Regularized Models for Fitting Zero-Inflated and Zero-Truncated Count Data: A Comparative Analysis

Abstract

Generalized Linear Models (GLMs) are widely recognized for their efficacy in fitting count data, superior to the Ordinary Least Squares (OLS) approach. The incapability of OLS to suitably handle count data can be attributed to its tendency to overfit. This study proposes the utilization of regularized models, specifically Ridge Regression and the Least Absolute Shrinkage and Selection Operator (LASSO), for fitting count data. These models are compared to frequentist and Bayesian models commonly used for count data fitting, such as the Dirichlet prior mixture of generalized linear mixed models and the discrete Weibull. The findings reveal Ridge Regression's superiority over all other models based on the Akaike Information Criterion (AIC). However, its performance diminishes when evaluated using the Bayesian Information Criterion (BIC), even though it still outperforms LASSO. The study thereby suggests the use of regularized regression models for fitting zero-inflated count data, as demonstrated with simulated data. Further, the appropriateness of regularized zero for zero-truncated count is exemplified using life data.