ArticleLiterature Review

Cutoff Criteria for Fit Indexes in Covariance Structure Analysis: Conventional Criteria Versus New Alternatives

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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.

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... 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. ...
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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.
... Only one is an exogenous variable. The endogenous variables are those that receive the effect of other variables [14]. Exogenous variables are those that exert an effect on the endogenous variables [14]. ...
... The endogenous variables are those that receive the effect of other variables [14]. Exogenous variables are those that exert an effect on the endogenous variables [14]. Due to the characteristics of the endogenous variables, the relationship between measurement reliability and the different indicators has been considered. ...
... When assessing the fit of the theoretical model, different indices were found. These are classified into absolute fit indices and comparative fit indices [14]. Within the absolute fit indices, the most common is the Chi-square/degrees of freedom (χ 2 /gl). ...
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Violent behaviour in the secondary education stage is a serious concern that comes from low emotional control. Judo is a sport that requires self-control and high emotional competence to mitigate aggressive behaviours. This research presents the objectives of analysing the correlations of different types of aggressive behaviours before an intervention program with those after said program, as well as study the effect of emotions on aggressive behaviours before and after the intervention program through multigroup structural equation modelling. A quasi-experimental study was planned. It used a pre-test–post-test design in a population of 139 secondary school students (M = 15.76; SD = 1.066). The instruments were an ad hoc questionnaire, the Schutte Self-Report Inventory and the Violent Behaviour at School Scale. The data show that the intervention decreased the correlations between different types of violent behaviours. The results show an increase in the effect of emotional intelligence on mitigating aggressive attitudes. The promotion and use of contact sports is necessary to prevent the emergence of aggressive behaviours within a school environment.
... So, for improvement purpose various covariance was drawn between error terms of the redundant items to get the model fit. In the second attempt, the model analysis generated a good model fit which indicated CMIN/DF 1.879 is in acceptable range, which should be between 1 and 3 (Tanaka, 1993;Hu & Bentler, 1999 which includes using the maximum likelihood (ML; Hair et al., 2010). Value of GFI = .898, ...
... The convergent validity considers the accepted value for all given constructs which are above 0.50 (Hu & Bentler, 1999 which includes using the maximum likelihood (ML; Hair et al., 2010). Composite reliability of each construct value is higher than 0.70 (Nunnally & Bernstein, 1994). ...
... The discriminant validity of the construct will be higher than correlation value of construct with the other construct. So, in the table all the mentioned standard condition were satisfied (Hu & Bentler, 1999 which includes using the maximum likelihood (ML; Hair et al., 2010). So, we can move for the further process of testing the hypothesis through structural equation modeling. ...
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The purpose of the article is to investigate how heuristic bias affects investors’ investment decision. Understanding heuristic biases is essential for predicting and explaining human behaviour in various contexts, from consumer choices to financial decision-making and beyond. By identifying and categorizing different types of biases, researchers can discern patterns in decision-making that might otherwise remain obscure. The study takes into account four different types of heuristic bias, that is, availability bias, representativeness bias, overconfidence bias and adjustment and anchoring bias. It is very important to study heuristics bias because these biases can lead to deviations from the rational decision making. The knowledge of these biases can be used to develop strategies to improve decision making. With the aid of a questionnaire, the data is gathered. The method of convenient sampling is employed to choose 358 respondents. The data are analysed using Structural Equation Modelling and Descriptive Statistics. The study of the data reveals that the investors’ investment decisions are highly impacted by availability and adjustment and anchoring bias. Overconfidence and representativeness bias are insignificant.
... 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). ...
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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). ...
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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.
... 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. ...
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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.
... comparative fit index (CFI) > .9, Tucker Lewis Index (TLI) > .9, and the standardized root mean squared residual (SRMR) < .1 to maximize the fit of items (Hu & Bentler, 1999). Model information criteria were determined using the Akaike information criterion (AIC) and the Bayesian information criteria (BIC). ...
... Internal reliability yielded Cronbach's alpha of .93 and McDonald's omega of .94. Based on recommendations (Hu & Bentler, 1999), the 8-item single factor solution met the minimum preregistered criteria for CFI and SRMR. The TLI and RMSEA indicated a less-thanadequate model fit, although these were marginal. ...
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How social media influences users depends largely on motivations for its use and how the user interprets social media-facilitated interactions. Contingent self-esteem, a construct rooted in self-determination theory (Deci & Ryan, 2000), can account for differential effects, including addictive use. Three preregistered studies (ntotal = 822) derived social media contingent self-esteem (SMCSE) and examined the factor structure and associations with social media use, addiction, and disorder criteria. Study 1 (N = 412) analyzed exploratory and confirmatory factors. Study 2 (N = 230) examined associations with other domains of contingent self-esteem, basic psychological needs satisfaction and frustration, and measures of social media use and addiction. Study 3 (N = 192) examined associations between SMCSE, identity bubble reinforcement (echo chambers), and social media outcomes. SMCSE was associated with greater social media use and intensity, identity bubble reinforcement, social media addiction, and disorder criteria. Exploratory support was found for mediation models in which identity bubble reinforcement predicted greater SMCSE, which in turn predicted a greater likelihood of social media addiction and disorder.
