This article is concerned with the large-sample parameter estimator behavior in applications of Bayesian confirmatory factor analysis in behavioral measurement. The property of strong convergence of the popular Bayesian posterior median estimator is discussed, which states numerical convergence with probability 1 of the resulting estimates to the…

In the context of Bayesian factor analysis, it is possible to compute plausible values, which might be used as covariates or predictors or to provide individual scores for the Bayesian latent variables. Previous simulation studies ascertained the validity of mean plausible values by the mean squared difference of the mean plausible values and the…

A Monte Carlo simulation study was conducted to compare fit indices used for detecting the correct latent class in three dichotomous mixture item response theory (IRT) models. Ten indices were considered: Akaike's information criterion (AIC), the corrected AIC (AICc), Bayesian information criterion (BIC), consistent AIC (CAIC), Draper's…

Purpose and Background: Despite the flexibility of multilevel structural equation modeling (MLSEM), a practical limitation many researchers encounter is how to effectively estimate model parameters with typical sample sizes when there are many levels of (potentially disparate) nesting. We develop a method-of-moment corrected maximum likelihood…

This Monte Carlo simulation study aimed to investigate confirmatory factor analysis (CFA) estimation methods under different conditions, such as sample size, distribution of indicators, test length, average factor loading, and factor structure. Binary data were generated to compare the performance of maximum likelihood (ML), mean and variance…

Cross-level invariance in a multilevel item response model can be investigated by testing whether the within-level item discriminations are equal to the between-level item discriminations. Testing the cross-level invariance assumption is important to understand constructs in multilevel data. However, in most multilevel item response model…

Lord's Wald test for differential item functioning (DIF) has not been studied extensively in the context of the multidimensional item response theory (MIRT) framework. In this article, Lord's Wald test was implemented using two estimation approaches, marginal maximum likelihood estimation and Bayesian Markov chain Monte Carlo estimation, to detect…

Calibration of new items online has been an important topic in item replenishment for multidimensional computerized adaptive testing (MCAT). Several online calibration methods have been proposed for MCAT, such as multidimensional "one expectation-maximization (EM) cycle" (M-OEM) and multidimensional "multiple EM cycles"…

Approaches to correcting correlation coefficients for range restriction have been developed under the framework of large sample theory. The accuracy of missing data techniques for correcting correlation coefficients for range restriction has thus far only been investigated with relatively large samples. However, researchers and evaluators are…

Survey data are often subject to various types of errors such as misclassification. In this article, we consider a model where interest is simultaneously in two correlated response variables and one is potentially subject to misclassification. A motivating example of a recent study of the impact of a sexual education course for adolescents is…

A simulation study was conducted to explore the performance of the linear logistic test model (LLTM) when the relationships between items and cognitive components were misspecified. Factors manipulated included percent of misspecification (0%, 1%, 5%, 10%, and 15%), form of misspecification (under-specification, balanced misspecification, and…

This article examines the effects of clustering in latent class analysis. A comprehensive simulation study is conducted, which begins by specifying a true multilevel latent class model with varying within- and between-cluster sample sizes, varying latent class proportions, and varying intraclass correlations. These models are then estimated under…

The purpose of this study is to compare the maximum likelihood (ML) and Bayesian estimation methods for polychoric correlation (PCC) under diverse conditions using a Monte Carlo simulation. Two new Bayesian estimates, maximum a posteriori (MAP) and expected a posteriori (EAP), are compared to ML, the classic solution, to estimate PCC. Different…

The educational field has now accumulated an extensive literature reporting on values of the intraclass correlation coefficient, a parameter essential to determining the required size of a planned cluster randomized trial. We propose here a simple simulation-based approach including all relevant information that can facilitate this task. An…

Cognitive diagnostic assessment (CDA) is a new theoretical framework for psychological and educational testing that is designed to provide detailed information about examinees' strengths and weaknesses in specific knowledge structures and processing skills. During the last three decades, more than a dozen psychometric models have been developed…