Mixed Membership Models (MMMs) are a popular family of latent structure models for complex multivariate data. Instead of forcing each subject to belong to a single cluster, MMMs incorporate a vector of subject-specific weights characterizing partial membership across clusters. With this flexibility come challenges in uniquely identifying,…

This article is concerned with the statistical detection of copying on multiple-choice exams. As an alternative to existing permutation- and model-based copy-detection approaches, a simple randomization p-value (RP) test is proposed. The RP test, which is based on an intuitive match-score statistic, makes no assumptions about the distribution of…

Takers of educational tests often receive proficiency levels instead of or in addition to scaled scores. For example, proficiency levels are reported for the Advanced Placement (AP®) and U.S. Medical Licensing examinations. Technical difficulties and other unforeseen events occasionally lead to missing item scores and hence to incomplete data on…

Multidimensional Item Response Theory (MIRT) is widely used in educational and psychological assessment and evaluation. With the increasing size of modern assessment data, many existing estimation methods become computationally demanding and hence they are not scalable to big data, especially for the multidimensional three-parameter and…

Recent advancements in testing differential item functioning (DIF) have greatly relaxed restrictions made by the conventional multiple group item response theory (IRT) model with respect to the number of grouping variables and the assumption of predefined DIF-free anchor items. The application of the L[subscript 1] penalty in DIF detection has…

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…

One of the most serious forms of cheating occurs when examinees have item preknowledge and prior access to secure test material before taking an exam for the purpose of obtaining an inflated test score. Examinees that cheat and have prior knowledge of test content before testing may have an unfair advantage over examinees that do not cheat. Item…

Although item response theory (IRT) models such as the bifactor, two-tier, and between-item-dimensionality IRT models have been devised to confirm complex dimensional structures in educational and psychological data, they can be challenging to use in practice. The reason is that these models are multidimensional IRT (MIRT) models and thus are…

Testing whether items fit the assumptions of an item response theory model is an important step in evaluating a test. In the literature, numerous item fit statistics exist, many of which show severe limitations. The current study investigates the root mean squared deviation (RMSD) item fit statistic, which is used for evaluating item fit in…

Categorical data become increasingly ubiquitous in the modern big data era. In this dissertation, we propose novel statistical learning and inference methods for large-scale categorical data, focusing on latent variable models and their applications to psychometrics. In psychometric assessments, the subjects' underlying aptitude often cannot be…

Analyzing heterogeneous treatment effects (HTEs) plays a crucial role in understanding the impacts of educational interventions. A standard practice for HTE analysis is to examine interactions between treatment status and preintervention participant characteristics, such as pretest scores, to identify how different groups respond to treatment.…

With the growing attention on large-scale educational testing and assessment, the ability to process substantial volumes of response data becomes crucial. Current estimation methods within item response theory (IRT), despite their high precision, often pose considerable computational burdens with large-scale data, leading to reduced computational…

With the widespread use of computers in modern assessment, online calibration has become increasingly popular as a way of replenishing an item pool. The present study discusses online calibration strategies for a joint model of responses and response times. The study proposes likelihood inference methods for item paramter estimation and evaluates…

Multidimensional Item Response Theory (MIRT) is widely used in assessment and evaluation of educational and psychological tests. It models the individual response patterns by specifying functional relationship between individuals' multiple latent traits and their responses to test items. One major challenge in parameter estimation in MIRT is that…

Among current state-of-art estimation methods for multilevel IRT models, the two-stage divide-and-conquer strategy has practical advantages, such as clearer definition of factors, convenience for secondary data analysis, convenience for model calibration and fit evaluation, and avoidance of improper solutions. However, various studies have shown…