... General guidelines indicate that the values of χ2/df ratios on the order of 3/1 or less indicate better-fitting models (Hair et al., 2013). CFI ≥ .95 is considered indicative of a good-fitting model (Bentler, 1990;Brown, 2006;Hu & Bentler, 1999;Kline, 2016). SRMR values of .08 or less are desired (with CFI above .92) ...
... SRMR values of .08 or less are desired (with CFI above .92) (Brown, 2006;Hair et al., 2013;Hu & Bentler, 1999). RMSEA values below .05 ...
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The research intended to adapt and validate the self-report job precariousness scale for the Brazilian gig work context and to investigate the association of the dimensions of job precariousness with gig workers' subjective experiences and work outcomes. Exploratory and confirmatory factor analyses were conducted on a sample of 504 Brazilian gig workers. In addition, zero-order correlations were performed on a sample of 304 Brazilian gig workers for criterion validity analysis. Results supported a four-factor structure and the bi-factor model, reinforcing the assumption that the job precarious scale is a multidimensional measure with a hierarchical structure. Reliability analysis (Alpha coefficient and bifactor indices) indicates that the scale presented adequate internal consistency for all four dimensions and the full scale. Results regarding criterion validity demonstrate that job precariousness is negatively linked to well-being and positively associated with ill-being; in addition, the dimensions of job precariousness and remuneration have significative associations with all variables of work outcome investigated. This study introduces the Brazilian version of the self-report job precariousness scale with robust psychometric qualities to assess workers' perception of precarious working conditions in the Brazilian gig work context. In addition, it broadens the scope of research on precarious working conditions and their impact on psychological experiences and work outcomes.
... The SEM model comprised three latent variables, with parental vaccination status, binary survey completion dates before and after the CDC's recommendation for the pediatric vaccine, gender, race and ethnicity included as observed variables. Several statistical parameters were employed to evaluate the model's fit to the data, including the chi-square (χ 2 ) test, comparative fit index (CFI), non-normed fit index (NNFI), root mean square error of approximation (RMSEA), and standardized root mean square residual (SRMR) [54]. A statistically non-significant result for the chi-square test (p > 0.05) would indicate a good fit for the model. ...
... With this, focus was placed on the remaining fit indices. In accordance with established guidelines [54,56], good fit is indicated by CFI and NNFI values exceeding 0.90 or 0.95, an RMSEA value below 0.06, and an SRMR value under 0.05. These fit indices served as key indicators to evaluate the adequacy of the hypothesized TPB model with the collected data. ...
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Background Public health guidance recommended that children who are 6 months or older be vaccinated against COVID-19 in June of 2022. In the U.S., 56% of children under 17 had not received the COVID-19 vaccination in 2023. We examine parents’ willingness to vaccinate their children against COVID-19 using the theory of planned behavior in order to design effective strategies to promote vaccine uptake. Methods The Philadelphia Community Engagement Alliance is part of an NIH community-engaged consortium focused on addressing COVID-19 disparities across the U.S. We surveyed 1,008 Philadelphia parents (mean age 36.86, SD 6.55; 42.3% racial/ethnic minorities) between September 2021 and February 2022, a period when guidance for child vaccination was anticipated. Structural Equation Modeling analysis examined associations between parental willingness and vaccine-related attitudes, norms, and perceived control. Covariates included parents’ COVID-19 vaccination status, race/ethnicity, gender, and survey completion post-CDC pediatric COVID-19 vaccination guidelines. Subgroup analyses by race/ethnicity and gender were conducted. Results Our model demonstrated good fit (χ2 = 907.37, df = 419, p<0.001; comparative fit index [CFI] = 0.951; non-normed fit index [NNFI] = 0.946; root mean square error of approximation [RMSEA] = 0.034 with 95% CI = 0.030–0.038). Attitudes (β^ = 0.447, p<0.001) and subjective norms (β^ = 0.309, p = 0.002) were predictors of intention. Racial/ethnic minority parents exhibited weaker vaccination intentions (β^ = -0.053, p = 0.028) than non-Hispanic White parents. Conclusions Parents’ attitudes and norms influence their vaccination intentions. Despite the survey predating widespread child vaccine availability, findings are pertinent given the need to increase and sustain pediatric vaccinations against COVID-19. Interventions promoting positive vaccine attitudes and prosocial norms are warranted. Tailored interventions and diverse communication strategies for parental subgroups may be useful to ensure comprehensive and effective vaccination initiatives.
... indicated a good fit for the CFI, and values less than .06 indicated good fit for RMSEA (Hu & Bentler, 1999). ...
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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). ...
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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. ...
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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. ...
Article
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). ...
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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). ...
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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). ...
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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). ...
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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). ...
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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. ...
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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.
