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Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review

Taylor & Francis
The Journal of Educational Research
Authors:
James B. Schreiber at Duquesne University
James B. Schreiber
Amaury Nora at University of Texas at San Antonio
Amaury Nora
Frances K. Stage at New York University
Frances K. Stage
Elizabeth A. Barlow
Elizabeth A. Barlow
Elizabeth A. Barlow
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Abstract

The authors provide a basic set of guidelines and recommendations for information that should be included in any manuscript that has confirmatory factor analysis or structural equation modeling as the primary statistical analysis technique. The authors provide an introduction to both techniques, along with sample analyses, recommendations for reporting, evaluation of articles in The Journal of Educational Research using these techniques, and concluding remarks.
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Reporting Structural Equation Modeling and Confirmatory Factor Analysis Results: A Review
Schreiber, James B;Nora, Amaury;Stage, Frances K;Barlow, Elizabeth A;King, Jamie
The Journal of Educational Research; Jul/Aug 2006; 99, 6; ProQuest Central
pg. 323
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
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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). ...
De-mystifying the Influence of PhET Simulation on Engagement, Satisfaction, and Academic Achievement of Bhutanese Students in the Physics Classroom
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  • Jun 2024
  • J Sci Educ Tech
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.
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... Kline (2016) recommends including model chi-square statistic, RMSEA, CFI, and the SRMR. Schreiber et al. (2006) recommend TLI, CFI, and RMSEA for one-time analyses (which is the case in this research). Adapted from: Schreiber et al. (2006) The main source for the strict cutoff criteria are Hu and Bentler (1999). ...
... Schreiber et al. (2006) recommend TLI, CFI, and RMSEA for one-time analyses (which is the case in this research). Adapted from: Schreiber et al. (2006) The main source for the strict cutoff criteria are Hu and Bentler (1999). They say that CFI and TLI values should be 'close to .95 or greater' . ...
THE ROLE OF SOCIAL FACTORS IN THE ACCEPTANCE OF ARTIFICIAL INTELLIGENCE-BASED SERVICES: THE EXAMPLE OF THE BANKING SECTOR OF BOSNIA AND HERZEGOVINA
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In times when AI's development and research is moving at an unprecedented speed, this paper explores its role in retail banking. The results presented are part of a wider research of market readiness and AI acceptance, especially in developing economies. The research was conducted in Bosnia and Herzegovina (B&H). The quantitative portion consisted of a survey completed by 671 respondents. This paper focuses on the influence of social factors (perceived humanness, perceived social interactivity, and perceived social presence) on the attitudes towards-and subsequently acceptance of-AI-based services. Chatbots, specifically ChatGPT-4, were the technology the research focused on. The results indicate that perceived humanness and perceived social interactivity have a positive effect on attitudes-and acceptance-of AI-based services. This research could not prove that there is a positive relationship between social presence and attitudes towards AI-based services. The positive relationship between attitude and acceptance was proven as well.
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... According to the results of CFA (Table 1), the factor loadings of all measurement tools used in the study were above the acceptable level (Kline, 2023;Schreiber et al., 2006). Cronbach's alpha results were very positive (α ≥ .70) ...
From Leisure to Leadership: Promoting Entrepreneurial Spirit in Turkish Women
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This study explores the influence of leisure involvement on the development of entrepreneurial orientation among Turkish women. It addresses a significant gap in the literature by examining how leisure activities can predict entrepreneurial traits, particularly within a cultural context where gender norms heavily influence women's activities and aspirations. The research involved 405 women aged between 18-60. Data were collected using survey method. Confirmatory Factor Analysis (CFA), Cronbach's alpha, composite reliability analysis, and regression analysis were employed to validate the constructs and test the hypotheses. Findings indicate that leisure involvement positively impacts risk-taking, innovativeness, proactiveness, and overall entrepreneurial orientation among Turkish women. These results highlight the potential of leisure activities to foster entrepreneurial traits, contributing to personal and economic development. The study underscores the importance of considering leisure involvement in strategies aimed at enhancing women's entrepreneurial spirit. This study uniquely integrates insights from leisure studies and entrepreneurship, offering a novel perspective on how leisure involvement can predict entrepreneurial orientation among women in Turkey. It provides empirical evidence supporting the role of leisure activities in promoting entrepreneurial traits, filling a critical gap in the literature on women's empowerment and gender equality.
