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In this paper, the third in a series illustrating the power of generalizedlinear models (GLMs) for the astronomical community, we elucidate the potentialof the class of GLMs which handles count data. The size of a galaxy's globularcluster population $N_{\rm GC}$ is a prolonged puzzle in the astronomicalliterature. It falls in the category of count data analysis, yet it is usuallymodelled as if it were a continuous response variable. We have developed aBayesian negative binomial regression model to study the connection between$N_{\rm GC}$ and the following galaxy properties: central black hole mass,dynamical bulge mass, bulge velocity dispersion, and absolute visual magnitude.The methodology introduced herein naturally accounts for heteroscedasticity,intrinsic scatter, errors in measurements in both axes (either discrete orcontinuous), and allows modelling the population of globular clusters on theirnatural scale as a non-negative integer variable. Prediction intervals of 99%around the trend for expected $N_{\rm GC}$comfortably envelope the data,notably including the Milky Way, which has hitherto been considered aproblematic outlier. Finally, we demonstrate how random intercept models canincorporate information of each particular galaxy morphological type. Bayesianvariable selection methodology allows for automatically identifying galaxytypes with different productions of GCs, suggesting that on average S0 galaxieshave a GC population 35% smaller than other types with similar brightness.

The Overlooked Potential of Generalized Linear Models in Astronomy-III: Bayesian Negative Binomial Regression and Globular Cluster Populations