A central problem in the application of exploratory factor analysis is deciding how many factors to retain ("m"). Although this is inherently a model selection problem, a model selection perspective is rarely adopted for this task. We suggest that Cudeck and Henly's (1991) framework can be applied to guide the selection process.…

The root mean square error of approximation (RMSEA) is a popular fit index in structural equation modeling (SEM). Typically, RMSEA is computed using the normal theory maximum likelihood (ML) fit function. Under nonnormality, the uncorrected sample estimate of the ML RMSEA tends to be inflated. Two robust corrections to the sample ML RMSEA have…

In many psychological questionnaires the need to analyze empirical data raises the fundamental problem of possible fake or fraudulent observations in the data. This aspect is particularly relevant for researchers working on sensitive topics such as, for example, risky sexual behaviors and drug addictions. Our contribution presents a new…

This study investigated the sensitivity of fit indices to model misspecification in within-individual covariance structure, between-individual covariance structure, and marginal mean structure in growth curve models. Five commonly used fit indices were examined, including the likelihood ratio test statistic, root mean square error of…

In this article, we directly question the common practice in growth mixture model (GMM) applications that exclusively rely on the fitting model without covariates for GMM class enumeration. We provide theoretical and simulation evidence to demonstrate that exclusion of covariates from GMM class enumeration could be problematic in many cases. Based…

The comparative format used in ranking and paired comparisons tasks can significantly reduce the impact of uniform response biases typically associated with rating scales. Thurstone's (1927, 1931) model provides a powerful framework for modeling comparative data such as paired comparisons and rankings. Although Thurstonian models are generally…

The logistic person response function (PRF) models the probability of a correct response as a function of the item locations. Reise (2000) proposed to use the slope parameter of the logistic PRF as a person-fit measure. He reformulated the logistic PRF model as a multilevel logistic regression model and estimated the PRF parameters from this…

We apply the Supplemented EM algorithm (Meng & Rubin, 1991) to address a chronic problem with the "two-stage" fitting of covariance structure models in the presence of ignorable missing data: the lack of an asymptotically chi-square distributed goodness-of-fit statistic. We show that the Supplemented EM algorithm provides a…

Evaluating the fit of a structural equation model via bootstrap requires a transformation of the data so that the null hypothesis holds exactly in the sample. For complete data, such a transformation was proposed by Beran and Srivastava (1985) for general covariance structure models and applied to structural equation modeling by Bollen and Stine…

Two recent indices of fit, the Relative Noncentrality Index (RNI) (R. P. McDonald and H. W. Marsh, 1990) and the Comparative Fit Index (P. M. Bentler, 1990), are shown to be algebraically equivalent in most applications, although one condition in which the RNI may be advantageous for model comparison is identified. (SLD)

Studied whether empirical multitrait multioccasion (MTMO) data conform more closely to multiplicative models than to additive models, using four additive models and two versions of the multiplicative Direct Product model. Results based on matrices from previous studies show that both additive and multiplicative models usually fit the same MTMO…

Issues the author has explored in his work on the philosophy of statistics are reviewed. Indeterminacy, the place of empiricism, questions of causation and causality, and explorations of language have preceded the study of objectivity. The relationship between objectivity and multivariate statistics is examined. (SLD)

Procedures are presented for conducting power analyses of tests of overall fit of covariance structure models when null and alternative levels of model fit are specified in terms of values of the GFI or AGFI fit indexes. Reasons the root mean square error of approximation fit index may be preferable are discussed. (SLD)

Proposed a method for extending the Bollen-Stine bootstrap model (K. Bollen and R. Stine, 1992) fit to structural equation models with missing data. Developed a Statistical Analysis System macro program to implement this procedure, and assessed its usefulness in a simulation. The new method yielded model rejection rates close to the nominal 5%…

Used computer simulation methods to examine the sensitivity of model fit criteria to misspecification of the first-level error structure in two-level models of change and to examine the impact of misspecification estimates on the variance parameters, estimates of the fixed effects, and tests of the fixed effects. Discusses problems caused by…