... According to some authors, RMSEA and SRMR values less than 0.05 indicate a good fit, while values between 0.05-0.08 indicate an acceptable fit (Byrne, 2009;Hu & Bentler, 1999). CFI and TLI values vary between 0 and 1, and values greater than 0.90 indicate an acceptable fit; values close to 1 can be interpreted as a better fit of the model (Hu & Bentler, 1998;Schermelleh-Engel et al., 2003;Şimşek, 2020). ...
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In the study, we aimed to evaluate the Turkish adaptation of the leisure motivation scale (LMS-A) for adolescents participating in recreational physical activities. We collected data from 331 people determined by the convenience sampling method, and conducted its Turkish adaptation with three different test phases after we performed Turkish language co-validation of the scale. Firstly, we determined the univariate and multivariate normality levels of the data. In the second stage we used confirmatory factor analysis (CFA) to assess the contextuality of the scale and in the third stage we utilized two types of construct validity, convergent and discriminant to evaluate the validity of the scale. The results revealed that the original structure of the scale fits well in the correlated factors model and best fit the data collected from the Turkish population. These results suggest that the leisure motivation scale could be a valid and reliable measurement tool for adolescents participating in recreational physical activities in Türkiye.
... The maximum-likelihood approach was used for model estimation (Brown, 2015;Kline, 2015). Conventional model fit indices, including the comparative fit index (CFI; Bentler, 1990), the root mean squared error of approximation (RMSEA; Steiger & Lind, 1980), and the square root mean residual (SRMR; Hu & Bentler, 1999) were used to evaluate each model. Threshold values of > 0.90 (CFI), < 0.08 (RMSEA) and < 0.06 (SRMR) were set as cut-points to establish model adequacy. ...
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Background Maternal birth experience is being increasingly recognised as a key clinical outcome parameter. The Birth Satisfaction Scale-Revised (BSS-R) is a short self-report measure designed to assess birth experience. The current investigation sought to trans-late the BSS-R into Polish and validate this version of the BSS-R (PL-BSS-R). Participants and procedure The BSS-R was translated into Polish by an expert panel using forward and backward translation. A complex within-subjects design with an embedded between-subjects component was used to determine the key psychometric characteristics of the PL-BSS-R. Two hundred ninety-four Polish-speaking women in Poland completed the follow-up component of the study where the PL-BSS-R was administered. The PL-BSS-R measurement properties were examined using confirmatory factor analysis, divergent, convergent validity analysis, internal consistency appraisal and investigation of known-groups discriminant characteristics. Results The PL-BSS-R was found to have generally very good measurement properties and to be equivalent to the original English-language version across key validity indices. The PL-BBS-R was found to be significantly correlated with neonatal physical health immediately postpartum and differed across delivery modes. Conclusions The PL-BSS-R is a psychometrically robust measure of birth experience appropriate for clinical and research use within Po-land. Important associations were noted between subjective maternal birth experience and objective measures of neonatal physical health, indicating a critically important future research direction.
... p = .00 -the CMIN/DF ratio (2.26) and other fit indices suggested adequate fit for the seven-factor model (Hu & Bentler, 1999;Kline, 1998): CFI = .98, TLI = .96, ...
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Research suggests that both applicants and organizations may withdraw from the recruitment and selection process without notice. This behaviour, referred to as ‘ghosting’, is prevalent yet empirical research on this topic is unfortunately scarce. To gain greater clarity, the current study examines the antecedents of applicant ghosting behaviour, which we place within the nomological network of maladaptive workplace behaviour. Drawing on an interactionist framework, we examine the role of aberrant dispositional characteristics – the Dark Triad, self‐control and fear of missing out (FoMO) – in predicting applicant ghosting behaviour. We also draw on trait activation and conservation of resources theories to examine how the experience of being ghosted before moderates these relationships between aberrant dispositional characteristics and ghosting behaviour. Results from a two‐wave design suggest that psychopathy and FoMO positively predicted ghosting behaviour and being ghosted before moderated relationships between both (a) self‐control and ghosting behaviour and (b) FoMO and ghosting behaviour. Qualitative data suggest that perceived fit and interest, communication and ghosting norms, company culture and behaviour, and compensation and benefits were the primary reasons why applicants engage in ghosting behaviour. We discuss the theoretical and practical implications of these results and offer future research directions in this nascent field.
... Turning now to matters of model-data fit, the conventional cut-offs in the goodness-of-fit indices were considered here. Specifically, CFI and TLI values close to/above 0.95, accompanied by an RMSEA value below 0.06 and a SRMR value below 0.08 are considered indicators of good fit (Hu and Bentler, 1999). The chi-square test is usually very sensitive to minor misspecifications and was, thus, not of primary interest here given the large sample size (Bearden et al., 1982). ...
