Abstract
Regression models are extensively used to explore the relationship between a dependent variable and its covariates. These models work well when the dependent variable is categorical and the data are supposedly independent, as is the case with generalized linear models (GLMs). However, trait data from related species do not operate under these conditions due to their shared common ancestry, leading to dependence that can be illustrated through a phylogenetic tree. In response to the analytical challenges of count-dependent variables in phylogenetically related species, we have developed a novel phylogenetic negative binomial regression model that allows for overdispersion, a limitation present in the phylogenetic Poisson regression model in the literature. This model overcomes limitations of conventional GLMs, which overlook the inherent dependence arising from shared lineage. Instead, our proposed model acknowledges this factor and uses the generalized estimating equation (GEE) framework for precise parameter estimation. The effectiveness of the proposed model was corroborated by a rigorous simulation study, which, despite the need for careful convergence monitoring, demonstrated its reasonable efficacy. The empirical application of the model to lizard egg-laying count and mammalian litter size data further highlighted its practical relevance. In particular, our results identified negative correlations between increases in egg mass, litter size, ovulation rate, and gestation length with respective yearly counts, while a positive correlation was observed with species lifespan. This study underscores the importance of our proposed model in providing nuanced and accurate analyses of count-dependent variables in related species, highlighting the often overlooked impact of shared ancestry. The model represents a critical advance in research methodologies, opening new avenues for interpretation of related species data in the field.