Van der Linden's hierarchical model for responses and response times can be used in order to infer the ability and mental speed of test takers from their responses and response times in an educational test. A standard approach for this is maximum likelihood estimation. In real-world applications, the data of some test takers might be partly…

Factor score regression (FSR) is widely used as a convenient alternative to traditional structural equation modeling (SEM) for assessing structural relations between latent variables. But when latent variables are simply replaced by factor scores, biases in the structural parameter estimates often have to be corrected, due to the measurement error…

In this article, a 2-way multigroup common factor model (MG-CFM) is presented. The MG-CFM can be used to estimate interaction effects between 2 grouping variables on 1 or more hypothesized latent variables. For testing the significance of such interactions, a likelihood ratio test is presented. In a simulation study, the robustness of the…

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…

Despite the widespread popularity of growth curve analysis, few studies have investigated robust growth curve models. In this article, the "t" distribution is applied to model heavy-tailed data and contaminated normal data with outliers for growth curve analysis. The derived robust growth curve models are estimated through Bayesian…

A simulation study compared the performance of robust normal theory maximum likelihood (ML) and robust categorical least squares (cat-LS) methodology for estimating confirmatory factor analysis models with ordinal variables. Data were generated from 2 models with 2-7 categories, 4 sample sizes, 2 latent distributions, and 5 patterns of category…

The likelihood ratio test statistic G[squared](dif) is widely used for comparing the fit of nested models in categorical data analysis. In large samples, this statistic is distributed as a chi-square with degrees of freedom equal to the difference in degrees of freedom between the tested models, but only if the least restrictive model is correctly…

A Monte Carlo study was conducted to investigate the robustness of the assumed error distribution in maximum likelihood estimation models for multidimensional scaling. Results show that violations of the assumed error distribution have virtually no effect on the estimated distance parameters. (SLD)

Dichotomous search strategies (DSSs) for computerized adaptive testing are similar to golden section search strategies (GSSSs). Each middle point of successive search regions is a testing point. After each item is administered, the subject's obtained score is compared with the expected score at successive testing points. If the subject's obtained…