A common method of checking person-fit in Bayesian item response theory (IRT) is the posterior-predictive (PP) method. In recent years, more powerful approaches have been proposed that are based on resampling methods using the popular L*[subscript z] statistic. There has also been proposed a new Bayesian model checking method based on pivotal…

This paper aims to advocate for a balanced approach to model fit evaluation in structural equation modeling (SEM). The ongoing debate surrounding chi-square test statistics and fit indices has been characterized by ambiguity and controversy. Despite the acknowledged limitations of relying solely on the chi-square test, its careful application can…

The purpose of this study was to evaluate the degree of classification quality in the basic latent class model when covariates are either included or are not included in the model. To accomplish this task, Monte Carlo simulations were conducted in which the results of models with and without a covariate were compared. Based on these simulations,…

Factor mixture modeling (FMM) has been increasingly used to investigate unobserved population heterogeneity. This study examined the issue of covariate effects with FMM in the context of measurement invariance testing. Specifically, the impact of excluding and misspecifying covariate effects on measurement invariance testing and class enumeration…

The present paper introduces a general multidimensional model to measure individual differences in learning within a single administration of a test. Learning is assumed to result from practicing the operations involved in solving the items. The model accounts for the possibility that the ability to learn may manifest differently for correct and…

Prior studies investigating the effects of non-normality in structural equation modeling typically induced non-normality in the indicator variables. This procedure neglects the factor analytic structure of the data, which is defined as the sum of latent variables and errors, so it is unclear whether previous results hold if the source of…

Model fit indices are being increasingly recommended and used to select the number of factors in an exploratory factor analysis. Growing evidence suggests that the recommended cutoff values for common model fit indices are not appropriate for use in an exploratory factor analysis context. A particularly prominent problem in scale evaluation is the…

In exploratory factor analysis, although the researchers decide which items belong to which factors by considering statistical results, the decisions taken sometimes can be subjective in case of having items with similar factor loadings and complex factor structures. The aim of this study was to examine the validity of classifying items into…

The recent popularity of models that capture the dynamic coevolution of both network structure and behavior has driven the need for summary indices to assess the adequacy of these models to reproduce dynamic properties of scientific or practical importance. Whereas there are several existing indices for assessing the ability of the model to…

Using Monte Carlo simulations, this research examined the performance of four missing data methods in SEM under different multivariate distributional conditions. The effects of four independent variables (sample size, missing proportion, distribution shape, and factor loading magnitude) were investigated on six outcome variables: convergence rate,…

Two Monte Carlo simulation studies investigated the effectiveness of the mean adjusted X[superscript 2]/df statistic proposed by Drasgow and colleagues and, because of problems with the method, a new approach for assessing the goodness of fit of an item response theory model was developed. It has been previously recommended that mean adjusted…

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…

The investigation of change in factor structure over time can provide new opportunities for the development of theory in psychology. The method proposed to investigate change in intraindividual factor structure over time is an extension of P-technique factor analysis, in which the P-technique factor model is fit within relatively small windows of…

In research concerning model invariance across populations, researchers have discussed the limitations of the conventional chi-square difference test ([Delta] chi-square test). There have been some research efforts in using goodness-of-fit indexes (i.e., [Delta]goodness-of-fit indexes) for assessing multisample model invariance, and some specific…

The authors examined the robustness of multilevel linear growth curve modeling to misspecification of an autoregressive moving average process. As previous research has shown (J. Ferron, R. Dailey, & Q. Yi, 2002; O. Kwok, S. G. West, & S. B. Green, 2007; S. Sivo, X. Fan, & L. Witta, 2005), estimates of the fixed effects were unbiased, and Type I…