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Introduction: Metacognitive self-regulation is a crucial factor that promotes students' learning and achievement. However, the evidence regarding age differences in metacognitive skills is rather mixed, with some evidence pointing toward further refinement and development and other evidence suggesting declining levels. Academic motivation, an important antecedent of metacognitive self-regulation, has also been reported to decline steeply in adolescence. Hence, this raises the question whether there are any age-related differences in academic motivation and metacognitive self-regulation of adolescents and whether age differences in academic motivation drive decreases in metacognitive self-regulation. Method: A large sample size of 1,027 Greek adolescents (ages 12-16, M age = 13.95, SD = 0.78) was utilized in the present study. Multigroup measurement invariance analyses were deployed to compare the latent means of motivational factors (self-efficacy, task value, mastery, and performance goals) and metacognitive self-regulation across age groups. Cholesky decomposition was applied to test the independent contribution of motivational factors to and the indirect effects of age on metacognitive self-regulation. Results: Invariance analyses revealed scalar invariance for metacognitive self-regulation, language self-efficacy, mastery and performance goal orientations and partially scalar invariance for task value. Older adolescents scored lower on metacognitive self-regulation, mastery and performance goals, and self-efficacy. Older students scored lower on metacognitive self-regulation via indirect effects through Cholesky decomposed motivational factors. Discussion: Self-efficacy, mastery and performance goals, and task value are similarly understood across adolescents in different age groups. Decreased mastery and performance goals and task value can lead to reduced metacognitive self-regulation in adolescents. The implications of the findings underscore the key role of making students more engaged with lessons' content in order to promote greater academic motivation and prevent decreases in metacognitive self-regulation.
... We only retained covariates that exhibited statistically significant paths with at least one endogenous variable; we trimmed non-statistically significant paths in one step, which left sexual and gender identity within the model. Adequate fit was based on Hu and Bentler's (1999) recommendations: a normed Chi-square CMIN/df value not greater than 2.0, a comparative fit index (CFI) of .95 or higher, and a root-meansquare error of approximation (RMSEA) less than .06. ...
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Compared to their heterosexual counterparts, sexual minority youth are disproportionally affected by suicidality, anxiety, depression, and other health disparities. The minority stress model claims that certain coping mechanisms such as receiving social support can act as a buffer against minority stress. In the current study, we tested whether LGBQ+ (e.g., lesbian, gay, bisexual) television exposure can effectively act within this role. Using a cross-sectional survey of sexual minority late adolescents (18–23 years old, N = 417), we found that LGBQ+ television exposure was not a significant moderator between minority stress and mental health outcomes. However, there were positive direct effects of LGBQ+ television exposure on resilience and identity affirmation. We provide tentative conclusions regarding the role of LGBQ+ television exposure on sexual minority youths’ identities and their propensity to persist in the face of adversity.
... CSWL = cross-situational word learning; CSWL 1:1 = CSWL in the 1:1 mapping condition (n = 184); CSWL 2:1 = CSWL in the 2:1 mapping condition (n = 184); VSWM = visuo-spatial working memory (n = 177); PWM = phonological working memory (n = 163). Browne & Cudeck, 1992;Hu & Bentler, 1999;Kline, 1998). Evaluation of model comparison was based on likelihood ratio test in base R. ...
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Cross-situational word learning (CSWL), the ability to resolve word–referent ambiguity across encounters, is a powerful mechanism found in infants, children, and adults. Yet, we know little about what predicts individual differences in CSWL, especially when learning different mapping structures, such as when referents have a single name (1:1 mapping structure) or two names (2:1 mapping structure). Here, we investigated how multilingual experience and working memory skills (visuo-spatial and phonological) contributed to CSWL of 1:1 and 2:1 structures. Monolingual (n = 78) and multilingual (n = 106) adults completed CSWL tasks of 1:1 and 2:1 structures, a symmetry span task, and a listening span task. Results from path models showed that multilingualism predicted visuo-spatial working memory but not CSWL. Additionally, phonological working memory predicted accuracy on CSWL of 1:1 structure, but not 2:1 structure. Findings highlight the importance of considering language experience and cognitive skills together to better understand the factors that promote individual CSWL skills.
... Since this revised scale was used for the first time, we conducted confirmatory factor analysis (CFA) to evaluate its construct validity. Model fit was considered satisfactory if CFI > 0.90, TLI > 0.90, SRMR < 0.08, and RMSEA < 0.08 (Hu & Bentler, 1999). positively correlated with psychological empowerment (r = 0.59, p < 0.001), normative commitment (r = 0.65, p < 0.001) and innovative behavior (r = 0.44, p < 0.001). ...
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Teachers play a pivotal role in advancing student learning outcomes and nurturing creativity by continuously innovating their practices. Based on the conservation of resources theory and social exchange theory, this study explored the relationship between institutional legitimacy and innovative behavior, examining the serial mediation of psychological empowerment and normative commitment. Data from 450 Chinese elementary, middle, and high school teachers were analyzed to find a significant positive correlation between institutional legitimacy and innovative behavior. While institutional legitimacy may not directly affect innovation behavior, it influences it through three pathways: the mediating effect of psychological empowerment, the mediating effect of normative commitment, and the serial mediating effect of psychological empowerment and normative commitment. These findings reveal the psychological mechanism through which institutional legitimacy affects innovative behavior, providing a scientific basis for devising effective strategies to promote teachers’ innovative practices.
