Abstract
A factor-analytic model for discrete variables which represent frequencies is developed. The model assumes that the frequencies are generated by the Poisson distribution, in which the logarithm of the parameter of the distribution takes a similar form to the factor-analysis model for continuous variables. The latent variables in the model, which correspond to common factors in factor analysis, are assumed to have independent distributions with fixed parameters or a multivariate normal distribution with unknown correlations. The individual factor scores are integrated out from the model and factor-loadings in the sense of the generalized linear model are obtained by the marginal maximum likelihood method. Numerical examples of non-verbal intelligence tests are given.
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