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Research & Reviews : Journal of Statistics Review Article

Modeling Dispersed Count Data: Evaluating the Conway–Maxwell–Poisson Regression with COVID-19 Mortality Data

  1. Nazmin Akter Department of Social Relations, East West University
  2. Md Rezaul Karim Department of Statistics and Data Science, Jahangirnagar University
  3. Sultana Begum Department of Statistics and Data Science, Jahangir Nagar

Abstract

Count data are prevalent in diverse fields such as biology, healthcare, psychology, and marketing, characterized by non-negativity and inherent heteroskedasticity, often exhibiting overdispersion or underdispersion. Traditional Poisson regression, which assumes equal mean and variance, is inadequate for such dispersed data. To address this, various generalized linear models (GLMs) and their extensions, including negative binomial (NB) and Conway–Maxwell–Poisson (CMP) regressions, are utilized. This study evaluates the performance of CMP regression compared to Poisson, NB, and generalized Poisson models using COVID-19 death data from Bangladesh. The CMP distribution, a flexible two-parameter generalization of the Poisson distribution, accommodates both overdispersion and underdispersion, enhancing model accuracy. Model comparisons based on the Akaike Information Criterion (AIC) indicate that the CMP model, influenced by temperature and humidity, provides the best fit with the lowest AIC value. The next-best models, NB, and generalized Poisson show significantly higher AIC values, underscoring CMP's superiority. Results indicate that while NB and CMP regressions provide superior accuracy over the Poisson model, CMP regression demonstrates the best fit in terms of log-likelihood and AIC. This research underscores the CMP distribution's efficacy and highlights the importance of using appropriate models for dispersed count data. Advances in computational power have enabled the revival and application of CMP regression, offering new insights into discrete data modeling.

Keywords

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