5L utility score: r = 0.21, p = 0.002; EQ VAS: r = 0.28, p < 0.001). Multivariate quantile regression analysis revealed that female sex, rural residence, and unstable job/unemployment were associated with lower COST scores. There was no statistically significant difference in other factors, including clinical factors (types of cancer, staging, and treatment modalities).
Conclusions
The COST is reliable and valid, making it suitable for assessing FT severity in Vietnamese patients with cancer.
... Due to the non-normal distribution of the sample size, which mostly consists of undergraduate students and students with HSK level 4-5, Mplus 1.4 was used to estimate the models using Maximum Likelihood with robust standard errors (MLR), as MLR estimates with standard errors and a chi-square test statistic that is robust to the non-normality of observations [49]. Various model fit indices-absolute goodness-of-fit indices (CMIN/DF ≤ 3), absolute measure of fit indices (SRMR ≤ 0.08), incremental fit indices (CFI ≥ 0.90 and TLI ≥ 0.90), and parsimonious indices (RMSEA ≤ 0.06)-were used to test the model fit [50][51][52]. ...
This study aimed to understand how different dimensions of online learning engagement were influenced by learners’ self-regulated learning (SRL) and their perceptions of teaching, cognitive, and social presence in the community of inquiry (CoI) framework. A structural equation modelling analysis of survey responses from 154 online Chinese-as-a-foreign-language learners showed that the level of learners’ SRL positively influenced their perceptions of teaching, cognitive, and social presence and consistently directly impacted all dimensions of students’ learning engagement. Regarding the different dimensions of engagement, learner’ perceived CoI had different mediating effects. Affective engagement was influenced by learners’ perceptions of cognitive and social presence, while social engagement was influenced by learners’ perceptions of social presence. Cognitive and behavioural engagements were influenced by learners’ perceptions of teaching presence. The results highlight the importance of SRL in the CoI framework for enhancing learning engagement, suggesting integrating SRL training into instructional design in the online learning environment. In addition, the effects of various dimensions of the CoI framework on learning engagement inform pedagogical implications to enhance online learning engagement, such as building an online learning community to strengthen affective and social engagement while strengthening teaching presence to improve cognitive and behavioural engagement.
... IFA yang digunakan merupakan limited-information IFA dengan data mentah matriks korelasi polychoric (Wirth & Edwards, 2007). Kriteria yang menunjukkan bahwa model fit terhadap data adalah Chisquare ( " ) yang tidak signifikan (p > 0.050), Root Mean Square Error of Approximation (RMSEA) < 0.060, Standardized Root Mean Square Residual (SRMR) < 0.080, serta Comparative Fit Index (CFI) dan Tucker-Lewis Index (TLI) > 0.900 (Hu & Bentler, 1999). Setelah ditemukan bahwa keseluruhan model fit terhadap data, dilakukan penelaahan apakah masing-masing butir terbukti valid mengukur apa yang hendak diukur. ...
Abstrak Penelitian ini dilakukan dengan tujuan untuk melaporkan hasil pengujian validitas konstruk terhadap Tes Penilaian Situasional Kecemasan Mahasiswa terhadap Statistika (TPS-KMS). TPS-KMS merupakan tes penilaian situasional (SJT; situational judgement test) yang terdiri dari 14 butir untuk mengukur model multidimensi dari kecemasan terhadap statistika yaitu examination anxiety (EA) dan asking for help anxiety (AH). Responden dalam penelitian ini merupakan 488 orang mahasiswa jurusan psikologi di Indonesia. TPS-KMS diuji validitasnya dengan Item Factor Analysis (IFA). Hasil analisis dengan IFA menunjukkan bahwa model pengukuran 2-faktor dari TPS-KMS fit dengan baik. Pada tingkat butir, ditemukan bahwa ke-14 butir valid untuk mengukur apa yang hendak diukur. Sebagai informasi tambahan, ditemukan bahwa reliabilitas TPS-KMS berada diatas nilai penerimaan yang menunjukkan konsistensi internal yang baik (w EA = 0.702; w AH = 0.756). Dapat disimpulkan bahwa TPS-KMS merupakan SJT pertama untuk mengukur kecemasan terhadap statistika yang telah teruji validitas konstruknya. Implikasi dan saran untuk penelitian mendatang turut didiskusikan.
... and between .68 and .91 for the injustice scale (α = .91). Model fit was deemed acceptable (Hu & Bentley, 1999;Schumacker & Lomax, 2010) for both revised models. ...
Pour tenter de limiter la propagation de la COVID-19, les autorités ont dû mettre en place des mesures sanitaires exceptionnelles. La réponse des citoyens à ces mesures a été très variable. L’objectif de cette étude était d’identifier les facteurs favorisant la conformité et minimisant la déviance de la population québécoise à ces mesures en s’appuyant sur les principes de la justice organisationnelle. Au total, 690 Québécois ont rempli un questionnaire au début de l’année 2021 évaluant leur perception de la justice et de l’injustice procédurales et distributives à l’égard des mesures sanitaires mises en place par les autorités, ainsi que leur tendance à se conformer et à déroger de ces mesures. Les résultats des régressions multiples prédisant les comportements des Québécois à partir de leur perception de la justice et de l’injustice procédurales et distributives, ainsi que des analyses de modération examinant l’effet interactif des deux types de justice et d’injustice, ont mis en évidence le rôle crucial joué par la justice et l’injustice distributives. En effet, la perception de l’injustice distributive était un prédicteur significatif de tous les types de comportements de conformité et de déviance, tandis que la justice et l’injustice procédurales n’étaient liées qu’à la tendance des personnes à déroger des mesures de restriction des contacts. Les résultats ont également montré que les perceptions de la justice et de l’injustice procédurales n’affectaient les comportements des personnes que lorsque la perception de la justice distributive était faible ou la perception de l’injustice distributive élevée. Les résultats sont discutés à la lumière de leur contribution à la littérature sur la justice organisationnelle, mais surtout aux stratégies qui pourraient être utilisées par les autorités dans le cas de futures crises mondiales nécessitant la collaboration de toute une population.
... Comparative fit index (CFI) values greater than 0.90 indicated adequate fit and greater than 0.95 indicated good fit. Root-mean-square error of approximation (RMSEA) values less than 0.08 indicated acceptable fit, and values less than or equal to 0.05 indicated good fit (T. A. Brown, 2015;Hu & Bentler, 1999). Fit of the measurement model was adequate, CFI = 0.976, RMSEA = 0.044, 90% CI [0.032, 0.056], standardized root-mean-square residual = 0.046. ...
Objectives: The purpose of this study was to test the roles of ethnic and racial identity (ERI) processes and autonomy-supportive parenting on college students’ psychological adjustment. Method: American college students of color (N = 505) completed questionnaires assessing ERI exploration and commitment, autonomy-supportive parenting, and psychological adjustment (self-esteem, depressive symptoms). Key variables were operationalized as latent constructs, and main and interaction effects were tested using the latent moderated structural equation modeling approach. Results: Higher levels of ERI commitment (but not exploration) and parental autonomy support each uniquely predicted higher levels of self-esteem and lower levels of depressive symptoms. Parental autonomy support moderated associations between ERI processes and psychological adjustment, and the nature of moderation did not differ across Black and Latino/a/x students. Conclusions: Supporting the psychological adjustment of college students of color necessitates acknowledging the importance of both parental and institutional efforts to encourage students’ autonomy strivings and ERI processes.
... root-mean-square error of approximation (RMSEA) < .06, and standardized root-mean-square residual (SRMR) < .08 (Hu & Bentler, 1999). ...
Objectives: The present study examined whether immigration stress was related to decreased capacities for psychophysiological stress regulation (as indexed by respiratory sinus arrhythmia [RSA]) and whether lower RSA, in turn, was related to decreased maternal sensitivity. The buffering effect of familism values was also evaluated, such that familism values were expected to minimize associations between immigration stress, RSA, and sensitivity. Method: Data were drawn from a longitudinal study of Mexican immigrant mothers (N = 277; Mage = 28 years). Mothers self-reported immigration stress and familism values, and mothers’ resting RSA and sensitivity were assessed during laboratory visits. Results: Higher immigration stress was associated with higher RSA (B = .15, SE = .07, p = .04) but was unrelated to maternal sensitivity. Moreover, links between more immigration stress and higher RSA were more pronounced among mothers who reported stronger familism values (B = .20, SE = .07, p = .003). Conclusions: The present study contributes to our understanding of the sequelae of immigration stress in Mexican immigrant mothers and the cultural resiliency factors that may alter its effects. In contrast to hypotheses, findings suggested that mothers who endorse more immigration stress may also exhibit higher RSA, and links may be more pronounced among those with strong familism values. Further research is needed to advance understanding of resiliency processes that promote family functioning in vulnerable populations.
... and standardized root-mean-square residual (SRMR) < .06 (Hu & Bentler, 1999). Next, the significance of each path was assessed ( p < .05). ...
