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

Relationship marketing—establishing, developing, and maintaining successful relational exchanges—constitutes a major shift in marketing theory and practice. After conceptualizing relationship marke...

The Commitment-Trust Theory of Relationship Marketing

Structural equation modeling (SEM) is a vast field and widely used by many applied researchers in the social and behavioral sciences. Over the years, many software packages for structural equation modeling have been developed, both free and commercial. However, perhaps the best state-of-the-art software packages in this field are still closed-source and/or commercial. The R package lavaan has been developed to provide applied researchers, teachers, and statisticians, a free, fully open-source, but commercial-quality package for latent variable modeling. This paper explains the aims behind the development of the package, gives an overview of its most important features, and provides some examples to illustrate how lavaan works in practice.

/pdf/lavaan-an-r-package-for-structural-equation-modeling-241rrq51a8.pdf

lavaan: An R Package for Structural Equation Modeling

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

A Monte Carlo study compared 14 methods to test the statistical significance of the intervening variable effect. An intervening variable (mediator) transmits the effect of an independent variable to a dependent variable. The commonly used R. M. Baron and D. A. Kenny (1986) approach has low statistical power. Two methods based on the distribution of the product and 2 difference-in-coefficients methods have the most accurate Type I error rates and greatest statistical power except in 1 important case in which Type I error rates are too high. The best balance of Type I error and statistical power across all cases is the test of the joint significance of the two effects comprising the intervening variable effect.

/pdf/a-comparison-of-methods-to-test-mediation-and-other-21xho8v2xm.pdf

A comparison of methods to test mediation and other intervening variable effects.

Introduction - Kenneth A Bollen and J Scott Long Multifaceted Conceptions of Fit in Structural Equation Models - J S Tanaka Monte Carlo Evaluations of Goodness-of-Fit Indices for Structural Equation Models - David W Gerbing and James C Anderson Some Specification Tests for the Linear Regression Model - J Scott Long and Pravin K Trivedi Bootstrapping Goodness-of-Fit Measures in Structural Equation Models - Kenneth A Bollen and Robert A Stine Alternative Ways of Assessing Model Fit - Michael W Browne and Robert Cudeck Bayesian Model Selection in Structural Equation Models - Adrian E Raftery Power Evaluations in Structural Equation Models - Willem E Saris and Albert Satorra Goodness-of-Fit with Categorical and Other Nonnormal Variables - Bengt O Muthen Some New Covariance Structure Model Improvement Statistics - P M Bentler and Chih-Ping Chou Nonpositive Definite Matrices in Structural Modeling - Werner Wothke Testing Structural Equation Models - Karl G Joreskog

Testing Structural Equation Models

In the presence of heteroscedasticity, ordinary least squares (OLS) estimates are unbiased, but the usual tests of significance are generally inappropriate and their use can lead to incorrect inferences. Tests based on a heteroscedasticity consistent covariance matrix (HCCM), however, are consistent even in the presence of heteroscedasticity of an unknown form. Most applications that use a HCCM appear to rely on the asymptotic version known as HC0. Our Monte Carlo simulations show that HC0 often results in incorrect inferences when N ≤ 250, while three relatively unknown, small sample versions of the HCCM, and especially a version known as HC3, work well even for N's as small as 25. We recommend that: (1) data analysts should correct for heteroscedasticity using a HCCM whenever there is reason to suspect heteroscedasticity; (2) the decision to use HCCM-based tests should not be determined by a screening test for heteroscedasticity; and (3) when N ≤ 250, the HCCM known as HC3 should be used. Since...

https://www.jstor.org/stable/pdfplus/2685594.pdf

Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model

Science is an institution with immense inequality in career attainments. Women and most minorities, as groups, have lower levels of participation, position, productivity, and recognition than do white men. Research in the sociology of science has focused on the degree to which different outcomes have resulted from universalistic and from particularistic processes. In this paper we 1) depict the career attainments of women and minorities in science, 2) consider the meaning and measurement of universalism compared to particularism, 3) analyze the causes of differential attainment with a view to assessing evidence for violations of universalism, 4) propose conditions under which particularism is likely to occur, and 5) consider methodological problems that affect this research.

Scientific Careers: Universalism and Particularism

Tests for Structural Equation Models: Introduction

Advancement in rank is critically important to the career of an academic scientist, and the highly visible nature of the event makes it idealfor studying stratification in science. Concern with universalistic factors in promotion has prompted debates over two issues. First, why do female scientists advance more slowly than male scientists, and why do so few reach the rank offull professor? Second, is promotion driven by the sheer volume of published work as opposed to its quality? Event history analyses clearly indicate that quantity of publications is far more important than various measures of quality of publications in predicting rank advancement; and women are less likely to be promoted than men. About one-half of this sex difference is attributable to differences in levels of variables affecting promotion. Remaining differences are a result of differences in expected timing of promotion to associate professor and to the negative effects of department prestige on promotion to full professor for women.

J. Scott Long

Papers

Testing Structural Equation Models

Using Heteroscedasticity Consistent Standard Errors in the Linear Regression Model

Scientific Careers: Universalism and Particularism

Tests for Structural Equation Models: Introduction

Rank Advancement in Academic Careers: Sex Differences and the Effects of Productivity.