Parallel analysis has been considered one of the most accurate methods for determining the number of factors in factor analysis. One major advantage of parallel analysis over traditional factor retention methods (e.g., Kaiser's rule) is that it addresses the sampling variability of eigenvalues obtained from the identity matrix, representing the…

The multidimensional mixture data structure exists in many test (or inventory) conditions. Heterogeneity also relatively exists in populations. Still, some researchers are interested in deciding to which subpopulation a participant belongs according to the participant's factor pattern. Thus, in this study, we proposed three analysis procedures…

In modeling missing data, the missing data latent variable of the confirmatory factor model accounts for systematic variation associated with missing data so that replacement of what is missing is not required. This study aimed at extending the modeling missing data approach to tetrachoric correlations as input and at exploring the consequences of…

Conceptualizing two-variable disturbances preventing good model fit in confirmatory factor analysis as item-level method effects instead of correlated residuals avoids violating the principle that residual variation is unique for each item. The possibility of representing such a disturbance by a method factor of a bifactor measurement model was…

Percentage of uncontaminated correlations (PUC), explained common variance (ECV), and omega hierarchical ([omega]H) have been used to assess the degree to which a scale is essentially unidimensional and to predict structural coefficient bias when a unidimensional measurement model is fit to multidimensional data. The usefulness of these indices…

Regression factor score predictors have the maximum factor score determinacy, that is, the maximum correlation with the corresponding factor, but they do not have the same inter-correlations as the factors. As it might be useful to compute factor score predictors that have the same inter-correlations as the factors, correlation-preserving factor…

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…

Identifying items with differential item functioning (DIF) in an assessment is a crucial step for achieving equitable measurement. One critical issue that has not been fully addressed with existing studies is how DIF items can be detected when data are multilevel. In the present study, we introduced a Lord's Wald X[superscript 2] test-based…

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…

Factor score regression has recently received growing interest as an alternative for structural equation modeling. However, many applications are left without guidance because of the focus on normally distributed outcomes in the literature. We perform a simulation study to examine how a selection of factor scoring methods compare when estimating…

Accounting for model misspecification in Bayesian structural equation models is an active area of research. We present a uniquely Bayesian approach to misspecification that models the degree of misspecification as a parameter--a parameter akin to the correlation root mean squared residual. The misspecification parameter can be interpreted on its…

We conducted an extensive Monte Carlo study of factor-rotation local solutions (LS) in multidimensional, two-parameter logistic (M2PL) item response models. In this study, we simulated more than 19,200 data sets that were drawn from 96 model conditions and performed more than 7.6 million rotations to examine the influence of (a) slope parameter…

A latent variable modeling-based procedure is discussed that permits to readily point and interval estimate the design effect index in multilevel settings using widely circulated software. The method provides useful information about the relationship of important parameter standard errors when accounting for clustering effects relative to…

In real-world situations, multidimensional data may appear on large-scale tests or psychological surveys. The purpose of this study was to investigate the effects of the quantity and magnitude of cross-loadings and model specification on item parameter recovery in multidimensional Item Response Theory (MIRT) models, especially when the model was…

Unit-weight sum scores (UWSSs) are routinely used as estimates of factor scores on the basis of solutions obtained with the nonlinear exploratory factor analysis (EFA) model for ordered-categorical responses. Theoretically, this practice results in a loss of information and accuracy, and is expected to lead to biased estimates. However, the…