Protective parenting, when enacted in contexts that do not require it, predicts child anxiety. Both child (e.g., temperament) and maternal (e.g., physiology and cognition) factors relate to parenting behavior, supporting family systems theory. In order to better understand the development of environmental risk for child anxiety, the present study applied the integrated social information and emotion processing theory to protective parenting, assessing concurrent relations among child temperament, maternal physiology, maternal cognitions, and protective parenting in toddlerhood. The present study also investigated whether the theory could be applied to longitudinal relations, testing cognition as a mechanism by which maternal physiology and child temperament predict maternal protective parenting over time. Study participants included 189 mothers (89.9% White, 2.1% Hispanic, 32.3% with annual household income ≤$40,000) and children (55.6% male, 81.0% White, 3.7% Hispanic). Results indicated that the theory was partially applicable to both concurrent and prospective mother–child relations implicated in child anxiety development. Namely, child inhibited temperament (IT) related concurrently to maternal beliefs about the harm of child anxiety at child age 1 year, and to maternal protective parenting at child ages 2 and 3 years. Maternal baseline respiratory sinus arrythmia related to protective parenting at child age 3 years. Longitudinally, maternal beliefs at child age 1 year predicted maternal perceptions of child IT at child age 2 years. Maternal beliefs at child age 2 years predicted maternal protective parenting at child age 3 years. Although the mechanistic role of cognition was not supported, child emotion processes and maternal cognitions may uniquely contribute to maternal protective parenting.
... indicated a good fit for the CFI, and values less than .06 indicated good fit for RMSEA (Hu & Bentler, 1999). ...
Self-regulation (SR; emotion-related, and behavioral), executive function, and theory of mind (ToM) all play an important role in child socioemotional functioning (SEF). However, much remains unknown about the interplay among these abilities when facing various challenging situations. Additionally, the role of these abilities in child SEF has not yet been studied among minority children from an Eastern culture. Thus, we conducted one study with two models to examine the combined contribution of these core abilities, concurrently, to children’s SEF during the transition to kindergarten, and longitudinally (about 3 years later) to children’s SEF during COVID-19. Overall, 202 kindergarten children (aged 4.9–6.5 years) participated, of which 136 of them in the longitudinal follow-up (aged 8.83–10.6 years). We used behavioral tasks and teacher and maternal reports. Mothers also reported their own distress during the COVID-19 pandemic. During the transition to kindergarten, we found that emotion-related SR was positively related to children’s SEF. We also found that emotion-related SR moderated the relation between inhibition and ToM. In the follow-up study, we found that emotion-related SR in kindergarten significantly predicted children’s SEF during the COVID-19 crisis, directly and indirectly, through children’s SEF in kindergarten and their maternal COVID-related distress. Moreover, emotion-related SR moderated the longitudinal association between children’s ToM at kindergarten age and their SEF during the COVID-19 crisis. Our findings highlight the central role that emotion-related SR plays in children’s ability to face different challenges.
... Non-significant values suggest a good fit, since they indicate only a minor discrepancy between the observed and the estimated covariance matrix. The Comparative Fit Index (CFI), Tucker-Lewis Index (TLI) and Incremental Fit Index (IFI) are indices that indicate reasonably good fit when values are greater than 0.90, while RMSEA is reasonable when values are close to 0.60 or below (Hu & Bentler, 1999). ...
The examination of the interpersonal behaviors of undergraduate student-athletes can contribute to the research on the perceptions of students for satisfaction and frustration of basic psychological behaviors by teachers in the context teaching classes. Aim of this study was to translate into Greek and investigate the factorial validity and internal consistency of the Interpersonal Behavior Questionnaire (IBQ; 24-item six factors). 252 full-time undergraduate student-athletes (125 males and 127 females) were used ranging in age 18 to 38 years. The results of CFA showed a good fit of the data to the model, while the multi-sample results indicated invariance for factor loadings and correlations between male and female samples. Internal consistency coefficients Cronbach alpha and interclass correlation were moderate significant. In conclusion, the IBQ-Gr version has valid and reliable psychometric properties and can be applied to examination of the perceptions interpersonal behaviors others into Greek population.
... To insulate χ 2 against the deviation from multivariate normality, and to produce robust standard errors and significance values, the robust Maximum Likelihood Method (MLR) was used when estimating model parameters (43). Goodness-of-fit was examined using absolute fit indices [Root Mean Square Error of Approximation (RMSEA) and Standardized Root Mean Square Residual (SRMR)], which are considered to be acceptable at <0.8 and < 0.06, respectively (44) and relative fit indices [Close Fit Index (CFI) and Tucker-Lewis Index (TLI)], which are considered to be acceptable at >0.90 (45). Inspection of modification indices (MIs) suggested that model fit could be improved if the error covariance for a number of items was constraint-free. ...
Introduction
Professional identity formation (PIF) is an ongoing, self-reflective process involving habits of thinking, feeling and acting like a physician and is an integral component of medical education. While qualitative work has suggested that PIF is informed by professionalism, resilience, and leadership, there is a dearth of quantitative work in this area. Multiple methods build rigor and the present study aimed to quantitatively assess the relative psychometric contributions of professionalism, resilience, and leadership constructs to informing PIF, using a latent factor analysis approach.
Methods
We analyzed data from the PILLAR study, which is an online cross-sectional assessment of a pre-clinical cohort of medical students in the RCSI University of Medicine and Health Sciences, Dublin, using established and validated quantitative measures in each area of interest: PIF, professionalism, leadership and resilience. A total of 76 items, combining four validated scales, along with a selection of demographic questions, were used. The hypothesis that PIF is informed by, and correlates with, professionalism, resilience and leadership was examined by conducting a confirmatory factor analysis of a proposed three-factor higher-order model. Model estimation used Maximum Likelihood Method (MLM) with geomin rotation. The hypothesized (measurement) model was examined against an alternative (saturated) model, as well as a three-factor model.
Results
Latent variable analysis from 1,311 students demonstrated that a three-factor higher-order model best fit the data; suggesting PIF is informed by professionalism, resilience, and leadership, and that these constructs are statistically distinct and account for differential aspects of PIF. This higher-order model of PIF outperformed both the saturated model and the three-factor model. The analysis of which component may be the most or least influential was inconclusive, and the overall model was not influenced by year of training.
Discussion
Building upon existing conceptual contentions, our study is the first to quantitatively support the contribution of professionalism, resilience, and leadership to the development of professional identity, and to delineate the inter-relationships between PIF and these constructs. This information can be used by medical educators when designing curricula and educational strategies intended to enhance PIF. Future work should seek to assess the influence of these constructs longitudinally.
... Following standard data screening procedures (Tabachnick & Fidell, 2013), a confirmatory factor analysis was conducted to assess the factorial validity of the athlete-reported version of the CLSS-Q using the lavaan package (Rosseel, 2012) in R Studio (R Core Team, 2022). Data-model fit was considered adequate if comparative-fit index and Tucker-Lewis index ≥ .90 and root mean square error of approximation and standardized root mean square residual ≤ .08 (Hu & Bentler, 1999;Marsh et al., 2004). For our main analyses, both theory-and data-driven approaches to multiple regression analysis were used to test our hypotheses concerning the associations of coaching approaches for life skills development with life skills outcomes. ...
Promoting life skills is a prominent focus of the mission of high school sports. The purpose of this study was to examine the relationship between perceived coaching approaches for life skills development and life skills outcomes for high school athletes. A total of 346 athletes participating in high school sports from the United States completed the athlete-reported version of the Coaching Life Skills in Sport Questionnaire (perceived implicit and explicit coaching approaches) and the Life Skills Scale for Sport. Findings from hierarchical and stepwise regression models revealed that perceived implicit and explicit levels of coaching were differentially associated with each of the eight life skills outcomes, with the most consistent and significant predictor of life skills outcomes being structuring and facilitating a positive climate. Findings are discussed in relation to the conceptual and practical utility of the implicit-explicit continuum of life skills development and transfer, the importance of coach and athlete awareness of coaching approaches for life skills development, and recognition of the strengths and limitations of a variety of ontological and epistemological approaches to studying life skills in sport.
... SEM was used to conduct a formal mediation test and disaggregate the relationship between health literacy and self-rated health through causally de ned indirect and direct pathways. The proportion of the total effect of health literacy on self-rated health attributable to the mediators was calculated by dividing the ratio of the indirect effect through the mediated pathway by the ratio of the total effect 33,34 . All statistical analyses were done by STATA14.2 software (StataCorp, College Station, TX, USA). ...
Background: Self-Rated Health is related to reduction of burden of diseases and health outcomes. Various factors affect Self-Rated Health. This study aimed to investigate the mediating role of lifestyle in the relationship between health literacy and Self-Rated Health.
Methods: In this cross-sectional study 495 people aged 18- 65 were participated in 2023. Health literacy questionnaire by Montazeri et al., healthy lifestyle assessment questionnaire of Eshaghi et al, and Self-rated health (SRH) by a question developed by the World Health Organization were used. Structural equation modeling (SEM) was used. Statistical analysis of data was performed using STATA 14.2 software.
Results: Based on the results, a significant total effect of health literacy on self-rated health (β= -0.005, P= 0.001), was identified. Life style (β = -0.004) had a direct effect on self-rated health (p < 0.005). The result from SEM indicated that health literacy exhibited a direct effect on life style (β = 78). In addition, considering that health literacy and lifestyle have a significant relationship with self-rated health, and there is a significant relationship between lifestyle and health literacy, it can be concluded that lifestyle plays a mediating role in the relationship between the two variables of health literacy and self-rated health.
Conclusion: Considering the mediating role of lifestyle in the relationship between health literacy and self-rated health, to improve self-rated health, in addition to paying attention to the role of health literacy, it is necessary to take effective measures to positively change people's lifestyle.
