The population relationship between coefficient alpha and scale reliability is studied in the widely used setting of unidimensional multicomponent measuring instruments. It is demonstrated that for any set of component loadings on the common factor, regardless of the extent of their inequality, the discrepancy between alpha and reliability can be…

Methods for optimal factor rotation of two-facet loading matrices have recently been proposed. However, the problem of the correct number of factors to retain for rotation of two-facet loading matrices has rarely been addressed in the context of exploratory factor analysis. Most previous studies were based on the observation that two-facet loading…

A procedure for evaluating the average R-squared index for a given set of observed variables in an exploratory factor analysis model is discussed. The method can be used as an effective aid in the process of model choice with respect to the number of factors underlying the interrelationships among studied measures. The approach is developed within…

Simulation studies involving mixture models inevitably aggregate parameter estimates and other output across numerous replications. A primary issue that arises in these methodological investigations is label switching. The current study compares several label switching corrections that are commonly used when dealing with mixture models. A growth…

A widely applicable procedure of examining proximity to unidimensionality for multicomponent measuring instruments with multidimensional structure is discussed. The method is developed within the framework of latent variable modeling and allows one to point and interval estimate an explained variance proportion-based index that may be considered a…

Mediation models have been widely used in many disciplines to better understand the underlying processes between independent and dependent variables. Despite their popularity and importance, the appropriate sample sizes for estimating those models are not well known. Although several approaches (such as Monte Carlo methods) exist, applied…

Multidimensionality and hierarchical data structure are common in assessment data. These design features, if not accounted for, can threaten the validity of the results and inferences generated from factor analysis, a method frequently employed to assess test dimensionality. In this article, we describe and demonstrate the application of the…

This study investigates polytomous item explanatory item response theory models under the multivariate generalized linear mixed modeling framework, using the linear logistic test model approach. Building on the original ideas of the many-facet Rasch model and the linear partial credit model, a polytomous Rasch model is extended to the item…

The purpose of this two-part study is to evaluate methods for multiple group analysis when the comparison group is at the within level with multilevel data, using a multilevel factor mixture model (ML FMM) and a multilevel multiple-indicators multiple-causes (ML MIMIC) model. The performance of these methods was evaluated integrally by a series of…

The frequent practice of overall fit evaluation for latent variable models in educational and behavioral research is reconsidered. It is argued that since overall plausibility does not imply local plausibility and is only necessary for the latter, local misfit should be considered a sufficient condition for model rejection, even in the case of…

This study compares two missing data procedures in the context of ordinal factor analysis models: pairwise deletion (PD; the default setting in Mplus) and multiple imputation (MI). We examine which procedure demonstrates parameter estimates and model fit indices closer to those of complete data. The performance of PD and MI are compared under a…

S-X[superscript 2] is a popular item fit index that is available in commercial software packages such as "flex"MIRT. However, no research has systematically examined the performance of S-X[superscript 2] for detecting item misfit within the context of the multidimensional graded response model (MGRM). The primary goal of this study was…

Although collecting data from multiple informants is highly recommended, methods to model the congruence and incongruence between informants are limited. Bauer and colleagues suggested the trifactor model that decomposes the variances into common factor, informant perspective factors, and item-specific factors. This study extends their work to the…

Cognitive diagnosis models (CDMs) are latent class multidimensional statistical models that help classify people accurately by using a set of discrete latent variables, commonly referred to as attributes. These models require a Q-matrix that indicates the attributes involved in each item. A potential problem is that the Q-matrix construction…

A first-order latent growth model assesses change in an unobserved construct from a single score and is commonly used across different domains of educational research. However, examining change using a set of multiple response scores (e.g., scale items) affords researchers several methodological benefits not possible when using a single score. A…