Research in education and behavioral sciences often involves the use of latent variable models that are related to indicators, as well as related to covariates or outcomes. Such models are subject to interpretational confounding, which occurs when fitting the model with covariates or outcomes alters the results for the measurement model. This has…

Popular item response theory (IRT) models are considered complex, mainly due to the inclusion of a random factor variable (latent variable). The random factor variable represents the incidental parameter problem since the number of parameters increases when including data of new persons. Therefore, IRT models require a specific estimation method…

Attribute hierarchy, the underlying prerequisite relationship among attributes, plays an important role in applying cognitive diagnosis models (CDM) for designing efficient cognitive diagnostic assessments. However, there are limited statistical tools to directly estimate attribute hierarchy from response data. In this study, we proposed a…

Bayesian methods to infer model dimensionality in factor analysis generally assume a lower triangular structure for the factor loadings matrix. Consequently, the ordering of the outcomes influences the results. Therefore, we propose a method to infer model dimensionality without imposing any prior restriction on the loadings matrix. Our approach…

This study proposes a Bayesian method for diagnostic classification models (DCMs) for a partially known Q-matrix setting between exploratory and confirmatory DCMs. This Q-matrix setting is practical and useful because test experts have pre-knowledge of the Q-matrix but cannot readily specify it completely. The proposed method employs priors for…

Item response theory (IRT) models typically rely on a normality assumption for subject-specific latent traits, which is often unrealistic in practice. Semiparametric extensions based on Dirichlet process mixtures (DPMs) offer a more flexible representation of the unknown distribution of the latent trait. However, the use of such models in the IRT…

Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the…

Score differencing is one of the six categories of statistical methods used to detect test fraud (Wollack & Schoenig, 2018) and involves the testing of the null hypothesis that the performance of an examinee is similar over two item sets versus the alternative hypothesis that the performance is better on one of the item sets. We suggest, to…

The issue of model uncertainty has been gaining interest in education and the social sciences community over the years, and the dominant methods for handling model uncertainty are based on Bayesian inference, particularly, Bayesian model averaging. However, Bayesian model averaging assumes that the true data-generating model is within the…

Item compromise has long posed challenges in educational measurement, jeopardizing both test validity and test security of continuous tests. Detecting compromised items is therefore crucial to address this concern. The present literature on compromised item detection reveals two notable gaps: First, the majority of existing methods are based upon…

Equating is a family of statistical models and methods used to adjust scores on different test forms so that they can be comparable and used interchangeably. Equated scores are obtained estimating the equating transformation function, which maps the scores on the scale of one test form into their equivalents on the scale of other one. All the…

Cognitive diagnosis models (CDMs) are the statistical framework for cognitive diagnostic assessment in education and psychology. They generally assume that subjects' latent attributes are dichotomous--mastery or nonmastery, which seems quite deterministic. As an alternative to dichotomous attribute mastery, attention is drawn to the use of a…

Change-point analysis (CPA) is a method for detecting abrupt changes in parameter(s) underlying a sequence of random variables. It has been applied to detect examinees' aberrant test-taking behavior by identifying abrupt test performance change. Previous studies utilized maximum likelihood estimations of ability parameters, focusing on detecting…

In this article, we propose a variational Bayes (VB) inference method for the deterministic input noisy AND gate model of cognitive diagnostic assessment. The proposed method, which applies the iterative algorithm for optimization, is derived based on the optimal variational posteriors of the model parameters. The proposed VB inference enables…

A Monte Carlo simulation was performed to compare methods for handling missing data in growth mixture models. The methods considered in the current study were (a) a fully Bayesian approach using a Gibbs sampler, (b) full information maximum likelihood using the expectation-maximization algorithm, (c) multiple imputation, (d) a two-stage multiple…