Profile analysis is one of the main tools for studying whether differential item functioning can be related to specific features of test items. While relevant, profile analysis in its current form has two restrictions that limit its usefulness in practice: It assumes that all test items have equal discrimination parameters, and it does not test…

Providing diagnostic feedback about growth is crucial to formative decisions such as targeted remedial instructions or interventions. This article proposed a longitudinal higher-order diagnostic classification modeling approach for measuring growth. The new modeling approach is able to provide quantitative values of overall and individual growth…

In order to evaluate the effect of a policy or treatment with pre- and post-treatment outcomes, we propose an approach based on a transition model, which may be applied with multivariate outcomes and accounts for unobserved heterogeneity. This model is based on potential versions of discrete latent variables representing the individual…

Mixture models have been developed to enable detection of within-subject differences in responses and response times to psychometric test items. To enable mixture modeling of both responses and response times, a distributional assumption is needed for the within-state response time distribution. Since violations of the assumed response time…

This article proposes a class of cognitive diagnosis models (CDMs) for polytomously scored items with different link functions. Many existing polytomous CDMs can be considered as special cases of the proposed class of polytomous CDMs. Simulation studies were carried out to investigate the feasibility of the proposed CDMs and the performance of…

School value-added models are widely applied to study, monitor, and hold schools to account for school differences in student learning. The traditional model is a mixed-effects linear regression of student current achievement on student prior achievement, background characteristics, and a school random intercept effect. The latter is referred to…

This article presents a latent class model for multilevel data to identify latent subgroups and estimate heterogeneous treatment effects. Unlike sequential approaches that partition data first and then estimate average treatment effects (ATEs) within classes, we employ a Bayesian procedure to jointly estimate mixing probability, selection, and…

Understanding whether or not different types of students master various attributes can aid future learning remediation. In this study, two-level diagnostic classification models (DCMs) were developed to represent the probabilistic relationship between external latent classes and attribute mastery patterns. Furthermore, variational Bayesian (VB)…

For surveys of complex issues that entail multiple steps, multiple reference points, and nongradient attributes (e.g., social inequality), this study proposes a new multiprocess model that integrates ideal-point and dominance approaches into a treelike structure (IDtree). In the IDtree, an ideal-point approach describes an individual's attitude…

A multidimensional Bayesian item response model is proposed for modeling item position effects. The first dimension corresponds to the ability that is to be measured; the second dimension represents a factor that allows for individual differences in item position effects called persistence. This model allows for nonlinear item position effects on…

Solving a constructed-response item usually requires successfully performing a sequence of tasks. Each task could involve different attributes, and those required attributes may be "condensed" in various ways to produce the responses. The sequential generalized deterministic input noisy "and" gate model is a general cognitive…

The traditional approach to estimating the consistency of school effects across subject areas and the stability of school effects across time is to fit separate value-added multilevel models to each subject or cohort and to correlate the resulting empirical Bayes predictions. We show that this gives biased correlations and these biases cannot be…

Multiple-choice exams are frequently used as an efficient and objective method to assess learning, but they are more vulnerable to answer copying than tests based on open questions. Several statistical tests (known as indices in the literature) have been proposed to detect cheating; however, to the best of our knowledge, they all lack mathematical…

This article promotes the use of modern test theory in testing situations where sum scores for binary responses are now used. It directly compares the efficiencies and biases of classical and modern test analyses and finds an improvement in the root mean squared error of ability estimates of about 5% for two designed multiple-choice tests and…

The purpose of this article is to introduce and review the capability and performance of the Stata item response theory (IRT) package that is available from Stata v.14, 2015. Using a simulated data set and a publicly available item response data set extracted from Programme of International Student Assessment, we review the IRT package from…