Rasch's multiplicative poisson model with covariates

As a multivariate model of the number of events, Rasch's multiplicative Poisson model is extended such that the parameters for individuals in the prior gamma distribution have continuous covariates. The parameters for individuals are integrated out and the hyperparameters in the prior distribution are estimated by a numerical method separately from difficulty parameters that are treated as fixed parameters or random variables. In addition, a method is presented for estimating parameters in Rasch's model with missing values. The author is now affiliated with the Otara University of Commerce. The author is grateful to Yoshio Takane, Haruo Yanai, Eiji Muraki, the editor and referees for their careful readings and helpful suggestions on earlier versions of this paper. Part of this work was presented at the third European Congress of Psychology at Tampere, Finland in 1993.