... We conducted the factor analyses using the Diagonally Weighted Least Squares (DWLS) estimator. We used the following fit indices to evaluate the models: Comparative Fit Index (CFI) and Tucker-Lewis Index (TLI), where ≥ 0.95 indicates a good fit, and ≥ 0.90 indicates an adequate fit); and the Root Mean Square Error of Approximation (RMSEA) and the Standardized Root Mean Residual (SRMR), where values < 0.05 are considered good and < 0.08 are considered adequate( (Hu and Bentler 1999;MacCallum, Browne, and Sugawara 1996;McDonald and Ho 2002;Schreiber et al. 2006). Because models with item-level data tend to yield lower relative fit indices (e.g., Marsh et al. 2004), we emphasized the absolute fit indices (i.e., RMSEA, SRMR) in our evaluation, which is consistent with previous ELSRP research (e.g., Sellbom et al. 2022). ...
We aimed to adapt the Expanded Levenson Self-Report Psychopathy (E-LSRP) to the Brazilian context, evaluate its internal structure and construct validity. We also aimed to expand the psychopathy nomological network by providing information about E-LSRP factors' associations with a Brazilian cultural phenomenon known as Brazilian Jeitinho. Our sample comprised 1,445 Brazilian adults, with ages varying from 18 to 81 years (M = 31.13; SD = 13.22). The participants completed the E-LSRP, as well as the Triarchic Psychopathy Measure, Crime and Analogous Behavior Scale, Affective and Cognitive Measure of Empathy, and Brazilian Jeitinho Questionnaire. Results showed general support for a three-factor structure, and that E-LSRP scores exhibited the expected associations with external criterion measures. Our results demonstrated that E-LSRP Egocentricity was the factor most related to Brazilian Jeitinho. Although we have initial validity evidence supporting the Brazilian version of E-LSRP, future studies need to replicate these findings in other samples.
... p < 0.001). However, the χ 2 test of model fit is over-sensitive with relatively large sample sizes and it is therefore recommended to report SRMR and RMSEA as further fit indices (Hooper et al., 2008;Hu & Bentler, 1999). SRMR indicated good fit (Schumacker & Lomax, 2016) for both models (HERO SRMR = 0.07, A-HERO SRMR = 0.07) and RMSEA also approached the suggested guideline of < 0.07 (Schumacker & Lomax, 2016), and decreased slightly for Model 2, indicating improved fit (Xia & Yang, 2019) (HERO RMSEA = 0.09, A-HERO RMSEA = 0.08). ...
Authenticity was proposed as a potential addition to the Psychological Capital construct several years ago, but the PsyCap model has not yet been expanded. We review the theoretical and empirical support for the inclusion of authenticity and test this proposal in two studies. Study 1 examines the structural model of A-HERO (Authenticity, Hope, Efficacy, Resilience, Optimism) as an extended representation of the PsyCap construct. Study 2 tests the extent to which A-HERO may explain well-being. CFA demonstrates that the addition of authenticity provides slight improvement in overall PsyCap model fit. Hierarchical regression shows that the addition of authenticity to the PsyCap model improves the explanation of well-being, with beta values of comparable size to optimism and greater than efficacy. We therefore recommend that authenticity be included in PsyCap to provide a more holistic understanding of personal resources and to enable the further identification of interactions and potential synergies amongst A-HERO components.
... The hypothesized model (Fig. 1) was tested through path analyses using Maximum Likelihood with Mplus 8.3. To evaluate the model fit, the following fit indices were examined (Hu & Bentler, 1999): the root mean square error of approximation (RMSEA < 0.08), standardized root mean square residual (SRMR < 0.08), comparative fit index (CFI > 0.90) and Tucker-Lewis index (TLI > 0.90). The mediation hypotheses were tested by bootstrapping analyses (Preacher & Hayes, 2004). ...
Guided by the perfectionism social disconnection model (PSDM), this study focused on understanding the perfectionism-suicidality link by including appearance-based rejection sensitivity and loneliness as mediators. In this study, the potential direct and indirect roles of self-oriented perfectionism and socially prescribed perfectionism on suicidal ideation were examined. A convenient sample of 1483 Chinese university students (42.9% male, Mage = 19.14; SDage = 1.03) completed self-report measures of the constructs above. The hypothesized model was tested through path analyses using a bootstrapping approach for the direct, indirect, and total effects. The results indicated that (a) socially prescribed–but not self-oriented– perfectionism has a significant direct path to suicidal ideation; (b) loneliness significantly mediated the association between the two kinds of perfectionism and suicidal ideation; and (c) appearance-based rejection sensitivity and loneliness serially mediated the association between socially prescribed perfectionism/ self-oriented perfectionism and suicidal ideation. The limitations, such as cross-sectional design, use of self-report instruments, and nonclinical samples, call for further investigation. Our findings provide important empirical data guiding future prevention programs for suicide in young adults from a new perspective and suggest that individuals high in perfectionism, particularly socially prescribed perfectionism, can be identified and recruited for early intervention.
... or greater), and root-mean-square error of approximation (RMSEA; should be less than .08) (Hu & Bentler, 1999;Kline, 2011). To examine the significance of the mediation effects, we conducted a Monte Carlo simulation with 5000 replications to estimate the 95% bias-corrected and accelerated confidence interval (CI) of the indirect effects of masculine gender role discrepancy on masculine depression, via masculine discrepancy stress, as well as drive for size, appearance intolerance, and functional impairment (MacKinnon et al., 2002). ...
Guided by the dynamic model of masculinity and men’s psychopathology, the current study aimed to explore the mediating role of masculine discrepancy stress and each of the muscle dysmorphia dimensions (drive for size, appearance intolerance, and functional impairments) in the association between masculine gender role discrepancy and masculine depression. For the present study, 936 Israeli men completed a structured self-report questionnaire. Masculine discrepancy stress and some of the muscle dysmorphia dimensions were found to partially mediate the association between masculine gender role discrepancy and masculine depression. The findings demonstrate how the internalization of social gender expectations and men’s gender role discrepancy is reflected in the gap between perception of self and the typical man, which is eventually related to mental health outcomes. In turn, men attempt to mitigate the stress through what they perceive as masculine, reflecting muscle dysmorphia: drive for size, appearance intolerance, and functional impairments, which in turn predict masculine depression. Therefore, mental and physical health professionals are advised to be aware of these mechanisms, in order to recognize the negative mental health outcomes arising from traditional societal gender role expectations and provide specific solutions for them.
... RMSEA less than or equal to.05, and SRMR less than.05 indicate a good model fit [64,65]. Missing data were handled using full information maximum likelihood estimation. ...
Although a robust body of previous empirical studies investigated the long-term trend of child behavior problems, limited research discussed the influences of various types of neighborhood factors on such trajectory (e.g., neighborhood structural characteristics and collective efficacy). Using a nationally representative longitudinal dataset the Fragile Families and Child Wellbeing Study (FFCWS), with six waves from 1998 to 2017, this study captures the longitudinal effects of two types of early childhood neighborhood factors on the co-development of internalizing and externalizing symptoms. Data was collected at the focal child’s age 3, age 5, age 9, age 15 (N = 2,385), and the parallel-process growth curve models were applied. Results suggest that the trajectories of both internalization and externalizing symptoms showed U-shape and bidirectional relationships among internalizing and externalizing problems. The long-term effects of neighborhood social cohesion and economic disadvantages were significantly associated with children’s internalizing and externalizing symptoms. The implication of this study was further discussed.
Objectives
The COHQoL is a set of questionnaires used to evaluate the impact of oral health on children’s quality of life. Although the CPQ8-10 and the P-CPQ have been translated and validated in French, the CPQ11-14 14 has not yet been validated. The aim was to develop a French version of the CPQ11-14 16-items.
Materials and methods
The French version of CPQ11-14 was obtained by a forward-backward translation process and pretested. The final version was tested on children aged 11–14 and divided into three groups: children with orofacial clefts, children with rare dental diseases other than clefts, and children without anomalies. We conducted a cross-sectional study and evaluated the reliability with test-retest and internal consistency, and the questionnaire validity with construct validity and discriminant validity. We performed an Exploratory Factory Analysis (EFA).
Results
187 children tested the questionnaire. The ICC of the test-retest was 0.76 and the Cronbach’s alpha was 0.77. The correlation between the CPQ11-14 and self-assessment of oral health and general well-being was > 0.2. Patients with orofacial clefts and rare diseases had significantly higher scores for overall short-form CPQ11-14. The EFA revealed six factors.
Conclusion
The French CPQ11-14 is valid to assess the impact of oral health on children’s quality of life.
Clinical relevance
The translation of this questionnaire into French will enable us to assess the impact of oral health on the quality of life of adolescents. This questionnaire complements the 8–10 years version of the CPQ, as well as the parental version that can be used in conjunction with the questionnaire.
Background: Specialty nurses play a crucial role in improving the quality of nursing care. Enhancing the work engagement of specialty nurses is a top priority for managers. Job crafting is an effective way to increase nurses' work engagement. Identifying and classifying features of work engagement, exploring their relationship with job crafting, and tailoring interventions to support specialty nurses are imperative.
