Estimating CDMs Using MCMC

Abstract

In this chapter, we provide a brief survey of Markov chain Monte Carlo (MCMC) methods used in estimating Cognitive Diagnostic Models (CDMs). MCMC techniques have been widely used for the Bayesian estimation of psychometric models. MCMC algorithms and general purpose MCMC software has been facilitating the development of modern psychometric models that are otherwise difficult to fit (Levy R, J Probab Stat 1–18, 2009. Retrieved from http://www.hindawi.com/journals/jps/2009/537139/, https://doi.org/10.1155/2009/ 537139). We introduce a Gibbs sampler for fitting the saturated Log-linear CDM model (LCDM, Henson RA, Templin JL, Willse JT, Psychometrika, 74(2):191–210, 2009. Retrieved from https://doi.org/10.1007/s11336-008-9089-5). The utility of Bayesian inference is demonstrated by analyzing the Examination for the Certificate of Proficiency in English (ECPE) dataset.