... Next, to test Hypothesis 1, we conducted regression analyses, including multiple and bivariate regressions, to estimate the relationship between all three types of wartime losses on support for war or peace. To test Hypotheses 2 and 3, we used structural equation modeling to examine the extent to which the previously described mediators may explain the relationship between wartime experiences and support for war or peace and conducted path analyses in the semTools package (Jorgensen et al., 2022) for Hypothesis 3. We applied fit criterion based on a comparative fit index (CFI) of .95 or above, a root-meansquare error of approximation (RMSEA) close to .06, and a standardized root-mean-square residual (SRMR) close to or below .08 (Hu & Bentler, 1999). We estimated robust confidence intervals for indirect effects using Monte Carlo estimation as described by MacKinnon et al. (2004). ...
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The purpose of this study is to advance our understanding of how exposure to war-related violence can affect civilians’ willingness to support peace negotiations. We surveyed 1,812 people in three eastern cities of war-torn Ukraine to examine how different forms of loss during war influenced people’s support for peace agreements and how the mechanisms of psychological distress, hate toward Russian leadership, and perceptions of outgroup threat mediated these effects. First, we found significant associations between experiences of war-related loss and perceptions of war and peace, with divergent effects for different types of loss on support for war and peace. Although property loss and displacement predicted increased support for peace, the loss of a friend, neighbor, or colleague predicted a preference to continue the war. Second, mediation analyses indicated that, to varying extents, psychological distress, outgroup threat, and group-based hate may be important pathways through which wartime losses may influence views toward war and peace. Further, advancing extant research indicating threat perceptions as a pathway through which war-related violence can influence support for war, our analysis suggests that different types of threat may provide varied mediating pathways between wartime losses and support for peace or war.
... We used maximum likelihood estimation and FIML to account for missing data, which ranged from 0 to 3%. We determined the fit of each model based on root mean squared error (RMSEA; <.08), standardized root mean square residual (SRMR; <.08), and comparative fit index (CFI; >.95) (Hu & Bentler, 1999). ...
Article
This study utilized data from a national longitudinal study of 277 early adolescent summer camp participants to examine the iterative links between youths’ experiences in two contexts – summer camp and school – and empathy over two years. Using a cross-lagged panel model, the authors examined how the quality of youths’ developmental experiences within each context, defined as a combination of supportive relationships and engaged learning opportunities, were related to youths’ empathy over time. Results showed that 1) higher quality developmental experiences in each context uniquely predicted improvements in empathy; 2) youths’ developmental experiences at camp and school were mutually reinforcing over time; and 3) school experiences partly mediated the effects of camp experiences and vice versa. Results illustrate the value of out-of-school-time contexts for supporting empathy, the importance of developmental experiences across settings, and the need for researchers and practitioners to attend to the ecosystem of social development.
... We evaluated each model by using the most common fit indices: chi-square coefficient (χ2), comparative fit index (CFI), Tucker-Lewis index (TLI) and the root mean square error of approximation (RMSEA). Interpretation was based on cut-off values suggested by Hu and Bentler [34]: 1) chi-square (χ2) value as a global estimation of fit, 2) CFI and TLI (values > .95), 3) Root Mean Square Error Approximation (RMSEA), and 4) Standardized Root Mean Residual (SRMR) (< .07). Given the chi-square statistic is highly sensitive to sample size (n > 1 000), we followed Kline's recommendations by inspecting the residual correlation matrix [35]. ...
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Despite the advantages of small area games in youth sport, some challenges remain regarding the implementation of the half-ice gameplay model in Canada. In youth sport, establishing a good line of communication between parents and coaches is a crucial step for a positive environment. The purpose of this study is to provide further knowledge on the mechanisms associated with parents’ and coaches’ perceptions regarding the half-ice model in Canada. Data came from a national survey distributed across Canada (N = 6 372). Parents and coaches completed questionnaires that assessed attitudes, norms and perceived facilitators-obstacles to half-ice hockey. Parents-coaches’ preferences towards the playing format and sociodemographic variables were also measured. Structural equation modelling was performed to verify associations between each variable. Beliefs were a key factor in parents-coaches’ preferences regarding the playing format. Previous sport background and knowledge about half-ice hockey were associated with favorable predispositions. Hockey associations administrators should consider parents and coaches’ predispositions in program implementation and should design promotional campaigns adapted to their members’ predispositions towards half-ice hockey. This research underlines the key factors to consider in successful program implementation in youth sport.
... The following fit indices were used to indicate model-data fit: comparative fit index (CFI; [94]), non-normed fit index (NNFI; [95]), root mean square error of approximation (RMSEA; [96]), standardized root mean square residual (SRMR; [97]), and Akaike information criterion (AIC; [98]). The chi-square (χ 2 ) test of model fit was reported, however due to the hypersensitivity of this statistic (e.g., to sample size), significance-level was not used to indicate model fit [34,70]. ...
