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

Interest in the problem of method biases has a long history in the behavioral sciences. Despite this, a comprehensive summary of the potential sources of method biases and how to control for them does not exist. Therefore, the purpose of this article is to examine the extent to which method biases influence behavioral research results, identify potential sources of method biases, discuss the cognitive processes through which method biases influence responses to measures, evaluate the many different procedural and statistical techniques that can be used to control method biases, and provide recommendations for how to select appropriate procedural and statistical remedies for different types of research settings.

/pdf/common-method-biases-in-behavioral-research-a-critical-53ocysaemj.pdf

Common method biases in behavioral research: a critical review of the literature and recommended remedies.

Hypotheses involving mediation are common in the behavioral sciences. Mediation exists when a predictor affects a dependent variable indirectly through at least one intervening variable, or mediator. Methods to assess mediation involving multiple simultaneous mediators have received little attention in the methodological literature despite a clear need. We provide an overview of simple and multiple mediation and explore three approaches that can be used to investigate indirect processes, as well as methods for contrasting two or more mediators within a single model. We present an illustrative example, assessing and contrasting potential mediators of the relationship between the helpfulness of socialization agents and job satisfaction. We also provide SAS and SPSS macros, as well as Mplus and LISREL syntax, to facilitate the use of these methods in applications.

https://link.springer.com/content/pdf/10.3758/BRM.40.3.879.pdf

Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models

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

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

Model Notation, Covariances, and Path Analysis. Causality and Causal Models. Structural Equation Models with Observed Variables. The Consequences of Measurement Error. Measurement Models: The Relation Between Latent and Observed Variables. Confirmatory Factor Analysis. The General Model, Part I: Latent Variable and Measurement Models Combined. The General Model, Part II: Extensions. Appendices. Distribution Theory. References. Index.

Structural Equations with Latent Variables

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

Structural Equations with Latent Variables.

The applicability of 5 conventional guidelines for construct measurement is critically examined: (a) Construct indicators should be internally consistent for valid measures, (b) there are optimal magnitudes of correlations between items, (c) the validity of measures depends on the adequacy with which a specified domain is sampled, (d) within-construct correlations must be greater than between-construct correlations, and (e) linear composites of indicators can replace latent variables. A structural equation perspective is used, showing that without an explicit measurement model relating indicators to latent variables and measurement errors, none of these conventional beliefs hold without qualifications. Moreover, a "causal" indicator model is presented that sometimes better corresponds to the relation of indicators to a construct than does the classical test theory "effect" indicator model.

Conventional wisdom on measurement: A structural equation perspective.

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 thr...

Kenneth A. Bollen

Papers

Structural Equations with Latent Variables

Testing Structural Equation Models

Structural Equations with Latent Variables.

Conventional wisdom on measurement: A structural equation perspective.

A New Incremental Fit Index for General Structural Equation Models