  In this paper, we present a method for factor analysis of discrete data. This
is accomplished by fitting a dependent Poisson model with a factor structure.
To be able to analyze ordinal data, we also consider a truncated Poisson
distribution. We try to find the model with the lowest AIC by employing a
forward selection procedure. The probability to find the correct model is
investigated in a simulation study. Moreover, we heuristically derive the
corresponding asymptotic probabilities. An empirical study is also included.