Methods: We conducted a cross-sectional study in Henan Province, China from July 2023 to August 2023. The study sample consisted of 758 specialty nurses who participated in an online survey. Latent profile analysis was conducted to identify work engagement classification criteria. Multinomial logistic regression models were usedto identify the predictors of profile inclusion.
Results:A fourprofile model yielded the best fit. The four profiles were titled “low work engagement” (n = 210), “medium work engagement” (n = 172), “high attitude-high enthusiasm” (n = 229), and “high work engagement” (n = 147). The regression analysis indicated that gender, age, level of education, monthly income, and job crafting all had significant effects on the work profile categories (P<0.05).
Conclusions: The characteristics of specialty nurses’ work engagement are heterogeneous and can be divided into four profiles. Our findings indicated that gender, education level, monthly income, and job crafting impact the varying types of work engagement exhibited by specialty nurses. We recommend that nursing managers adopt effective measures, such as flexible scheduling and improved job management, to enhance specialty nurses’ work engagement.
Trust is important for a range of societal outcomes. Despite its significance, there is considerable debate about how best to measure trust. In the context of a newly developed measure of generalized trust—the Stranger Face Trust scale (SFT)—this study evaluates whether different features of survey scales affect the reliability and validity of SFT, which relies on the standard 4-point unipolar scale used by many survey institutes. In a survey experiment conducted with a non-probability sample of U.S. adults (N = 4252), we randomly assigned intensity scale midpoints, polarity, and “don’t know” options to SFT. Results indicate that 7- and 9-point bipolar scales without a “don’t know” option slightly outperform all other scales on some psychometric tests, particularly those related to formal properties of the scales and factorial validity, but not on psychometric tests assessing survey environment or convergent, discriminant, and concurrent validity.
Measures such as education, improving knowledge, attitude and taking preventive action to protect against COVID-19 are vital strategies for prevention. The aim of this study was to determine the predictability of Health Belief Model (HBM) constructs in performing preventive behaviors against COVID-19 among secondary school students in Chabahar, Iran. In this cross-sectional-analytical study, 400 secondary school students of Chabahar city were investigated by simple random sampling. The data collection tool was a questionnaire including demographic characteristics, knowledge, behavior, and Health Belief Model constructs’ questions. Exploratory Factor Analysis (EFA) was used to evaluate the validity of HBM constructs, and the structural equation modeling (SEM) method was used to evaluate the direct and indirect effects of the relationship between knowledge, HBM constructs, and preventive behavior against COVID-19 based on the conceptual model. Based on the results of the structural modeling, the direct effect of knowledge on the constructs of the health belief model was positive and significant (β = 0.34, P-value < 0.001), and on the preventive behavior of students was insignificant (β = 0.12, P-value = 0.07) while the indirect effect of knowledge through increasing the constructs of the HBM on student behavior was positive and significant (β = 0.30, P < 0.001). The relationship between the constructs of the HBM constructs and student behavior was also positive and significant (β = 0.89, P-value < 0.001).Due to the fact that knowledge and HBM structures played a role in predicting the adoption of preventive behavior from COVID-19, it is possible to design appropriate interventions to increase knowledge, sensitivity, perceived severity, and self-efficacy, in order to recover from COVID-19 by adopting preventive behaviors.
Background
Medical professionalism is a core competency for medical students during clerkships for further professional development. Given that the behavior-based framework could provide clear insight and is easy to assess, the study aimed to create a self-administered scale to measure the professional behaviors of medical students during their clerkships.
Methods
A comprehensive literature review on medical professional behaviors in English or Chinese and Delphi interviews were used to develop the initial version of the Self-Administered Scale for Professional Behavior of Medical Students During Clerkships. The reliability and validity analysis based on a survey of medical students from China, Cronbach’s α calculations, and Confirmatory Factor Analysis (CFA) specifically were conducted to finalize the scale. The associations of professional behaviors with gender, medical programs, and clerkship duration were examined using Wilcoxon rank-sum tests.
Results
We included 121 studies and extracted 57 medical professionalism assessment tools, initially forming a pool of 48 items. To refine these items, eighteen experts participated in two rounds of Delphi interviews, ultimately narrowing down the item pool to 24 items. A total of 492 participants effectively completed the questionnaire. One item was removed due to its correlated item-total correlation (CITC) value, resulting in a final scale containing 23 items with six domains: Respect, Altruism, Communication and Collaboration, Integrity, Duty, and Excellence. The overall Cronbach’s alpha value was 0.98, ranging from 0.88 to 0.95 for each domain. The fit indices (χ²/df = 4.07, CFI = 0.96, TLI = 0.95, RMSEA = 0.08, and SRMR = 0.02) signified a good fit for the six-domain model. Medical students’ professional behavior was significantly associated with gender (p = 0.03) and clerkship duration (p = 0.001).
Conclusion
The scale was demonstrated to be reliable and valid in assessing the professional behaviors of Chinese medical students during clerkships.
Objective
Given the high prevalence of hypertension among Chinese adults, this population is at a significantly increased risk of severe COVID-19 complications. The purpose of this study is to assess the willingness of Chinese hypertensive adults to receive the COVID-19 vaccine and to identify the diverse factors that shape their vaccination decisions.
Methods
Sampling was conducted utilizing multistage stratified random sampling, and ultimately, a total of 886 adult hypertensive patients from Luzhou City in Southwest China were included in this study. The questionnaire design was based on the Theory of Planned Behaviour and was used to investigate their willingness to be vaccinated with COVID-19. Structural equation modeling was employed for data analysis.
Results
The results showed that 75.6% of hypertensive individuals were willing to receive COVID-19 vaccination. The structural equation modeling revealed that Subjective Norms (path coefficient = 0.361, CR = 8.049, P < 0.001) and Attitudes (path coefficient = 0.253, CR = 4.447, P < 0.001) had positive effects on vaccination willingness, while Perceived Behavioral Control (path coefficient=-0.004, CR=-0.127, P = 0.899) had no significant impact on Behavioral Attitudes. Mediation analysis indicated that Knowledge (indirect path coefficient = 0.032, LLCI = 0.014, ULCI = 0.058), Risk Perception (indirect path coefficient = 0.077, LLCI = 0.038, ULCI = 0.124), and Subjective Norms (indirect path coefficient = 0.044, LLCI = 0.019, ULCI = 0.087) significantly influenced vaccination willingness through Attitudes as a mediating factor.
Conclusion
The willingness of hypertensive individuals to receive the COVID-19 vaccination is not satisfactory. The Theory of Planned Behavior provides valuable insights into understanding their vaccination intentions. Efforts should be concentrated on enhancing the subjective norms, attitudes, and knowledge about vaccination of hypertensive patients.
For children in the United States, family instability following parental relationship dissolution is common and efforts to promote effective post‐divorce co‐parenting arrangements have grown substantially in recent decades. To help families navigate transitions through the divorce process, most states require divorcing parents to complete divorce education programming. In the present study we used pre‐post data from three divorce education programs ( n = 1026 parents) to explore programmatic effects on self‐reported adjustment, intentions to co‐parent, and likelihood to relitigate, and attempt to determine mechanisms that may account for or explain those programmatic effects. Overall, we found support that these programs are able to impact perceived adjustment and co‐parenting intentions. Specifically, we documented small, but significant, increases in perceived adjustment and that post‐program adjustment was associated with greater intentions to engage in supportive co‐parenting with former spouses. Further, co‐parenting intentions were shaped by how useful parents found the programs with greater perceived utility being associated with more positive co‐parenting intentions. The relitigation outcomes, however, were not associated with post‐program adjustment or perceived program utility. Instead, they were primarily associated with pre‐program experiences such as the quality of co‐parenting prior to the program and whether an order of protection was present between co‐parents.
Bu araştırmanın amacı, örgüt kültürü tipinin zorunlu vatandaşlık davranışına etkisinde örgütsel adalet algısının aracı rolünü incelemektir. Araştırmanın evrenini, “Türkiye’nin 500 Büyük Sanayi Kuruluşu” (İSO-500) listesindeki firmaların çalışanları (N=430132) oluşturmaktadır. Evrende yer alan firmaların hepsine ulaşılmaya çalışılmış, bunlar arasındaki 100 firma yöneticisinden olumlu geri dönüş alınmıştır. Her firmaya 5’er anket gönderilmiş ve geri dönen 414 anket değerlendirmeye alınmıştır. Elde edilen veriler, SPSS 25.0 ve AMOS 23.0 programları kullanılarak çözümlenmiştir. Elde edilen bulgulara göre katılımcıların çalıştıkları örgüte ait kültür tipini algılama düzeylerinin orta seviyede olduğu, örgütsel adalet algılarının orta düzeyde olduğu ve zorunlu vatandaşlık davranışını orta düzeyde sergiledikleri tespit edilmiştir. Araştırmanın bir başka bulgusu, örgüt kültürü tipinin zorunlu vatandaşlık davranışı üzerinde istatistiksel açıdan anlamlı ve negatif yönde bir etkisi olduğu ve bu etkide örgütsel adalet algısının kısmi aracı rolüne sahip olduğudur. Elde edilen bulguların, örgüt kültürü ve tipleri, zorunlu vatandaşlık davranışı ve örgütsel adalet ile ilgilenen örgütsel davranış alan yazınına katkı sağlaması umulmaktadır.
Purpose
Empirical evidence of the value creation process through which internationalizing small and medium-sized enterprises (SMEs) develop international branding capability (IBC) to build a value-creating brand in international markets is incomplete. This research aims to investigate a theoretical framework for the determinants and outcomes of IBC in internationalizing SMEs.