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Compassion towards oneself and towards others has been associated with positive psychological outcomes, however, research is limited by the availability of valid psychometric measures, particularly in languages other than English. The current study translated (English to French) and validated the following measures: the Compassionate Engagement and Action Scales (CEAS), assessing self-compassion (CEAS-SC), compassion to others (CEAS-TO), and compassion from others (CEAS-FROM); the Compassion Scale (CS); and the Sussex-Oxford Compassion Scales for Self (SOCS-S) and Others (SOCS-O). French-speaking participants were recruited online (N = 384) and completed the translated measures as well as questionnaires assessing self-compassion, depression, anxiety, stress, insecure attachment, mindfulness, and well-being. Confirmatory Factor Analysis supports the original factor structures proposed for the CEAS-FROM (two-factor hierarchical), CS (four-factor hierarchical), SOCS-S and SOCS-O (five-factor hierarchical), with alternate factor structures proposed for CEAS-SC (three-factor) and CEAS-TO (two-factor). Results showed good internal consistency and convergent validity for all scales, supporting the use of total scores for the translated measures.
... The CMIN/DF value of 1.311, which is less than 3, suggests a good fit for the model. Furthermore, the Comparative Fit Index (Hu and Bentler, 1999). Which provide a foundation for further construct validation and analysis of the hypothesized model. ...
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Amidst a significant uptick in organic product consumption driving the growth of organic agriculture, formulating policies to promote this method necessitates a thorough grasp of the factors influencing farmers' decisions to embrace organic cultivation. This study aims to investigate the determinants of farmers' choices to shift toward green agriculture. A sample of 150 rural paddy farmers was selected from Puttalam district using a multistage sampling technique, and data were collected through face-to-face interviews using a structured questionnaire. Seven key determinants have been discerned as critical contributors to this paradigm shift, such as Health Enhancement, Environmental Protection, Attitude, Economic Profitability, Knowledge of organic farming, Perceived Risk, and Government Support. In light of this, a conceptual model with seventeen hypotheses was created. Structural Equation Model (SEM) analysis was conducted using the Statistical Package for the Social Science (SPSS) and Analysis of Moment Structure (AMOS) to identify the direct, indirect, and mediating effects among the relevant variables. The estimated model revealed strong direct effects of economic profitability and perceived risk on organic farming adoption behavior, while government support had an indirect effect. Moreover, health enhancement demonstrated SLJM Vol a significant direct effect on attitude, and knowledge emerged as a strong predictor with both significant direct and indirect effects on the dependent variable. The hypotheses concerning mediated pathways were also supported with partial and full mediators. These findings provide crucial insights for policymakers, guiding the development of appropriate policies and the implementation of sustainable organic farming practices among paddy farmers.
... The CMIN/DF value of 1.311, which is less than 3, suggests a good fit for the model. Furthermore, the Comparative Fit Index (Hu and Bentler, 1999). Which provide a foundation for further construct validation and analysis of the hypothesized model. ...
Article
Full-text available
Amidst a significant uptick in organic product consumption driving the growth of organic agriculture, formulating policies to promote this method necessitates a thorough grasp of the factors influencing farmers' decisions to embrace organic cultivation. This study aims to investigate the determinants of farmers' choices to shift toward green agriculture. A sample of 150 rural paddy farmers was selected from Puttalam district using a multistage sampling technique, and data were collected through face-to-face interviews using a structured questionnaire. Seven key determinants have been discerned as critical contributors to this paradigm shift, such as Health Enhancement, Environmental Protection, Attitude, Economic Profitability, Knowledge of organic farming, Perceived Risk, and Government Support. In light of this, a conceptual model with seventeen hypotheses was created. Structural Equation Model (SEM) analysis was conducted using the Statistical Package for the Social Science (SPSS) and Analysis of Moment Structure (AMOS) to identify the direct, indirect, and mediating effects among the relevant variables. The estimated model revealed strong direct effects of economic profitability and perceived risk on organic farming adoption behavior, while government support had an indirect effect. Moreover, health enhancement demonstrated SLJM Vol a significant direct effect on attitude, and knowledge emerged as a strong predictor with both significant direct and indirect effects on the dependent variable. The hypotheses concerning mediated pathways were also supported with partial and full mediators. These findings provide crucial insights for policymakers, guiding the development of appropriate policies and the implementation of sustainable organic farming practices among paddy farmers.
... Model fit was evaluated using χ 2 , the root mean square error of approximation (RMSEA), the comparative fit index (CFI), and the standardized root mean square residual (SRMR). Hu and Bentler's (1999) cutoff values of < 0.06 on the RMSEA, Content courtesy of Springer Nature, terms of use apply. Rights reserved. ...
