Estimation of careless error and lucky guess probabilities for dichotomous test items: A psychometric application of a biometric latent class model with random effects

Medical research has extensively dealt with the estimation of the accuracy (sensitivity and specificity) of a diagnostic test for screening individuals. In this paper we apply the biometric latent class model with random effects by Qu, Tan, and Kutner [(1996). Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics, 52, 797-810] to estimate the response error (careless error and lucky guess) probabilities for dichotomous test items in the psychometric theory of knowledge spaces. The approach is illustrated with simulated data. In particular, we extend this approach to give a generalization of the basic local independence model in knowledge space theory. This allows for local dependence among the indicators given the knowledge state of an examinee and/or for the incorporation of covariates.