Design/methodology/approach
Using surveys of 519 internationalizing SMEs, this research empirically verified the antecedents to and effects of IBC on SMEs’ value creation, which thus translates into superior performance. Furthermore, this research explores contextual factors influencing the value creation process in SME internationalization.
Findings
Findings show that SMEs with strong international marketing resource orchestration (IMRO) and relational capability are more competent in developing IBC, which assists resource-constrained SMEs to create value, as manifested through international brand equity (IBE) and improved international performance. Moreover, environmental uncertainty enhances the interplay between IMRO, relational capability, and IBC, while new entrant pressure strengthens the relationship between IBC and IBE, and price competition pressure magnifies the impact of IBE on international performance.
Originality/value
Our study pioneers conceptualization of the value creation process through which SMEs develop IBC to build value-creating brands in international markets, overcoming the liabilities of smallness and outsidership.
Cultural heritage tourism has created opportunities for small and medium‐sized enterprises in the hospitality industry, including cultural boutique hotels that offer visitors personalized experiences around local arts and culture. To identify effective marketing strategies for these hotels, a study surveyed 300 tourists who stayed at Thai cultural boutique hotels. The study used a synthesis model with two antecedent factors (storytelling and co‐design) and one impact factor (customer value), with hedonism ties as an intervention factor. The results indicated that both antecedent factors positively affected hedonism ties, which positively impacted customer value. The study also found that two target segments played a crucial role in determining the relationship between co‐design and hedonism ties. By adopting marketing strategies based on these findings, cultural boutique hotels can attract and retain customers while contributing to the growth of cultural heritage tourism.
Dựa trên lý thuyết hành vi dự định, nghiên cứu này khám phá vai trò của niềm tin xanh đối với ý định mua sản phẩm xanh của sinh viên Trường Đại học Mở Thành phố Hồ Chí Minh. Bài viết này tập trung vào việc điều tra thái độ đối với tiêu dùng xanh, chuẩn mực chủ quan và kiểm soát hành vi nhận thức làm trung gian cho mối quan hệ giữa niềm tin xanh và ý định mua sản phẩm xanh. Một cách tiếp cận định lượng đã được sử dụng. Tổng cộng có 294 sinh viên được chọn bằng kỹ thuật lấy mẫu thuận tiện. Các đáp viên được chọn tại Trường Đại học Mở Thành phố Hồ Chí Minh. Dữ liệu được phân tích bằng mô hình phương trình cấu trúc (SEM). Các phát hiện này chỉ ra rằng, có mối quan hệ tích cực và đáng kể giữa niềm tin xanh và ý định mua sản phẩm xanh, và cũng có mối quan hệ tích cực và đáng kể giữa niềm tin xanh và tiêu dùng xanh, chuẩn mực chủ quan và kiểm soát hành vi nhận thức. Các phát hiện còn cho biết thêm rằng, tiêu dùng xanh và chuẩn mực chủ quan cũng có tác động đáng kể đến ý định mua sản phẩm xanh. Tuy nhiên, kiểm soát hành vi nhận thức không có tác động đến ý định mua sản phẩm xanh. Bài viết này xác định các yếu tố ảnh hưởng đến ý định mua sản phẩm xanh của sinh viên và cung cấp những hàm ý mang tính chiến lược cho các doanh nghiệp nhằm tạo cơ hội tiếp thị tốt hơn cho các sản phẩm xanh của mình.
The biggest difference in statistical training from previous decades is the
increased use of software. However, little research examines how software
impacts learning statistics. Assessing the value of software to statistical learning
demands appropriate, valid, and reliable measures. The present study
expands the arsenal of tools by reporting on the psychometric properties of the
Value of Software to Statistical Learning (VSSL) scale in an undergraduate student
sample. We propose a brief measure with strong psychometric support to
assess students' perceived value of software in an educational setting. We provide
data from a course using SPSS, given its wide use and popularity in the
social sciences. However, the VSSL is adaptable to any statistical software, and
we provide instructions for customizing it to suit alternative packages. Recommendations for administering, scoring, and interpreting the VSSL are provided
to aid statistics instructors and education researchers understand how software
influences students' statistical learning.
Although the growth mindset is essential to students' math achievement, its mechanism of influence remains uncertain, particularly for college students. Accordingly, this study explored the relationship between college students' growth mindset and their math achievement, as mediated by their self‐efficacy and reasoning ability. The study data were gathered by surveying 576 undergraduates taking various undergraduate programs at a Chinese university. Our results showed that (1) students' growth mindset did not directly predict their math achievement; (2) self‐efficacy mediated the relationship between students' growth mindset and their math achievement; and (3) the growth mindset affected students' math achievement through the chain‐mediation of self‐efficacy and reasoning ability. Overall, the finding that the growth mindset indirectly benefits Chinese college students' math achievement provides invaluable guidance to higher education professionals aiming to develop more effective math programs. Moreover, the mediating effects of self‐efficacy and reasoning ability were also theoretically important to better understand the potential influence mechanism of the growth mindset on college students' math achievement.
Purpose
In this study, the authors developed a conceptual model to investigate sustainable consumption behavior, specifically the intention to use reusable bags, and its relationship with two crucial factors influencing the use of single-use plastic bags: cost savings and convenience. This study also aims to explore the mediating roles of environmental concern, guilt and self-efficacy.
Design/methodology/approach
A quantitative study using online survey involving 421 respondents was conducted, and data analysis performed using structural equation modeling.
Findings
The results indicate that self-efficacy influenced environmental concern and sustainable consumption, while perceived savings did not. Perceived convenience significantly influenced sustainable consumption behavior. Environmental concern had indirect effects on the relationships between perceived savings, perceived convenience and sustainable consumption behavior, whereas guilt did not moderate the relationship between environmental concern and sustainable consumption behavior.
Originality/value
The main contribution lies in the insights for promoting the sustainable use of reusable shopping bags, benefiting both theoretical understanding and practical applications in efforts to encourage sustainable consumption behavior.
Purpose
Given the dynamic and fast-evolving labour market, developing students’ employability competences has become of utmost importance for higher education institutions. The ability to reflect is essential to develop these competences, as it helps students to identify their learning needs and make plans for further development. However, reflective abilities are not easy to acquire and students need guidance to help them reflect. Therefore, mentoring is often used as an instructional approach to stimulate students to reflect. Empirical evidence on the relation between mentoring and employability competences is scarce, and the mediating role of reflection especially has rarely been researched. Consequently, the present study aims to investigate this mediating relationship, employing a pre-test post-test design.
Design/methodology/approach
Questionnaire data were collected from students before and after participation in four similar 1-year mentoring programmes in higher education within the Netherlands and Belgium ( n = 160).
Findings
The path analysis demonstrated that, first, trust and availability, autonomy support and empathy were significantly related to students’ employability competences. Secondly, autonomy support and similarity were significantly related to students’ critical reflection. Thirdly, critical reflection was significantly related to students’ employability competences. Last, reflection partially mediated the relationship between mentoring (autonomy support and similarity) and employability.
Originality/value
To the best of the authors’ knowledge, this study is the first attempt to demonstrate that mentoring programmes in higher education enable students to reflect and, in turn, develop their employability competences. Furthermore, it provides mentoring programme directors and mentors with concrete guidelines for developing students’ reflection and employability competences.
Monte Carlo computer simulations were used to investigate the performance of three χ–2 test statistics in confirmatory factor analysis (CFA). Normal theory maximum likelihood χ–2 (ML), Browne's asymptotic distribution free χ–2 (ADF), and the Satorra-Bentler rescaled χ–2 (SB) were examined under varying conditions of sample size, model specification, and multivariate distribution. For properly specified models, ML and SB showed no evidence of bias under normal distributions across all sample sizes, whereas ADF was biased at all but the largest sample sizes. ML was increasingly overestimated with increasing nonnormality, but both SB (at all sample sizes) and ADF (only at large sample sizes) showed no evidence of bias. For misspecified models, ML was again inflated with increasing nonnormality, but both SB and ADF were underestimated with increasing nonnormality. It appears that the power of the SB and ADF test statistics to detect a model misspecification is attenuated given nonnormally distributed data. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Covariance structure analysis uses χ–2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics was evaluated with a Monte Carlo confirmatory factor analysis study. The tests performed dramatically differently under 7 distributional conditions at 6 sample sizes. Two normal-theory tests worked well under some conditions but completely broke down under other conditions. A test that permits homogeneous nonzero kurtoses performed variably. A test that permits heterogeneous marginal kurtoses performed better. A distribution-free test performed spectacularly badly in all conditions at all but the largest sample sizes. The Santorra-Bentler scaled test performed best overall. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
This article compares two structural equation modeling fit indexes—Bentler's ( 1990; Bentler & Bonett, 1980) Confirmatory Fit Index (CFI) and Steiger and Lind's (1980; Browne & Cudeck, 1993) Root Mean Square Error of Approximation (RMSEA). These two fit indexes are both conceptually linked to the noncentral chi‐square distribution, but CFI has seen much wider use in applied research, whereas RMSEA has only recently been gaining attention. The article suggests that use of CFI is problematic because of its baseline model. CFI seems to be appropriate in more exploratory contexts, whereas RMSEA is appropriate in more confirmatory contexts. On the other hand, CFI does have an established parsimony adjustment, although the adjustment included in RMSEA may be inadequate.
