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A Mixed Effects Randomized Item Response ModelUniversity of Twente
Tanglewood Research
The randomized response technique ensures that individual item responses, denoted as true item responses, are randomized before observing them and so-called randomized item responses are observed. A relationship is specified between randomized item response data and true item response data. True item response data are modeled with a (non)linear mixed effects and/or item response theory model. Although the individual true item responses are masked through randomizing the responses, the model extension enables the computation of individual true item response probabilities and estimates of individuals’ sensitive behavior/attitude and their relationships with background variables taking into account any clustering of respondents. Results are presented from a College Alcohol Problem Scale (CAPS) where students were interviewed via direct questioning or via a randomized response technique. A Markov Chain Monte Carlo algorithm is given for estimating simultaneously all model parameters given hierarchical structured binary or polytomous randomized item response data and background variables.
Key Words: item response theory model • MCMC • mixed effects • randomized response data
This version was published on December
1, 2008 Journal of Educational and Behavioral Statistics, Vol. 33, No. 4,
389-415 (2008) 
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