Recently, there has been increasing interest in reporting subscores. This paper examines reporting of subscores using multidimensional item response theory (MIRT) models (e.g., Reckase in "Appl. Psychol. Meas." 21:25-36, 1997; C.R. Rao and S. Sinharay (Eds), "Handbook of Statistics, vol. 26," pp. 607-642, North-Holland, Amsterdam, 2007; Beguin &…

If data exhibit multidimensionality, key conditional independence assumptions of unidimensional models do not hold. The current work pursues posterior predictive model checking, a flexible family of model-checking procedures, as a tool for criticizing models due to unaccounted for dimensions in the context of item response theory. Factors…

The reporting methods used in large-scale educational assessments such as the National Assessment of Educational Progress (NAEP) rely on a "latent regression model". There is a lack of research on the assessment of fit of latent regression models. This paper suggests a simulation-based model-fit technique to assess the fit of such…

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 theory (IRT) to a latent variable model with covariates…

Bounds are established for log cross-product ratios (log odds ratios) involving pairs of items for item response models. First, expressions for bounds on log cross-product ratios are provided for unidimensional item response models in general. Then, explicit bounds are obtained for the Rasch model and the two-parameter logistic (2PL) model.…

Bayesian networks are frequently used in educational assessments primarily for learning about students' knowledge and skills. There is a lack of works on assessing fit of Bayesian networks. This article employs the posterior predictive model checking method, a popular Bayesian model checking tool, to assess fit of simple Bayesian networks. A…

Assessing fit of psychometric models has always been an issue of enormous interest, but there exists no unanimously agreed upon item fit diagnostic for the models. Bayesian networks, frequently used in educational assessments (see, for example, Mislevy, Almond, Yan, & Steinberg, 2001) primarily for learning about students' knowledge and…