Testing fit is a critical and controversial step in structural equation modeling (SEM), and alternative fit indices have been proposed. To provide guidance, a simulation study was conducted to evaluate the effects of estimation method, number of indicators per factor (p/r ratio), sample size, and loading size on six SEM fit indices: chi-square/degree of freedom ratio (chi(2)/df), Normed Fit Index (NFI), Nonnormed Fit Index (NNFI), Centrality m index, Relative Noncentrality Index (RNI), and Comparative Fit Index (CFI). When improper solutions occurred, the effects of constraining out-of-bounds estimates to a reasonable range (the method used in EQS software) on the fit indices was evaluated. Four levels of sample size (50, 100, 200, and 500), three levels of loading size (0.50, 0.70, and 0.90), five levels of p/r ratio (2, 3, 4, 5, and 6), and two levels of estimation method (Generalized Least Squares [GLS] and Maximum Likelihood [ML]) were examined. The results of this study indicated that: (a) improper solutions occurred frequently when p/r = 2 and sample size was small or loadings were low; (b) GLS produced more improper solutions than ML in general; (c) there was no effect of improper solutions (constrained to some boundary) found for any of the fit indices but NFI (more downward bias occurred for NFI when improper solutions were present); (d) four incremental fit indices (NFI, NNFI, RNI, and CFI) were negatively affected by increasing the p/r ratio; (e) NFI was affected much more seriously than the other three fit indices and should not be used; (f) all fit indices except NNFI were found to be significantly affected by estimation method (less bias occurred for GLS than for ML); and (g) interaction effects between estimation method, p/r ratio, sample size, and loading size also occurred. Recommendations regarding selection of a fit index are made based on the findings.
Anumber of goodness-of-fit indices for the evaluation of multivariate structural models are expressed as functions of the noncentrality parameter in order to elucidate their mathematical properties and, in particular, to explain previous numerical findings. Most of the indices considered are shown to vary systematically with sample size. It is suggested that H. Akaike's (1974; see record
1989-17660-001) information criterion cannot be used for model selection in real applications and that there are problems attending the definition of parsimonious fit indices. A normed function of the noncentrality parameter is recommended as an unbiased absolute goodness-of-fit index, and the Tucker–Lewis (see record
1973-30255-001) index and a new unbiased counterpart of the Bentler–Bonett (see record
1981-06898-001) index are recommended for those investigators who might wish to evaluate fit relative to a null model. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
P. M. Bentler and D. G. Bonett (1980) argue that it is often useful to compare a hypothesized covariance structure model or set of models to a nested null model using fit coefficients and they propose both generic null models for a variety of cases and 2 new measures of fit
extends the work of Bentler and Bonett in 2 ways / 1st, we provide general analytic conditions for ascertaining whether their generic null models are nested under a substantive model of interest, an issue they do not address clearly and completely / 2nd, we show that the null models they propose are inappropriate in all but the purely exploratory case / in other cases, we argue that the comparison should be developed in terms of baseline models that reflect the state of prior theory and knowledge, unlike the null models of Bentler and Bonett (PsycINFO Database Record (c) 2012 APA, all rights reserved)
[Correction Notice: An erratum for this article was reported in Vol 75(1) of
Journal of Applied Psychology (see record
2008-10492-001). An error exists in Figure 2 and the accompanying text of the article. The corrected information is included in the erratum.] The problem of assessing fit of structural equation models is reviewed, and two sampling studies are reported that examine the effects of sample size, estimation method, and model misspecification on fit indices. In the first study, the behavior of indices in a known-population confirmatory factor analysis model is considered. In the second study, the same problem in an empirical data set is examined by looking at antecedents and consequences of work motivation. The findings across the two studies suggest that (a) as might be expected, sample size is an important determinant in assessing model fit; (b) estimator-specific, as opposed to estimator-general, fit indices provide more accurate indications of model fit; and (c) the studied fit indices are differentially sensitive to model misspecification. Some recommendations for the use of structural equation model fit indices are given. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models (CSMs). Large-sample theory provides a chi-square goodness-of-fit test for comparing a model (M) against a general alternative M based on correlated variables. It is suggested that this comparison is insufficient for M evaluation. A general null M based on modified independence among variables is proposed as an additional reference point for the statistical and scientific evaluation of CSMs. Use of the null M in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal Ms and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical Ms is also emphasized. Normed and nonnormed fit indices are developed and illustrated. (43 ref) (PsycINFO Database Record (c) 2012 APA, all rights reserved)
In confirmatory factor analysis, hypothesized models reflect approximations to reality so that any model can be rejected if the sample size is large enough. The appropriate question is whether the fit is adequate to support the model, and a large number of fit indexes have been proposed for this purpose. In the present article, we examine the influence of sample size on different fit indexes for both real and simulated data. Contrary to claims by Bentler and Bonett (1980), their incremental fit index was substantially affected by sample size. Contrary to claims by Joreskog and Sorbom (1981), their goodness-of-fit indexes provided by LISREL were substantially affected by sample size. Contrary to claims by Bollen (1986), his new incremental fit index was substantially affected by sample size. Hoelter's (1983) critical N index was also substantially affected by sample size. Of the more than 30 indexes considered, the Tucker-Lewis (1973) index was the only widely used index that was relatively independent of sample size. However, four new indexes based on the same form as the Tucker-Lewis index were also relatively independent of sample size., (C) 1988 by the American Psychological Association <2>
Bentler and Bonett's nonnormed fit index is a widely used measure of goodness of fit for the analysis of covariance structures. This note shows that contrary to what has been claimed the nonnormed fit index is dependent on sample size. Specifically for a constant value of a fitting function, the nonnormed index is inversely related to sample size. A simple alternative fit measure is proposed that removes this dependency. In addition, it is shown that this new measure as well as the old nonnormed fit index can be applied to any fitting function that measures the deviation of the observed covariance matrix from the covariance matrix implied by the parameter estimates for a model.
We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large samplex
2 test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.
Normed and nonnormed fit indexes are frequently used as adjuncts to chi-square statistics for evaluating the fit of a structural model. A drawback of existing indexes is that they estimate no known population parameters. A new coefficient is proposed to summarize the relative reduction in the noncentrality parameters of two nested models. Two estimators of the coefficient yield new normed (CFI) and nonnormed (FI) fit indexes. CFI avoids the underestimation of fit often noted in small samples for Bentler and Bonett's (1980) normed fit index (NFI). FI is a linear function of Bentler and Bonett's non-normed fit index (NNFI) that avoids the extreme underestimation and overestimation often found in NNFI. Asymptotically, CFI, FI, NFI, and a new index developed by Bollen are equivalent measures of comparative fit, whereas NNFI measures relative fit by comparing noncentrality per degree of freedom. All of the indexes are generalized to permit use of Wald and Lagrange multiplier statistics. An example illustrates the behavior of these indexes under conditions of correct specification and misspecification. The new fit indexes perform very well at all sample sizes.
Assessing overall model fit is an important problem in general structural equation models. One of the most widely used fit measures is Bentler and Bonett's (1980) normed index. This article has three purposes: (1) to propose a new incremental fit measure that provides an adjustment to the normed index for sample size and degrees of freedom, (2) to explain the relation between this new fit measure and the other ones, and (3) to illustrate its properties with an empirical example and a Monte Carlo simulation. The simulation suggests that the mean of the sampling distribution of the new fit measure stays at about one for different sample sizes whereas that for the normed fit index increases with N. In addition, the standard deviation of the new measure is relatively low compared to some other measures (e.g., Tucker and Lewis's (1973) and Bentler and Bonett's (1980) nonnormed index). The empirical example suggests that the new fit measure is relatively stable for the same model in different samples. In sum, it appears that the new incremental measure is a useful complement to the existing fit measures.
Marsh and Balla (1986) and Marsh, Balla, and McDonald (1988) proposed an index of fit called χI2, but McDonald and Marsh (1990) subsequently demonstrated that the index is biased and recommended that it not be used. Bollen (1989) independently proposed Δ2 which is the same as χI2 (hereafter referred to as χI2‐Δ2), indicating that it adjusts for sample size and degrees of freedom (df). Gerbing and Anderson (1992), apparently based on the assumption that the χI2‐Δ2 index is unbiased and appropriately corrects for df (penalizes a lack of parsimony), recommended its use, and the index is routinely presented by major computer programs (e.g., EQS and LISREL 8). However, a more critical evaluation of the χI2‐Δ2 index reveals that: (a) it is systematically biased (i.e., its value varies systematically with N) although the size of the bias may be small; (b) the adjustment for df is inappropriate in that it penalizes model parsimony instead of model complexity; and (c) the inappropriate penalty for model parsimony is larger for small N. Because of these undesirable properties, the χI2‐Δ2 index is not recommended for routine use.
