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Under the Bayesian approach, posterior predictive model checking (PPMC) has become a popular tool for fit assessment of item response theory (IRT) models. In this study, we propose the use of the Hellinger distance within PPMC to quantify the distance between the realized and the predictive distribution of the model-based covariance for item pairs. Specifically, the case of multidimensional data analyzed with a unidimensional approach is taken into account. The results of the simulation study show the effectiveness of the method in detecting model misfit and the sensitivity to the trait correlations. An application to real data on tourism perceptions shows the feasibility of the method in practice and especially the capability of detecting potential misfit attributed to specific items. [ABSTRACT FROM AUTHOR]

The aim of the article is to propose a Bayesian estimation through Markov chain Monte Carlo of a multidimensional item response theory model for graded responses with an additive structure with correlated latent traits. A simulation study is conducted to evaluate the model parameter recovery under different conditions (sample size, test and subtest length, number of response categories, and correlation structure). The results show that the parameters are well reproduced when the sample size is sufficiently large (n= 1, 000), while the worst recovery is observed for small sample size (n= 500), and four response categories with a short number of test items. [ABSTRACT FROM PUBLISHER]

The article aims at evaluating the parameter recovery for the multidimensional additive IRT model (Sheng, 2005; Sheng and Wikle, 2009). By estimating the model parameters via Gibbs sampler, a simulation study is conducted under different testing conditions, e.g., dimensionality, test and subtest lengths, correlation matrices, and different values of discrimination parameters. The results show that, especially when the test length is short and the abilities are highly correlated, the accuracy of the parameter estimates is reduced and more iterations are required to convergence. An application in educational testing is also described to show the effectiveness of the model in use. [ABSTRACT FROM PUBLISHER]

In testing, item response theory models are widely used in order to estimate item parameters and individual abilities. However, even unidimensional models require a considerable sample size so that all parameters can be estimated precisely. The introduction of empirical prior information about candidates and items might reduce the number of candidates needed for parameter estimation. Using data for IQ measurement, this work shows how empirical information about items can be used effectively for item calibration and in adaptive testing. First, we propose multivariate regression trees to predict the item parameters based on a set of covariates related to the item-solving process. Afterwards, we compare the item parameter estimation when tree-fitted values are included in the estimation or when they are ignored. Model estimation is fully Bayesian, and is conducted via Markov chain Monte Carlo methods. The results are two-fold: (a) in item calibration, it is shown that the introduction of prior information is effective with short test lengths and small sample sizes and (b) in adaptive testing, it is demonstrated that the use of the tree-fitted values instead of the estimated parameters leads to a moderate increase in the test length, but provides a considerable saving of resources. [ABSTRACT FROM AUTHOR]

The focus of this article is on the choice of suitable prior distributions for item parameters within item response theory (IRT) models. In particular, the use of empirical prior distributions for item parameters is proposed. Firstly, regression trees are implemented in order to build informative empirical prior distributions. Secondly, model estimation is conducted within a fully Bayesian approach through the Gibbs sampler, which makes estimation feasible also with increasingly complex models. The main results show that item parameter recovery is improved with the introduction of empirical prior information about item parameters, also when only a small sample is available. [ABSTRACT FROM AUTHOR]