Given the frequent presence of slipping and guessing in item responses, models for the inclusion of their effects are highly important. Unfortunately, the most common model for their inclusion, the four-parameter item response theory model, potentially has severe deficiencies related to its possible unidentifiability. With this issue in mind, the…

Standard item response theory (IRT) models have been extended with testlet effects to account for the nesting of items; these are well known as (Bayesian) testlet models or random effect models for testlets. The testlet modeling framework has several disadvantages. A sufficient number of testlet items are needed to estimate testlet effects, and a…

Bayesian statistics has gained great momentum since the computational developments of the 1990s. Gradually, advances in Bayesian methodology and software have made Bayesian techniques much more accessible to applied statisticians and, in turn, have potentially transformed Bayesian education at the undergraduate level. This article provides an…

The uncertainty arising from item parameter estimation is often not negligible and must be accounted for when calculating latent variable (LV) scores in item response theory (IRT). It is particularly so when the calibration sample size is limited and/or the calibration IRT model is complex. In the current work, we treat two-stage IRT scoring as a…

In this article, we propose using the Bayes factors (BF) to evaluate person fit in item response theory models under the framework of Bayesian evaluation of an informative diagnostic hypothesis. We first discuss the theoretical foundation for this application and how to analyze person fit using BF. To demonstrate the feasibility of this approach,…

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…

A family of learning models that integrates a cognitive diagnostic model and a higher-order, hidden Markov model in one framework is proposed. This new framework includes covariates to model skill transition in the learning environment. A Bayesian formulation is adopted to estimate parameters from a learning model. The developed methods are…

We extend a unified and easy-to-use approach to measurement error and missing data. In our companion article, Blackwell, Honaker, and King give an intuitive overview of the new technique, along with practical suggestions and empirical applications. Here, we offer more precise technical details, more sophisticated measurement error model…

A Bayesian model formulation of the deterministic inputs, noisy "and" gate (DINA) model is presented. Gibbs sampling is employed to simulate from the joint posterior distribution of item guessing and slipping parameters, subject attribute parameters, and latent class probabilities. The procedure extends concepts in Béguin and Glas,…

In this article, a proposed Bayesian extension of the generalized beta spatial regression models is applied to the analysis of the quality of education in Colombia. We briefly revise the beta distribution and describe the joint modeling approach for the mean and dispersion parameters in the spatial regression models' setting. Finally, we motivate…

Developed Markov Chain Monte Carlo procedures to perform Bayesian inference, model checking, and model comparison in heterogeneous factor analysis. Tested the approach with synthetic data and data from a consumption emotion study involving 54 consumers. Results show that traditional psychometric methods cannot fully capture the heterogeneity in…

Introduces a new technique for estimating the parameters of models with continuous latent data. To streamline presentation of this Markov Chain Monte Carlo (MCMC) method, the Rasch model is used. Also introduces a new sampling-based Bayesian technique, the DA-T-Gibbs sampler. (SLD)

A Bayesian approach to sensitivity of inferences to possible outliers involves recalculating marginal posterior distributions of parameters of interest under assumptions of heavy tails. This strategy is implemented in the hierarchical model setting through Gibbs sampling, a Monte Carlo technique, and illustrated through a reanalysis of data on…

Bias, standard error, and reliability of five ability estimators were evaluated using Monte Carlo estimates of the unknown conditional means and variances of the estimators. Results indicate that estimates based on Bayesian modal, expected a posteriori, and weighted likelihood estimators were reasonably unbiased with relatively small standard…

A predictive adaptive testing (PAT) strategy was developed based on statistical predictive analysis, and its feasibility was studied by comparing PAT performance to those of the Flexilevel, Bayesian modal, and expected a posteriori (EAP) strategies in a simulated environment. The proposed adaptive test is based on the idea of using item difficulty…