Robust median regression for count data with general lower truncation using a contaminated discrete Weibull model

Area of Science:

• Statistics
• Biostatistics
• Econometrics

Background:

• Right-skewed count data often exhibit heavy upper tails, making the mean an unreliable measure of central tendency.
• The standard Discrete Weibull (DW) regression model, while median-centered, can struggle with distributions having extremely heavy upper tails.
• Existing models may not adequately accommodate outliers or the complexities of highly skewed distributions.

Purpose of the Study:

• To introduce a novel contaminated Discrete Weibull (cDW) regression model for analyzing skewed count data.
• To enhance the robustness and accuracy of median-based regression for count outcomes with heavy upper tails.
• To provide a flexible modeling framework that accommodates lower truncation and structural zeros.

Main Methods:

• Developed a finite mixture model augmenting the Discrete Weibull distribution with a secondary, more dispersed component.
• Incorporated a single shifted-median link to maintain median-centered inference.
• Extended the model to handle general lower truncation (c=0 or c=1) and structural zeros via a hurdle framework.
• Employed Bayesian Markov chain Monte Carlo (MCMC) estimation using JAGS, with accompanying R code.

Main Results:

• The contaminated Discrete Weibull (cDW) regression demonstrated superior performance in handling extreme counts and stabilizing median-based coefficients compared to a single-component DW model.
• Application to hospital length-of-stay data showed reduced outlier influence and improved predictive accuracy (leave-one-out cross-validation, Kullback-Leibler diagnostic).
• Simulation studies confirmed accurate coefficient recovery and improved performance under heavy-tailed mixture settings.

Conclusions:

• The cDW regression model offers a robust, median-centered alternative for analyzing skewed and truncated count data, particularly those with heavy upper tails.
• The mixture approach effectively accommodates extreme values, leading to more reliable regression estimates.
• The model's flexibility, including truncation and hurdle extensions, makes it suitable for diverse count data applications.