Exploring Discrete Factor Analysis with the discFA Package in R

TL;DR

This paper introduces the discFA package in R for discrete factor analysis, enabling modeling of count data with Poisson or Negative Binomial distributions, including zero inflation and truncation, with an algorithm to select optimal models based on AIC.

Contribution

It presents a new R package for discrete factor analysis that handles various count data complexities and provides an algorithm for optimal model selection.

Findings

The package supports eight modeling alternatives combining distributions, zero inflation, and truncation.

It employs a forward search algorithm to identify the best model based on AIC.

Illustrative examples demonstrate its application across diverse fields.

Abstract

Literature suggested that using the traditional factor analysis for the count data may be inappropriate. With that in mind, discrete factor analysis builds on fitting systems of dependent discrete random variables to data. The data should be in the form of non-negative counts. Data may also be truncated at some positive integer value. The discFA package in R allows for two distributions: Poisson and Negative Binomial, in combination with possible zero inflation and possible truncation, hence, eight different alternatives. A forward search algorithm is employed to find the model optimal factor model with the lowest AIC. Several different illustrative examples from psychology, agriculture, car industry, and a simulated data will be analyzed at the end.