Bayesian Estimation of a Multilevel IRT Model Using Gibbs Sampling

Jean‐Paul Fox · Cees A. W. Glas

398 citations0/0 files storedPsychometrika

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Psychometric Methodologies and Testing Educational Assessment and Pedagogy Statistical Methods and Bayesian Inference

Abstract

In this article, a two-level regression model is imposed on the ability parameters in an item response theory (IRT) model. The advantage of using latent rather than observed scores as dependent variables of a multilevel model is that it offers the possibility of separating the influence of item difficulty and ability level and modeling response variation and measurement error. Another advantage is that, contrary to observed scores, latent scores are test-independent, which offers the possibility of using results from different tests in one analysis where the parameters of the IRT model and the multilevel model can be concurrently estimated. The two-parameter normal ogive model is used for the IRT measurement model. It will be shown that the parameters of the two-parameter normal ogive model and the multilevel model can be estimated in a Bayesian framework using Gibbs sampling. Examples using simulated and real data are given.

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References

1981Marginal Maximum Likelihood Estimation of Item Parameters: Application of an EM Algorithm 1992Full-Information Item Bi-Factor Analysis 1999A Straightforward Approach to Markov Chain Monte Carlo Methods for Item Response Models 1992Bayesian Estimation of Normal Ogive Item Response Curves Using Gibbs Sampling

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