A latent variable model for observed variables representing frequencies is proposed. The data type for the model is a subjects by variables two-way frequency table. The model has two groups of latent variables. The first group of latent variables represents the characteristics of subjects and corresponds to common factors in factor analysis. On the other hand, each of latent variables in the second group is related to one of the manifest variables and corresponds to a specific factor in factor analysis. The manifest variables in the model, when given the values of common latent variables, follow the negative binomial distributions. The latent variables in the first and second groups are integrated out of the model. The parameters in the model are estimated by the marginal maximum likelihood method, using a kind of the EM algorithm. The communality, specificity, and reliability for an observed variable are defined.
The Behaviormetric Society of Japan