Multilevel IRT using dichotomous and polytomous response data


Fox, J.-P. (2005) Multilevel IRT using dichotomous and polytomous response data. British Journal of Mathematical and Statistical Psychology, 58 (1). pp. 145-172. ISSN 0007-1102

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Abstract:A structural multilevel model is presented where some of the variables cannot be
observed directly but are measured using tests or questionnaires. Observed dichotomous or ordinal polytomous response data serve to measure the latent variables using an item response theory model. The latent variables can be defined at any level of the multilevel model. A Bayesian procedure Markov chain Monte Carlo (MCMC), to estimate all parameters simultaneously is presented. It is shown that certain model checks and model comparisons can be done using the MCMC output. The techniques are illustrated using a simulation study and an application involving students’ achievements on a mathematics test and test results regarding management characteristics of teachers and principles.
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Copyright:© 2005 The British Psychological Society
Faculty of Behavioural, Management and Social sciences (BMS)
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