The most probable distribution method is applied to derive the logistic model as the distribution accounting for the maximum number of possible outcomes in a dichotomous test while introducing latent traits and item characteristics as constraints to the system. The item response theory logistic...

Traditional testing procedures typically utilize unidimensional item response theory (IRT) models to provide a single, continuous estimate of a student’s overall ability. Advances in psychometrics have focused on measuring multiple dimensions of ability to provide more detailed feedback for...

If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking (PPMC) as a tool for criticizing models due to unaccounted for dimensions in data structures that follow conjunctive...

In the human sciences, ability tests or psychological inventories are often repeatedly conducted to measure growth. Standard item response models do not take into account possible autocorrelation in longitudinal data. In this study, the authors propose an item response model to account for...

Patz and Junker (1999) describe a general Markov chain Monte Carlo (MCMC) strategy, based on Metropolis-Hastings sampling, for Bayesian inference in complex item response theory (IRT) settings. They demonstrate the basic methodology using the two-parameter logistic (2PL) model. In this paper we...

This paper demonstrates Markov chain Monte Carlo (MCMC) techniques that are particularly well-suited to complex models with item response theory (IRT) assumptions. MCMC may be thought of as a successor to the standard practice of first calibrating the items using E-M methods and then taking the...

This article presents an application of a stochastic approximation expectation maximization (EM) algorithm using a Metropolis-Hastings (MH) sampler to estimate the parameters of an item response latent regression model. Latent regression item response models are extensions of item response...

In this paper, a method for studying DIF is demonstrated that can used with either dichotomous or polytomous items. The method is shown to be valid for data that follow a partial credit IRT model. It is also shown that logistic regression gives results equivalent to those of the proposed method....

We extend a recent didactic by Magis, Raîche, and Béland on the use of the lz and lz * person-fit statistics. We discuss a number of possibly confusing details and show that it is important to first investigate item response theory model fit before assessing person fit. Furthermore, it is...

Adaptive testing under a multidimensional logistic response model is addressed. An algorithm is proposed that minimizes the (asymptotic) variance of the maximum-likelihood estimator of a linear combination of abilities of interest. The criterion results in a closed-form expression that is easy...