A Likelihood-Based Multiple Change Point Algorithm for Count Data with Allowance for Over-dispersion: A Case of COVID-19 Infections in Kenya

Abstract

Count data frequently exhibit over-dispersion, where the variance exceeds the mean, limiting the effectiveness of conventional changepoint detection methods that assume equi-dispersion. ThisstudyaddressesthislimitationbydevelopingahybridLikelihood Based Negative Binomial Multiple Changepoint Algorithm (NBMCPA) capable of detecting multiple changepoints in both equi-dispersed and over-dispersed count pro cesses within a unified framework. The algorithm exploits the limiting relationship between the Negative Binomial and Poisson distributions, allowing a single likelihood formulation for both data types. It integrates Stepwise Recursive Binary Segmentation, maximum likelihood estimation, and likelihood ratio testing to identify statistically significant changepoints, while Monte Carlo simulation provides critical values for reliable statistical inference. Performance is evaluated using simulated datasets with varying sample sizes and changepoint locations. Results show that the algorithm accu rately detects true changepoints with low false detection rates, with detection accuracy improving as sample size increases. Application to daily averaged COVID-19 infection data from Kenya (March 2020–August 2021) identified four statistically significant changepoints corresponding to major epidemiological developments and public health interventions. Lag analysis showed that observable changes in infection trends oc curred, on average, approximately 38 days after policy implementation, while infection peaks followed interventions by about one week. The study introduces a novel hybrid likelihood-based framework thatextendsexistingchangepointmethodologybyunifying the analysis of equi-dispersed and over-dispersed count data within a single Negative Binomial likelihood approach. The proposed algorithm provides a robust, flexible, and computationally efficient tool for detecting structural changes in count data, with applications in epidemiology, public health surveillance, environmental monitoring, finance, and industrial quality control.