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 article is concerned with measures of fit of a model. Two types of error involved in fitting a model are considered. The first is error of approximation which involves the fit of the model, wi...

Alternative Ways of Assessing Model Fit

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

Comparative fit indexes in structural models

G*Power is a free power analysis program for a variety of statistical tests. We present extensions and improvements of the version introduced by Faul, Erdfelder, Lang, and Buchner (2007) in the domain of correlation and regression analyses. In the new version, we have added procedures to analyze the power of tests based on (1) single-sample tetrachoric correlations, (2) comparisons of dependent correlations, (3) bivariate linear regression, (4) multiple linear regression based on the random predictor model, (5) logistic regression, and (6) Poisson regression. We describe these new features and provide a brief introduction to their scope and handling.

/pdf/statistical-power-analyses-using-g-power-3-1-tests-for-dnxl4mlxpv.pdf

Statistical power analyses using G*Power 3.1: tests for correlation and regression analyses.

Dans les differentes procedures existantes pour l'evaluation et les modifications sequentielles des modeles structuraux, l'auteur s'attache a discuter celle connue sous le terme PMM. Plus generalement, les propositions de KAPLAN (1990) sont critiquees dans le detail

Structural Model Evaluation and Modification: An Interval Estimation Approach.

In a variety of situations in psychological research, it is desirable to be able to make statistical comparisons between correlation coefficients measured on the same individuals. For example, an experimenter may wish to assess whether two predictors correlate equally with a criterion variable. In another situation, the experimenter may wish to test the hypothesis that an entire matrix of correlations has remained stable over time. The present article reviews the literature on such tests, points out some statistics that should be avoided, and presents a variety of techniques that can be used safely with medium to large samples. Several illustrative numerical examples are provided.

Tests for comparing elements of a correlation matrix.

Statistically based tests for the number of common factors

Understanding the limitations of global fit assessment in structural equation modeling

Contents: Preface. Part I: Overview. L.L. Harlow, Significance Testing Introduction and Overview. Part II: The Debate: Against and For Significance Testing. J.Cohen, The Earth Is Round. F.L. Schmidt, J. Hunter, Eight Objections to the Discontinuation of Significance Testing in the Analysis of Research Data. S.A. Mulaik, N.S. Raju, R. Harshman, There Is a Time and Place for Significance Testing. R.P. Abelson, A Retrospective on the Significance Test Ban of 1999 (If There Were No Significance Tests, They Would Be Invented). Part III: Suggested Alternatives to Significance Testing. R.J. Harris, Reforming Significance Testing via Three-Valued Logic. J.S. Rossi, Spontaneous Recovery of Verbal Learning: A Case Study in the Failure of Psychology as a Cumulative Science. J.H. Steiger, R.T. Fouladi, Noncentrality Interval Estimation and the Evaluation of Statistical Models. R.P. McDonald, Goodness of Approximation in the Linear Model. Part IV: A Bayesian Approach to Hypothesis Testing. R.M. Pruzek, An Introduction to Bayesian Inference and Its Application. D. Rindskopf, Testing 'Small,' Not Null, Hypotheses: Classical and Bayesian Approaches. C.S. Reichardt, H.F. Gollob, When Confidence Intervals Should Be Used Instead of Statistical Significance Tests, and Vice Versa. Part V: Philosophy of Science Issues. W.W. Rozeboom, Good Science Is Abductive, Not Hypothetico-Deductive. P.E. Meehl, The Problem Is Epistemology, Not Statistics: Replace Significance Tests by Confidence Intervals and Quantify Accuracy of Risky Numerical Predictions.

James H. Steiger

Papers

Structural Model Evaluation and Modification: An Interval Estimation Approach.

Tests for comparing elements of a correlation matrix.

Statistically based tests for the number of common factors

Understanding the limitations of global fit assessment in structural equation modeling

What if there were no significance tests