This article shows how interfactor correlation is affected by error correlations. Theoretical and practical justifications for error correlations are given, and a new equivalence class of models is presented to explain the relationship between interfactor correlation and error correlations. The class allows simple, parsimonious modeling of error…

Bayesian approaches to modeling are receiving an increasing amount of attention in the areas of model construction and estimation in factor analysis, structural equation modeling (SEM), and related latent variable models. However, model diagnostics and model criticism remain relatively understudied aspects of Bayesian SEM. This article describes…

An interval estimation procedure for proportion of explained observed variance in latent curve analysis is discussed, which can be used as an aid in the process of choosing between linear and nonlinear models. The method allows obtaining confidence intervals for the R[squared] indexes associated with repeatedly followed measures in longitudinal…

We highlight critical conceptual and statistical issues and how to resolve them in conducting Satorra-Bentler (SB) scaled difference chi-square tests. Concerning the original (Satorra & Bentler, 2001) and new (Satorra & Bentler, 2010) scaled difference tests, a fundamental difference exists in how to compute properly a model's scaling correction…

Linear factor analysis (FA) models can be reliably tested using test statistics based on residual covariances. We show that the same statistics can be used to reliably test the fit of item response theory (IRT) models for ordinal data (under some conditions). Hence, the fit of an FA model and of an IRT model to the same data set can now be…

In multilevel structural equation modeling, the "standard" approach to evaluating the goodness of model fit has a potential limitation in detecting the lack of fit at the higher level. Level-specific model fit evaluation can address this limitation and is more informative in locating the source of lack of model fit. We proposed level-specific test…

Assessing the correctness of a structural equation model is essential to avoid drawing incorrect conclusions from empirical research. In the past, the chi-square test was recommended for assessing the correctness of the model but this test has been criticized because of its sensitivity to sample size. As a reaction, an abundance of fit indexes…

Two-level data sets are frequently encountered in social and behavioral science research. They arise when observations are drawn from a known hierarchical structure, such as when individuals are randomly drawn from groups that are randomly drawn from a target population. Although 2-level data analysis in the context of structural equation modeling…

Traditional estimators of fit measures based on the noncentral chi-square distribution (root mean square error of approximation [RMSEA], Steiger's [gamma], etc.) tend to overreject acceptable models when the sample size is small. To handle this problem, it is proposed to employ Bartlett's (1950), Yuan's (2005), or Swain's (1975) correction of the…

Most personality tests are made up of Likert-type items and analyzed by means of factor analysis (FA). In this type of application, the fit of the model at the level of individual respondents is almost never assessed. This article proposes procedures for assessing individual fit (scalability). The procedures are intended for the analysis of…

Exploratory factor analysis (EFA) is a frequently used multivariate analysis technique in statistics. Jennrich and Sampson (1966) solved a significant EFA factor loading matrix rotation problem by deriving the direct Quartimin rotation. Jennrich was also the first to develop standard errors for rotated solutions, although these have still not made…

A structural equation modeling based method is outlined that accomplishes interval estimation of individual optimal scores resulting from multiple-component measuring instruments evaluating single underlying latent dimensions. The procedure capitalizes on the linear combination of a prespecified set of measures that is associated with maximal…

Amos 5.0 (Arbuckle, 2003) permits exploratory specification searches for the best theoretical model given an initial model using the following fit function criteria: chi-square (C), chi-square--df (C--df), Akaike Information Criteria (AIC), Browne-Cudeck criterion (BCC), Bayes Information Criterion (BIC) , chi-square divided by the degrees of…

The goals of this article are twofold: (a) briefly highlight the merits of residual centering for representing interaction and powered terms in standard regression contexts (e.g., Lance, 1988), and (b) extend the residual centering procedure to represent latent variable interactions. The proposed method for representing latent variable…

A bias-corrected estimator of noncentrality parameters of covariance structure models is discussed. The approach represents an application of the bootstrap methodology for purposes of bias correction, and utilizes the relation between average of resample conventional noncentrality parameter estimates and their sample counterpart. The…