Many mechanistic rules of thumb for evaluating the goodness of fit of structural equation models (SEM) emphasize model parsimony; all other things being equal, a simpler, more parsimonious model with fewer estimated parameters is better than a more complex model. Although this is usually good advice, in the present article a heuristic counterexample is demonstrated in which parsimony as typically operationalized in indices of fit may be undesirable. Specifically, in simplex models of longitudinal data, the failure to include correlated uniquenesses relating the same indicators administered on different occasions will typically lead to systematically inflated estimates of stability. Although simplex models with correlated uniquenesses are substantially less parsimonious and may be unacceptable according to mechanistic decision rules that penalize model complexity, it can be argued a priori that these additional parameter estimates should be included. Simulated data are used to support this claim and to evaluate the behavior of a variety of fit indices and decision rules. The results demonstrate the validity of Bollen and Long's (1993) conclusion that "test statistics and fit indices are very beneficial, but they are no replacement for sound judgment and substantive expertise" (p. 8).
This article reviews proposed goodness-of-fit indices for structural equation models and the Monte Carlo studies that have empirically assessed their distributional properties. The cumulative contributions of the studies are summarized, and the variables under which the indices are studied are noted. A primary finding is that many of the indices used until the late 1980s, including Joreskog and Sorbom's (1981) GFI and Bentler and Bonett's (1980) NFI, indicated better fit when sample size increased. More recently developed indices based on the chi-square noncentrality parameter are discussed and the relevant Monte Carlo studies reviewed. Although a more complete understanding of their properties and suitability requires further research, the recommended fit indices are the McDonald (1989) noncentrality index, the Bentler (1990)-McDonald and Marsh (1990) RNI (or the bounded counterpart CFI), and Bollen's (1989) DELTA2.
A major problem encountered in covariance structure analyses involves decisions concerning whether or not a given theoretical model adequately represents the data used for its assessment. Given that X2 goodness-of-fit tests are joint functions of the difference between theoretical and empirical covariance structures and sample size, gauging the impact of sample size on such tests is essential. In this paper, we propose a simple index (critical N) and tentative acceptance criterion, which, by focusing on sample size, provide an improved method for assessing goodness-of-fit. Both small- and large-sample examples are presented, illustrating the utility of the proposed method for assessing theoretical models.
The large-sample statistical theory for latent-variable structural equation models offers little solace to the developmental psychologist, who is often confronted with less than optimally large sample sizes. This article reviews previously proposed alternatives to the sample-size and goodness-of-fit issue in latent-variable structural equation models. Various nonparametric fit indices for latent-variable systems are reviewed with their strengths and weaknesses discussed. An alternative estimation strategy called ME2 estimation is introduced as a possible alternative solution to the small-sample problem.
This article considers single sample approximations for the cross-validation coefficient in the analysis of covariance structures. An adjustment for predictive validity which may be employed in conjunction with any correctly specified discrepancy function is suggested. In the case of maximum likelihood estimation under normality assumptions the coefficient obtained is a simple linear function of the Akaike Information Criterion. Results of a random sampling experiment are reported.
This study examined the role language plays in mediating the influence of verbal descriptions of persons on trait ratings of those persons. Subjects were given written descriptions of the behavior of fictitious persons in a work situation and were asked to rate them on fifteen trait- adjective scales. In one condition of the experiment, specific information about certain traits was withheld, forcing subjects to rate persons on traits for which they had no direct behavioral clues. In the other two conditions, the specific information was provided. Providing specific information about a trait directly influenced ratings on that trait even when sufficient general information on that trait was given. In one condition, the influence on the ratings of the additional behavioral clues was such that a new latent variable representing an additional component of meaning was called for in the structural equation model.
This paper examines methods for comparing the suitability of alternative models for covariance matrices. A cross-validation procedure is suggested and its properties are examined. To motivate the discussion, a series of examples is presented using longitudinal data.
In a typical study involving covariance structure modeling, fit of a model or a set of alternative models is evaluated using several indicators of fit under one estimation method, usually maximum likelihood. This study examined the stability across estimation methods of incremental and non incremental fit measures that use the information about the fit of the most restricted (null) model as a reference point in assessing the fit of a more substantive model to the data. A set of alternative models for a large empirical dataset was analyzed by asymptotically distribution-free, generalized least squares, maximum likelihood, and ordinary least squares estimation methods. Four incremental and four nonincremental fit indexes were com pared. Incremental indexes were quite unstable across estimation methods—maximum likelihood and ordinary least squares solutions indicated better fit of a given model than asymptotically distribution-free and generalized least squares solu tions. The cause of this phenomenon is explained and illustrated, and implications and recommenda tions for practice are discussed.
Let S represent the usual unbiased estimator of a covariance matrix, Σ0, whose elements are functions of a parameter vector . A generalized least squares (G.L.S) estimate, of may be obtained by minimizing where V is some positive definite matrix. Asymptotic properties of the G.L.S. estimators are investigated assuming only that satisfies certain regularity conditions and that the limiting distribution of S is multivariate normal with specified parameters. The estimator of which is obtained by maximizing the Wishart likelihood function (M.W.L. estimator) is shown to be a member of the class of G.L.S. estimators with minimum asymptotic variances. When is linear in a G.L.S. estimator which converges stochastically to the M.W.L. estimator involves far less computation. Methods for calculating estimates of , estimates of the dispersion matrix of , and test statistics, are given for certain linear models.
J. S. Tanaka and G. J. Huba (see record
1986-10882-001) introduced a general fit index for covariance structure models under generalized least squares estimation that in some cases specialized to the fit indices presented by K. G. Jöreskog and D. Sörbom (1981). For a wide class of models, the general form of this fit index can be expressed as a weighted coefficient of determination. This coefficient is given as the ratio of weighted trace functions of predicted and observed covariance matrix elements. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
consider the following issues: (a) the usefulness of the χ[superscript]2 statistic based on various estimation methods for model evaluation and selection; (b) the conceptual elaboration of and selection criteria for fit indexes; and (c) identifying some crucial factors that will affect the magnitude of χ[superscript]2 statistics and fit indexes / review previous research findings as well as report results of some new, unpublished research (PsycINFO Database Record (c) 2012 APA, all rights reserved)
The structure of the covariance matrix of sample covariances under the class of linear latent variate models is derived, using properties of cumulants. This derivation is employed to provide a general framework for robustness of statistical inference in the analysis of covariance structures arising from linear latent variate models. Conditions for normal theory estimators and test statistics to retain each of their usual asymptotic properties under nonnormality of latent variates are given. Factor analysis and LISREL analysis are discussed as examples. (PsycINFO Database Record (c) 2012 APA, all rights reserved)
A general fit index for covariance structure models is obtained for all estimators that can be considered under generalized least squares (GLS) approaches including asymptotically efficient, robust, and resistant methods of estimation. This fit index is expressed as a function of the ratio of two trace functions. Normal theory ordinary least squares (OLS) and maximum likelihood (ML) fit indices previously given by Jöreskog and Sörbom can be derived from this framework. Fit indices for normal theory and generic GLS approaches including robust/resistant estimation methods are also obtained.
A condition is given by which optimal normal theory methods, such as the maximum likelihood methods, are robust against violation of the normality assumption in a general linear structural equation model. Specifically, the estimators and the goodness of fit test are robust. The estimator is efficient within some defined class, and its standard errors can be obtained by a correction formula applied to the inverse of the information matrix. Some special models, like the factor analysis model and path models, are discussed in more detail. A method for evaluating the robustness condition is given.
The purpose of the present investigation is to examine the influence of sample size (N) and model parsimony on a set of 22 goodness-of-fit indices including those typically used in confirmatory factor analysis and some recently developed indices. For sample data simulated from two known population data structures, values for 6 of 22 fit indices were reasonably independent ofN and were not significantly affected by estimating parameters known to have zero values in the population: two indices based on noncentrality described by McDonald (1989; McDonald and Marsh, 1990), a relative (incremental) index based on noncentrality (Bentler, 1990; McDonald & Marsh, 1990), unbiased estimates of LISREL's GFI and AGFI (Joreskog & Sorbom, 1981) presented by Steiger (1989, 1990) that are based on noncentrality, and the widely known relative index developed by Tucker and Lewis (1973). Penalties for model complexity designed to control for sampling fluctuations and to address the inevitable compromise between goodness of fit and model parsimony were evaluated.
In covariance structure analysis, alternative methods of estimation are now regularly available. A variety of statistics, such as estimators, test statistics, and residuals, are computed. The sampling variability of these statistics is known to depend on a matrix Γ which is based on the fourth-order moments of the data. Estimates of these fourth-order moments are expensive to compute, require a lot of computer storage, and have high sampling variability in small to moderate samples. By exploiting the linear relations that typically generate the covariance structure, we have developed conditions under which a matrix Γ*, which depends only on second-order moments of the data, can be used as a substitute for Γ to obtain correct asymptotic distributions for the statistics of interest. In contrast to related work on asymptotic robustness in covariance structure analysis, our theory is developed in the general setting of arbitrary discrepancy functions and addresses a broader class of statistics that include, for instance, goodness of fit statistics that are not necessarily asymptotically χ2 distributed, and statistics based on the residuals. Basically, our theory shows that the normal theory form Γ* for Γ can be used whenever an independence assumption (not only uncorrelatedness), which will always hold under normality, carries over to the model with nonnormal variables. This theory is spelled out in sufficient detail and simplicity so that it can be used in every day practice.