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... According to the results of CFA (Table 1), the factor loadings of all measurement tools used in the study were above the acceptable level (Kline, 2023;Schreiber et al., 2006). ...
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  • Jun 2024
This study examines the relationship between leisure crafting and life satisfaction among Muslim young adults, focusing on the mediating role of Islamic well-being. While leisure crafting's benefits for psychological well-being are known, its intersection with spiritual well-being in Islamic contexts is underexplored. The study involved 328 participants aged 18-24 from Turkey. Data were collected through online and face-to-face surveys. Confirmatory factor analysis, reliability analysis, and multiple regression were used. Results indicated significant positive effects of leisure crafting on life satisfaction and Islamic well-being. Islamic well-being was found to mediate the relationship between leisure crafting and life satisfaction, highlighting the importance of integrating spiritual dimensions into leisure activities. The study highlights the importance of integrating spiritual dimensions into leisure activities for enhancing life satisfaction. It provides insights for designing culturally and spiritually sensitive leisure programs to promote overall well-being in Islamic contexts.
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... Confirmatory factor analysis (CFA) was conducted for assessing construct validity by using the lavaan and semPlot packages in R. Standardized factor loadings between 0.5 and 0.95 are considered ideal for fit optimization [24]. Model fit was assessed using five fit indices: a χ2 value to degrees of freedom ratio (CMIN/DF) of < 3, standardized root-mean-square residual (SRMR) of < 0.08, root-mean-square error of approximation (RMSEA) of < 0.06, Tucker-Lewis index (TLI) of > 0.95, and comparative fit index (CFI) of > 0.95 [25]. Convergent validity was confirmed by an average variance extracted (AVE) ≥ 0.5 and composite reliability (CR) ≥ 0.6 [24]. ...
Psychometric and structural properties of the traditional Chinese version of the sleep condition indicator for patients undergoing hemodialysis
Article
Full-text available
  • Jun 2024
  • SLEEP BREATH
Purpose Insomnia is a prevalent sleep disorder among patients undergoing hemodialysis for chronic kidney disease. This study aimed to translate the sleep condition indicator (SCI), an insomnia screening tool based on the Diagnostic and Statistical Manual of Mental Disorders, Fifth Edition (DSM-5), into a traditional Chinese version (SCI-TC) and evaluate the reliability and validity of this version for patients undergoing hemodialysis. Methods This cross-sectional study conducted from November 2022 to June 2023 involved 200 patients on hemodialysis (mean age, 65.56 years; 61.5% men). Participants completed a series of questionnaires, with insomnia diagnosed according to DSM-5 criteria as the gold standard. A receiver operating characteristic (ROC) curve analysis was conducted to examine the sensitivity and specificity of the SCI-TC. Results According to the DSM-5 criteria, 38% of the participants had insomnia. Cronbach’s alpha for the SCI-TC was 0.92. The SCI-TC exhibited a good fit as a two-factor model, and its scores were significantly associated with those of the traditional Chinese versions of the Insomnia Severity Index, Patient Health Questionnaire-9, Generalized Anxiety Disorder-7, EuroQol 5-Dimensions scale, and EuroQol Visual Analogue Scale (r = − 0.94, − 0.53, − 0.38, 0.27, and 0.30, respectively; all p < 0.05). The ROC curve analysis revealed an optimal cutoff of 16 points, with the sensitivity, specificity, and area under curve of 88.2%, 84.7%, and 0.91(95% confidence interval, 0.87–0.95), respectively. Conclusion The SCI-TC demonstrates robust reliability and validity in detecting insomnia among patients undergoing hemodialysis. These findings suggest that health-care providers should considering using the SCI as an easy-to-use tool for the timely detection of insomnia in this population.
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... Subsequently, the path model was tested using the lavaan package in R, employing the full information maximum likelihood estimation method with robust standard errors to address missing and nonnormal data [36,37]. To evaluate the goodness of fit of the hypothesized path model, we followed the recommendation of Schreiber et al. [38], considering the chi-square test (χ 2 ; p > .05), comparative fit index (CFI; ≥ 0.95), root mean square error of approximation (RMSEA; < 0.06), standardized root mean square residual (SRMR; ≤ 0.08), and Tucker-Lewis index (TLI; ≥ 0.95). ...