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This study examined the perceived preparedness of educators working in Title 1 schools to address the mental health needs of students. Data were gathered from educators (defined as teachers and other school personnel; N = 299) employed by eight Title 1 public schools within one district in Florida, most of whom were K-5 teachers (n = 199). Participants completed measures of perceived role breadth (i.e., the degree to which they believe that attending to mental health needs is part of their role as an educator), self-efficacy in addressing student mental health needs, and attitudes toward trauma-informed care principles and ideals. Results showed that participants had a relatively high average score on the role breadth measure [M = 4.31 on a scale from 1 (low) to 5 (high)], indicating that they believe their role includes responsibility not only for student learning but also for attending to the mental health of students. Scores on the self-efficacy measure showed a moderate level of confidence in addressing the mental health needs of students [M = 3.08 on a scale from 1 (low) to 4 (high)], although there was variability in mean levels of confidence across different types of tasks. In terms of attitudes toward trauma-informed care, participants showed moderately positive attitudes on the ARTIC-10 [M = 5.05 on a scale from 1 (low) to 7 (high)]. Structural equation modeling was used to examine the relation between the outcome variable of attitudes toward trauma-informed care and the following predictor variables: school, role (teacher vs. non-teacher), role breadth, and self-efficacy. Results showed that role breadth and self-efficacy were significant and positive predictors (p < 0.01) of attitudes toward trauma-informed care. Implications for school-level trauma initiatives are discussed.
... Indicators of the degree of goodness of fit of the model Model Adjustment (Hu & Bentler, 1999;Manzano & Zamora, 2010). Prepared by the author based on the survey data processed with the SPSS see. 25 (IBM, 2017). ...
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The objective of the study was to test the empirical sustainability of the theoretical model for men and women on the relationship between the organizational and contextual support perceived in high school students in Mexico, on the interest in studying professions in STEM disciplines. 249 men and 235 women from 14 educational establishments participated, distributed in the six semesters that make up upper secondary education. The results indicate statistical differences between men and women only with respect to interest in studying STEM professions, being higher in men. The overall model presents acceptable fit indicators. The measurement invariance for the models (males and females) was estimated, with the female model being the one with the best fit to the proposed theoretical relationship. It is concluded that there is a need for high school organizations to generate career models and strategies to promote the interest of women in STEM disciplines
... The fit of the model was evaluated with multiple indicators: the comparative fit index (CFI), the Tucker-Lewis Index (TLI), and the root mean square error of approximation (RMSEA). Based on Hu and Bentler (1999), we considered CFI and TLI values greater than 0.90 as indicative of acceptable fit and values greater than 0.95 as indicative of good fit. As for RMSEA, values less than 0.06 were considered indicative of good fit, while RSMEA values between 0.06 and 0.08 were considered an adequate fit. ...
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Introduction The current study aimed to examine the longitudinal associations among basic psychological need satisfaction at school (BPNSS), self‐esteem, and suicidal ideation (SI), including whether self‐esteem functioned as a mediator of the relations between BPNSS and SI at the within‐person level after disentangling between‐ and within‐person associations encompassing middle childhood to early adolescence. Methods A total of 650 Chinese students (53.54% boys, Mage = 9.95, SD = 0.75 at Time 1) completed measures on four occasions across 1.5 years, using 6‐month intervals. Random intercept cross‐lagged panel models were applied to disaggregate between‐ and within‐person effects, thus providing greater confidence in elucidating the causal relations among study variables. Results The results showed that at the within‐person level: (a) BPNSS negatively predicted SI; (b) BPNSS positively predicted self‐esteem; (c) Self‐esteem negatively predicted SI; and (d) BPNSS indirectly predicted SI via self‐esteem. Conclusion These findings advanced the literature by demonstrating longitudinal associations among BPNSS, self‐esteem, and SI at the within‐person level, and highlighting the significance of distinguishing between‐ and within‐person effects in developing prevention and intervention programs aimed at reducing SI over time from middle childhood to early adolescence.
... In this study, the sample size is 548, which qualifies as a large sample. Therefore, a higher Chi-Square value is permissible (Hu and Bentler 1999). The Goodness-of-Fit Index (GFI) gauges agreement between sample data and the theoretical model, with values between 0 and 1, where larger values indicate better fit. ...
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The relationship between tree radial growth and climate factors is intricate and affected by various factors related to global climate change. Chinese fir [Cunninghamia lanceolata (Lamb.) Hook.)] is a crucial fast-growing timber species in subtropical China. Its productivity, primarily determined by radial growth, has been influenced by climate change. Our study aimed to explore growth patterns and elucidate the correlation between radial growth and climate factors in Chinese fir plantations across four distinct climatic regions. Through correlation analysis and structural equation model (SEM), we explained the relationship between radial growth trends and climate factors. The results showed that monthly radial growth differed among the four production areas, with an “unimodal curve” in Fujian and Jiangxi, a “bimodal curve” in Hunan, and a “trimodal curve” in Yunnan. Radial growth was positively correlated with temperature and precipitation. The dryness index had a weak correlation with radial growth in Fujian and Jiangxi but a significant positive correlation in Hunan and Yunnan. SEM analyses indicated path coefficients for biological factors influencing radial growth (0.352 in Fujian, 0.616 in Jiangxi, 0.595 in Hunan, and 0.528 in Yunnan) and climate factors ( -0.003 in Fujian, 0.150 in Jiangxi, 0.265 in Hunan, and 0.005 in Yunnan). The factors affecting radial growth were the least in Fujian and the most in Yunnan, indicating greater climate sensitivity in the radial growth of Chinese fir from coastal to inland areas. These results enhance our understanding of climate impacts on forest productivity and offer a scientific basis for sustainably managing subtropical plantations under climate change.