A framework for hypothesis testing and power analysis in the assessment of fit of covariance structure models is presented. We emphasize the value of confidence intervals for fit indices, and we stress the relationship of confidence intervals to a framework for hypothesis testing. The approach allows for testing null hypotheses of not-good fit, reversing the role of the null hypothesis in conventional tests of model fit, so that a significant result provides strong support for good fit. The approach also allows for direct estimation of power, where effect size is defined in terms of a null and alternative value of the root-mean-square error of approximation fit index proposed by J. H. Steiger and J. M. Lind (1980). It is also feasible to determine minimum sample size required to achieve a given level of power for any test of fit in this framework. Computer programs and examples are provided for power analyses and calculation of minimum sample sizes., (C) 1996 by the American Psychological Association
Asymptotic properties of estimators for the confirmatory factor analysis model are discussed. The model is identified by restrictions on the elements of the factor loading matrix; the number of restrictions may exceed that required for identification. It is shown that a particular centering of the maximum likelihood estimator derived under assumed normality of observations yields an asymptotic normal distribution that is common to a wide class of distributions of the factor vectors and error vectors. In particular, the asymptotic covariance matrix of the factor loading estimator derived under the normal assumption is shown to be valid for the factor vectors containing a fixed part and a random part with any distribution having finite second moments and for the error vectors consisting of independent components with any distributions having finite second moments. Thus the asymptotic standard errors of the factor loading estimators computed by standard computer packages are valid for virtually any type of nonnormal factor analysis. The results are extended to certain structural equation models.
Three types of asymptotic $\chi^2$ goodness-of-fit tests derived under the normal assumption have been used widely in factor analysis. Asymptotic behavior of the test statistics is investigated here for the factor analysis model with linearly or nonlinearly restricted factor loadings under weak assumptions on the factor vector and the error vector. In particular the limiting $\chi^2$ result for the three tests is shown to hold for the factor vector, either fixed or random with any distribution having finite second-order moments, and for the error vector with any distribution having finite second-order moments, provided that the components of the error vector are independent, not just uncorrelated. As special cases the result holds for exploratory and confirmatory factor analysis models and for certain nonnormal structural equation (LISREL) models.
A class of latent variable models which includes the unrestricted factor analysis model is considered. It is shown that minimum discrepancy test statistics and estimators derived under normality assumptions retain their asymptotic properties when the common factors are not normally distributed but the unique factors do have a multivariate normal distribution. The minimum discrepancy test statistics and estimators considered include the usual likelihood ratio test statistic and maximum likelihood estimators.
The information criterion AIC was introduced to extend the method of maximum likelihood to the multimodel situation. It was obtained by relating the successful experience of the order determination of an autoregressive model to the determination of the number of factors in the maximum likelihood factor analysis. The use of the AIC criterion in the factor analysis is particularly interesting when it is viewed as the choice of a Bayesian model. This observation shows that the area of application of AIC can be much wider than the conventional i.i.d. type models on which the original derivation of the criterion was based. The observation of the Bayesian structure of the factor analysis model leads us to the handling of the problem of improper solution by introducing a natural prior distribution of factor loadings.
A procedure for computing the power of the likelihood ratio test used in the context of covariance structure analysis is derived. The procedure uses statistics associated with the standard output of the computer programs commonly used and assumes that a specific alternative value of the parameter vector is specified. Using the noncentral Chi-square distribution, the power of the test is approximated by the asymptotic one for a sequence of local alternatives. The procedure is illustrated by an example. A Monte Carlo experiment also shows how good the approximation is for a specific case.
Current practice in structural modeling of observed continuous random variables is limited to representation systems for first and second moments (e.g., means and covariances), and to distribution theory based on multivariate normality. In psychometrics the multinormality assumption is often incorrect, so that statistical tests on parameters, or model goodness of fit, will frequently be incorrect as well. It is shown that higher order product moments yield important structural information when the distribution of variables is arbitrary. Structural representations are developed for generalizations of the Bentler-Weeks, Jöreskog-Keesling-Wiley, and factor analytic models. Some asymptotically distribution-free efficient estimators for such arbitrary structural models are developed. Limited information estimators are obtained as well. The special case of elliptical distributions that allow nonzero but equal kurtoses for variables is discussed in some detail. The argument is made that multivariate normal theory for covariance structure models should be abandoned in favor of elliptical theory, which is only slightly more difficult to apply in practice but specializes to the traditional case when normality holds. Many open research areas are described.
Maximum likelihood factor analysis provides an effective method for estimation of factor matrices and a useful test statistic
in the likelihood ratio for rejection of overly simple factor models. A reliability coefficient is proposed to indicate quality
of representation of interrelations among attributes in a battery by a maximum likelihood factor analysis. Usually, for a
large sample of individuals or objects, the likelihood ratio statistic could indicate that an otherwise acceptable factor
model does not exactly represent the interrelations among the attributes for a population. The reliability coefficient could
indicate a very close representation in this case and be a better indication as to whether to accept or reject the factor
solution.
Akaike's Information Criterion is systematically dependent on sample size, and therefore cannot be used in practice as a basis for model selection. An alternative measure of goodness-of-fit, based like Akaike's on the noncentrality parameter, appears to be consistent over variations in sample size.
Factor analysis, path analysis, structural equation modeling, and related multivariate statistical methods are based on maximum likelihood or generalized least squares estimation developed for covariance structure models. Large-sample theory provides a chi-square goodness-of-fit test for comparing a model against a general alternative model based on correlated variables. This model comparison is insufficient for model evaluation: In large samples virtually any model tends to be rejected as inadequate, and in small samples various competing models, if evaluated, might be equally acceptable. A general null model based on modified independence among variables is proposed to provide an additional reference point for the statistical and scientific evaluation of covariance structure models. Use of the null model in the context of a procedure that sequentially evaluates the statistical necessity of various sets of parameters places statistical methods in covariance structure analysis into a more complete framework. The concepts of ideal models and pseudo chi-square tests are introduced, and their roles in hypothesis testing are developed. The importance of supplementing statistical evaluation with incremental fit indices associated with the comparison of hierarchical models is also emphasized. Normed and nonnormed fit indices are developed and illustrated.
Covariance structure analysis uses chi 2 goodness-of-fit test statistics whose adequacy is not known. Scientific conclusions based on models may be distorted when researchers violate sample size, variate independence, and distributional assumptions. The behavior of 6 test statistics is evaluated with a Monte Carlo confirmatory factor analysis study. The tests performed dramatically differently under 7 distributional conditions at 6 sample sizes. Two normal-theory tests worked well under some conditions but completely broke down under other conditions. A test that permits homogeneous nonzero kurtoses performed variably. A test that permits heterogeneous marginal kurtoses performed better. A distribution-free test performed spectacularly badly in all conditions at all but the largest sample sizes. The Satorra-Bentler scaled test statistic performed best overall.
Although covariance structure analysis is used increasingly to analyze nonexperimental data, important statistical requirements for its proper use are frequently ignored. Valid conclusions about the adequacy of a model as an acceptable representation of data, which are based on goodness-of-fit test statistics and standard errors of parameter estimates, rely on the model estimation procedure being appropriate for the data. Using analogies to linear regression and anova, this review examines conditions under which conclusions drawn from various estimation methods will be correct and the consequences of ignoring these conditions. A distinction is made between estimation methods that are either correctly or incorrectly specified for the distribution of data being analyzed, and it is shown that valid conclusions are possible even under misspecification. A brief example illustrates the ideas. Internet access is given to a computer code for several methods that are not available in programs such as EQS or LISREL.
Statistically based tests for the number of common factors. Pa-per presented at the annual meeting of the Psychometric Society Effect of estimation method on incremental fit indexes for covariance structure models
- J H Steiger
- J C Lind
Steiger, J. H., & Lind, J. C. (1980, May). Statistically based tests for the number of common factors. Pa-per presented at the annual meeting of the Psychometric Society, Iowa City, IA. Sugawara H. M., & MacCallum, R. C. (1993). Effect of estimation method on incremental fit indexes for covariance structure models. Applied Psychological Measurement, 17, 365-377.
An evaluation of incremental fit indices: A clarification of mathematical and empirical properties Ad-vanced structural equation modeling: Issues and techniques Goodness-of-fit indices in confirmatory factor analysis: Effects of sample size
- H W Marsh
- J R Balla
- K.-T H W Hau
- J R Balla
- R P Mcdonald
Marsh, H. W., Balla, J. R., & Hau, K.-T. (1996). An evaluation of incremental fit indices: A clarification of mathematical and empirical properties. In G. A. Marcoulides & R. E. Schumacker (Eds.), Ad-vanced structural equation modeling: Issues and techniques (pp. 315-353). Mahwah, NI: Lawrence Erlbaum Associates, Inc. Marsh, H. W., Balla, J. R., & McDonald, R. P. (1988). Goodness-of-fit indices in confirmatory factor analysis: Effects of sample size. Psychological Bulletin, 103, 391-411.
EQS for Windows user's guide. Encino, CA: Multivariate Software Sample size and Bentler and Bonett's nonnormed fit index
- P M Bentler
- E J C Wu
Bentler, P. M, & Wu, E. J. C. (1995). EQS for Windows user's guide. Encino, CA: Multivariate Software. Bollen, K. A. (1986). Sample size and Bentler and Bonett's nonnormed fit index. Psychometrika, 51, 375-377.
USREL V: Analysis of linear structural relationships by the method of maximum likelihood
- K G Jöreskog
- D Sörbom
Jöreskog, K. G., & Sörbom, D. (1981). USREL V: Analysis of linear structural relationships by the method of maximum likelihood. Chicago: National Educational Resources.