Multidimensional item response theory (MIRT) models use data from individual item responses to estimate multiple latent traits of interest, making them useful in educational and psychological measurement, among other areas. When MIRT models are applied in practice, it is not uncommon to see that some items are designed to measure all latent traits…

Stan is a new Bayesian statistical software program that implements the powerful and efficient Hamiltonian Monte Carlo (HMC) algorithm. To date there is not a source that systematically provides Stan code for various item response theory (IRT) models. This article provides Stan code for three representative IRT models, including the…

Standard approaches for estimating item response theory (IRT) model parameters generally work under the assumption that the latent trait being measured by a set of items follows the normal distribution. Estimation of IRT parameters in the presence of nonnormal latent traits has been shown to generate biased person and item parameter estimates. A…

The study utilised a fine-grained diagnostic checklist to assess first-year undergraduates in Hong Kong and evaluated its validity and usefulness for diagnosing academic writing in English. Ten English language instructors marked 472 academic essays with the checklist. They also agreed on a Q-matrix, which specified the relationships among the…

This article examines the problem of specification error in 2 models for categorical latent variables; the latent class model and the latent Markov model. Specification error in the latent class model focuses on the impact of incorrectly specifying the number of latent classes of the categorical latent variable on measures of model adequacy as…

Relatively little research has been conducted with the noncompensatory class of multidimensional item response theory (MIRT) models. A Monte Carlo simulation study was conducted exploring the estimation of a two-parameter noncompensatory item response theory (IRT) model. The estimation method used was a Metropolis-Hastings within Gibbs algorithm…

In behavioural sciences, local dependence and DIF are common, and purification procedures that eliminate items with these weaknesses often result in short scales with poor reliability. Graphical loglinear Rasch models (Kreiner & Christensen, in "Statistical Methods for Quality of Life Studies," ed. by M. Mesbah, F.C. Cole & M.T.…

As is the case for any statistical model, a multidimensional latent growth model comes with certain requirements with respect to the data collection design. In order to measure growth, repeated measurements of the same set of individuals are required. Furthermore, the data collection design should be specified such that no individual is given the…

In the social sciences, latent traits often have a hierarchical structure, and data can be sampled from multiple levels. Both hierarchical latent traits and multilevel data can occur simultaneously. In this study, we developed a general class of item response theory models to accommodate both hierarchical latent traits and multilevel data. The…

Item factor analysis has a rich tradition in both the structural equation modeling and item response theory frameworks. The goal of this paper is to demonstrate a novel combination of various Markov chain Monte Carlo (MCMC) estimation routines to estimate parameters of a wide variety of confirmatory item factor analysis models. Further, I show…

The randomized response (RR) technique is often used to obtain answers on sensitive questions. A new method is developed to measure latent variables using the RR technique because direct questioning leads to biased results. Within the RR technique is the probability of the true response modeled by an item response theory (IRT) model. The RR…

The 9th International Conference on Educational Data Mining (EDM 2016) is held under the auspices of the International Educational Data Mining Society at the Sheraton Raleigh Hotel, in downtown Raleigh, North Carolina, in the USA. The conference, held June 29-July 2, 2016, follows the eight previous editions (Madrid 2015, London 2014, Memphis…

SCORIGHT is a very general computer program for scoring tests. It models tests that are made up of dichotomously or polytomously rated items or any kind of combination of the two through the use of a generalized item response theory (IRT) formulation. The items can be presented independently or grouped into clumps of allied items (testlets) or in…

The Standardized Letter of Recommendation (SLR), a 28-item form, was created by ETS to supplement the qualitative rating of graduate school applicants' nonacademic qualities with a quantitative approach. The purpose of this study was to evaluate the following psychometric properties of the SLR using the Rasch rating-scale model: dimensionality,…