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 G...

Cutoff criteria for fit indexes in covariance structure analysis : Conventional criteria versus new alternatives

In this article, we provide guidance for substantive researchers on the use of structural equation modeling in practice for theory testing and development. We present a comprehensive, two-step modeling approach that employs a series of nested models and sequential chi-square difference tests. We discuss the comparative advantages of this approach over a one-step approach. Considerations in specification, assessment of fit, and respecification of measurement models using confirmatory factor analysis are reviewed. As background to the two-step approach, the distinction between exploratory and confirmatory analysis, the distinction between complementary approaches for theory testing versus predictive application, and some developments in estimation methods also are discussed.

/pdf/structural-equation-modeling-in-practice-a-review-and-1ue2omj492.pdf

Structural equation modeling in practice: a review and recommended two-step approach

This study evaluated the sensitivity of maximum likelihood (ML)-, generalized least squares (GLS)-, and asymptotic distribution-free (ADF)-based fit indices to model misspecification, under conditions that varied sample size and distribution. The effect of violating assumptions of asymptotic robustness theory also was examined. Standardized root-mean-square residual (SRMR) was the most sensitive index to models with misspecified factor covariance(s), and Tucker-Lewis Index (1973; TLI), Bollen's fit index (1989; BL89), relative noncentrality index (RNI), comparative fit index (CFI), and the MLand GLS-based gamma hat, McDonald's centrality index (1989; Me), and root-mean-square error of approximation (RMSEA) were the most sensitive indices to models with misspecified factor loadings. With ML and GLS methods, we recommend the use of SRMR, supplemented by TLI, BL89, RNI, CFI, gamma hat, Me, or RMSEA (TLI, Me, and RMSEA are less preferable at small sample sizes). With the ADF method, we recommend the use of SRMR, supplemented by TLI, BL89, RNI, or CFI. Finally, most of the ML-based fit indices outperformed those obtained from GLS and ADF and are preferable for evaluating model fit.

Fit indices in covariance structure modeling : Sensitivity to underparameterized model misspecification

Practical problems that are frequently encountered in applications of covariance structure analysis are discussed and solutions are suggested. Conceptual, statistical, and practical requirements fo...

Practical Issues in Structural Modeling

We provide a comprehensive and user-friendly compendium of standards for the use and interpretation of structural equation models (SEMs). To both read about and do research that employs SEMs, it is necessary to master the art and science of the statistical procedures underpinning SEMs in an integrative way with the substantive concepts, theories, and hypotheses that researchers desire to examine. Our aim is to remove some of the mystery and uncertainty of the use of SEMs, while conveying the spirit of their possibilities.

Specification, evaluation, and interpretation of structural equation models

This study was designed to gain more insight in the different ways in which work and family roles can benefit each other. Both qualitative (N=25) and quantitative (N=352) results obtained in a financial service organization supported the distinction between energy-based, time-based, behavioral, and psychological work-family facilitation, in addition to different types of work-family conflict that were identified in previous research. As expected, facilitation contributed substantially and differentially to the prediction of work and nonwork outcomes, over and above the effects of conflict. As predicted, women experienced higher levels of facilitation than men did. Furthermore, results indicate that examining facilitation, in addition to conflict, is especially important to predict the work and home life experiences of women.

How work and family can facilitate each other: Distinct types of work-family facilitation and outcomes for women and men.

In the present longitudinal study, early adopted children (N = 160) were followed from infancy to adolescence to assess the influence of previous and concurrent factors on the children's social development. This study allowed for more conclusive evidence of the influence of early and concurrent rearing experiences and temperament on adolescents' social development, independent of shared genetic factors between children and parents. Results showed that social development and temperament were stable over time and that both previous and current parental sensitivity were important in predicting social development in adolescence. Quality of the early parent-child relationship was indirectly associated with social development in adolescence through the influence on social development in middle childhood. Maternal sensitivity in middle childhood and in adolescence partly buffered the negative effects of difficult temperament on social development in adolescence. Adaptation emerged as the product of both developmental history and current circumstances.

https://faculty.buffalostate.edu/hennesda/attachment/temperament%20and%20attachment%20in%20early%20adoption.pdf

Social development from infancy to adolescence: longitudinal and concurrent factors in an adoption sample.

This study is the first to address the need for mental health Care (MHC) and the patterns of utilization of MHC services among Unaccompanied Refugee Minors (URM). Information concerning the well being, mental health need, and utilization of services of URM was collected from three informants, the minors themselves (n = 920), their legal guardians (n = 557), and their teachers (n = 496). The well-being, need and utilization of MHC services of URM was compared with those of a representative Dutch adolescent sample (n = 1059). The findings of this study indicated that URM that report a mental health care need (57.8%) also report higher levels of emotional distress than Dutch adolescents who report a similar need for MHC (8.2%). In addition, guardians and teachers detect emotional distress and mental health care needs in only a small percentage (30%) of URM. The referral of URM to mental health care services does not appear to be driven by the reported needs of the URM, but by the need and emotional distress as observed and perceived by guardians. This resulted in the fact that 48.7% of the URM total sample reported that their need for mental health care was unmet.

/pdf/factors-associated-with-mental-health-service-need-and-52hbvna60b.pdf

Factors associated with mental health service need and utilization among unaccompanied refugee adolescents

Factor analysis for nonnormally distributed variables is discussed in this paper. The main difference between our approach and more traditional approaches is that not only second order cross-products (like covariances) are utilized, but also higher order cross-products. It turns out that under some conditions the parameters (factor loadings) can be uniquely determined. Two estimation procedures will be discussed. One method gives Best Generalized Least Squares (BGLS) estimates, but is computationally very heavy, in particular for large data sets. The other method is a least squares method which is computationally less heavy. In one example the two methods will be compared by using the bootstrap method. In another example real life data are analyzed.

Factor analysis for non-normal variables

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.

Ab Mooijaart

Papers

How work and family can facilitate each other: Distinct types of work-family facilitation and outcomes for women and men.

Social development from infancy to adolescence: longitudinal and concurrent factors in an adoption sample.

Factors associated with mental health service need and utilization among unaccompanied refugee adolescents

Factor analysis for non-normal variables

Robustness of normal theory statistics in structural equation models