# Discrete factor analysis

## TL;DR

This paper introduces a novel factor analysis method for discrete and ordinal data using dependent and truncated Poisson models, employing model selection and simulation to evaluate accuracy.

## Contribution

It proposes a new factor analysis approach tailored for discrete data, including ordinal data, with model selection and theoretical analysis of model probabilities.

## Key findings

- Successfully fits factor models to discrete data
- Demonstrates effectiveness through simulation and empirical studies
- Provides asymptotic probability insights for model selection

## Abstract

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.