... The first theme identified was the commitment to safety and the culture of construc- As presented in Table 4, the results demonstrated no multi-collinearity concerns, as all the Variance Inflation Factor (VIF) values were below 3, ranging from 1.000 to 2.765 [89]. Furthermore, the structural framework exhibited a good fit, as the Standardized Root Mean Squared residual (SRMR) values were less than 0.08 [90]. The R 2 values revealed that the structural model explained 57.1% and 67.3% of the variation in safety performance and safety culture, respectively. ...
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The Ghanaian construction industry faces challenges in managing safety, especially for small and medium-sized enterprises (SMEs) that need more resources. This research addressed the critical need for a positive safety culture framework specifically designed for SMEs in Ghana. The study adopts the Delphi research approach, which involves a series of questionnaire ‘rounds’ to gather and refine information and develop a collaborative safety culture framework with SME stakeholders. The study employed a mixed-methods strategy, harnessing quantitative and qualitative data to meet the research goals. The critical components of the developed framework included safety commitment, adaptability, information, awareness, culture, and performance. The research offered evidence-based recommendations for effective positive safety practices across Ghana’s SMEs by analysing the relationship between these interventions and safety outcomes. Applying the framework should reduce workplace accidents and foster a positive safety culture that aligns with international best practices.
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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.
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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.
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Cross‐cultural adaptation and validation of measures are necessary to provide evidence‐based educational intervention services among children with autism spectrum disorder (ASD) across countries. Language plays an integral role in the cross‐cultural adaptation and validation process of measures. Currently, there are limited validated tools in Chinese available to assess special education teachers' skills in functional behavior assessments and interventions in Mainland China to effectively support students with ASD. This study aimed to validate a Chinese version of the Skills and Needs Inventories in Functional Behavior Assessments and Interventions (SNI‐FBAI‐CN) in mainland China. The SNI‐FBAI, originally developed and validated in Singapore, in the English language, was translated, culturally adapted, and then administered to 239 special education teachers in two schools for children with ASD in China. Results show that the SNI‐FBAI‐CN has a three‐factor structure (i.e., skills in behavioral assessment, skills in behavioral interventions, and needs for training) that fits the data well, with good reliability for the overall scale, as well as the three subscales. Partial measurement invariance was established between the Chinese and the original Singapore samples, providing additional construct validity evidence for this tool. Limitations of this study and directions for future research are discussed.
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Given much attention associated with learner engagement in second language (L2) writing, an increasing body of studies has reported that learner engagement with feedback is a critical construct to enhance English as a foreign language (EFL) learners’ writing achievement. However, little research has been conducted to explore the predictive effect of grit and examine the mediating role of learner engagement with feedback in the relationship between grit and English writing achievement (EWA) in the underlying mechanism of L2 writing. Therefore, the current study aims to address these under-researched issues by investigating a mediation model of L2 grit, learner engagement with feedback, and EWA among English major students. The findings demonstrated that: (1) perseverance-of-effort variation in L2 grit predicted variance in learner affective, cognitive, and behavioral engagement, while the consistency of interest exerted a great influence on cognitive engagement; and (2) affective and behavioral engagement mediated the relationship between L2 grit and EWA. The results have notable pedagogical and practical implications for L2 teaching and learning.
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Persuasive testimonials are common in commercial, nonprofit, and public health contexts. They pose challenges to existing theories of narrative persuasion because they are typically both narrative and overtly persuasive. Prior research has suggested testimonials may be effective with counter-attitudinal recipients by decreasing negative affective responses and increasing meaningful affect. Often, however, testimonials may address behaviors that are anxiety provoking rather than counter-attitudinal; prior research provides little theoretical or empirical guidance concerning message influence in the face of such anxiety. An experiment comparing a testimonial versus a non-narrative message advocating end-of-life conversations found that the testimonial message increased behavioral intentions via meaningful affect and self-efficacy. The testimonial did not decrease anxiety, and there was no differential impact on high versus low anxiety recipients. The authors conclude that a eudaimonic testimonial may serve as a motivator of behavior regardless of anxiety concerning the message topic, as well as a means of increasing self-efficacy.
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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)
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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)
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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.
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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.
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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)
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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)
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[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)
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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)
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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>
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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.
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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.
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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.
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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)
Article
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)
Article
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)
Article
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.
Article
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.
Article
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.
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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.
Article
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
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.
Article
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.