Multilevel IRT using dichotomous and polytomous response data

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...

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Bibliographic Details
Published in:British journal of mathematical & statistical psychology 2005-05, Vol.58 (1), p.145-172
Main Author: Fox, J. -P.
Format: Article
Language:English
Subjects:
Academic achievement
Analysis of Variance
Bayes Theorem
Bayesian analysis
Biological and medical sciences
Educational Measurement - statistics & numerical data
Educational Status
Fundamental and applied biological sciences. Psychology
Humans
Markov analysis
Markov Chains
Mathematics
Models, Statistical
Monte Carlo Method
Monte Carlo simulation
Parameter estimation
Psychological Tests - statistics & numerical data
Psychology. Psychoanalysis. Psychiatry
Psychology. Psychophysiology
Psychometrics - statistics & numerical data
Psychometrics. Statistics. Methodology
School effectiveness
Statistics. Mathematics
Surveys and Questionnaires
Variables
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Summary: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.
ISSN:0007-1102
2044-8317
DOI:10.1348/000711005X38951