Can watching the World Cup make you mentally healthier? Positive associations between involvement in physical activities and flourishing were mediated by psychological need satisfaction
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  • Jun 2024
Background The current understanding of the relationship between physical activity involvement and flourishing, as well as the underlying psychological mechanisms, remains limited. Building upon the basic psychological need theory, this study investigates whether and how engaging in physical activities, either as a spectator (e.g., in sports events such as the World Cup) or a participant, explains individual differences in flourishing. Methods A total of 1201 Hong Kong-based Chinese adults (Mage = 42.90, SD = 11.40; 54% female) completed an anonymous online survey from the quarter-final to final stages of the 2022 FIFA World Cup in December 2022. Results Findings showed that spectator (World Cup) involvement and participant involvement were positively correlated. Moreover, both types of involvements were correlated with flourishing. In addition to the hypothesized positive association with relatedness satisfaction, spectator (World Cup) involvement was also demonstrated significant associations with autonomy and competence satisfaction. Path analysis indicated that associations between physical activities and flourishing were partially mediated by the satisfaction of all three basic psychological needs. Conclusions This study is the first to apply the basic psychological need theory in the context of physical activity and supports its relevance in understanding individual differences in flourishing. Different stakeholders are encouraged to recognize the benefits of both spectator and participant involvements in physical activities, which may help them develop supportive strategies (e.g., physical activities with parents, sports events for spectators and participants, and funding for media/communities) in mental health promotion.
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... 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). ...
Validity of the Expanded Levenson Self-Report Psychopathy (E-LSRP) in a Brazilian Sample: Factor Structure, Construct Validity, and Associations with the Brazilian Jeitinho
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  • DEVIANT BEHAV
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.
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... In this research, the focus was on fit criteria such as the Chi-Square (X2/Df), Goodness-of-Fit Index (GFI), Adjusted Goodness-of-Fit Index (AGFI), Comparative Fit Index (CFI), and the Root Mean Square Error of Approximation (RMSEA). After necessary adjustments were made to the statements, Table 3 presents the confirmatory factor analysis's calculated fit indices and their acceptability conditions (Schumacker & Lomax, 2004;Schreiber, Nora, Stage, Barlow & King, 2006). After implementing adjustments to the model, a detailed review of the calculated fit indices for the confirmatory factor analysis has been conducted. ...
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... Confirmatory factor analysis was conducted in order to achieve the objective stated i.e. factor influencing while purchasing as apparels (Schreiber et al., 2006). ...
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Each student expects fantastic stage for study where he can learn numerous new things and satisfy their folks' dreams by getting elevated place that he wanted. Understudies put away cash and 3-4 years to earn a college education for splendid future. When it comes time for the student to choose a career, the majority of options are presented to them, though the selection process may vary for a variety of reasons, including: availability of the course at a particular institute, college, or university, as well as the student's interest in the course. In such a unique climate, understudies are presently cautiously picking their advanced education organization. The paper is an attempt to see the factor influencing students to the factors that influence students for the selection of higher education institutions. The data consists of a sample of 277 student respondents who has taken admission in an educational institute in the recent past. It was found from the study that theory of planned behaviour is the best fit for students in taking admission in higher educational institute, so the marketers need to giving due importance to all the aspects of theory of planned behaviour while making any strategy.
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... The direct and indirect paths between the variables were assessed by the software of AMOS (version 24). For approval of the final model, the goodness of fit indexes of X2/df, RFI, CFI, GFI, IFI, RMSEA, NFI, TLI, and AGFI were checked[42][43][44][45][46]. ...
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This research applied evolving conceptions of learning to tackle the difficult problems of how students' and experts' cognitive structures might be represented and evaluated. A diverse sample of high school students was selected to complete several tasks purporting to measure domain-specific knowledge of the Great Depression period of U.S. history, including prior knowledge, written explanation, similarity ratings, and concept mapping tasks. In this study, the technical characteristics of a method for scoring student concept maps were explored by comparing directly the quality of student maps with expert maps. Results showed that experts' concept maps could be used to score students' concept maps reliably. Further analyses showed that students who judged similarities of pairs of concepts, facts, and events from the Great Depression era in an expert-like manner constructed more correct links for those same pairs in their concept maps. MIMIC (multiple indicators, multiple causes) structural modeling was used to analyze relationships among causal and indicator measures of the construct “cognitive structure.” Two concept-mapping measures (semantic content score, organizational structure score) and two writing task dimensions (content quality and argumentation) were chosen to represent indicators of the construct. The findings provided some evidence to support the theoretical position that domain-specific measures, not general achievement measures, predict performance on construct indicators
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