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.
