A structural model of the ability distribution in the item response theory is proposed in which continuous covariates representing the properties of groups to which the subjects belong are involved. The ability parameter which is treated as a random variable, is regressed on the covariates. It is assumed that the ability parameter is normally distributed with the mean and variance which are functions of the covariates. A two-parameter logistic model is adopted as the probability model of an item response. It is shown that item parameters and hyperparameters in the ability distribution can be estimated simultaneously using the EM algorithm. Examples are provided, where the mean and standard deviation of the ability parameter are represented by polynomials of age for data of an adult intelligence test.
The Behaviormetric Society of Japan