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Multilevel IRT using dichotomous and polytomous response data
Author(s) -
Fox J. P.
Publication year - 2005
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1348/000711005x38951
Subject(s) - polytomous rasch model , item response theory , markov chain monte carlo , latent variable , multilevel model , measure (data warehouse) , ordinal data , bayesian probability , econometrics , statistics , hierarchical database model , mathematics , structural equation modeling , markov chain , test (biology) , computer science , psychometrics , data mining , paleontology , biology
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.