  The scaling relation between the size of a galaxy's globular cluster (GC)
population ($N_{GC}$) and the galaxy's stellar mass ($M_*$) is usually
described with a continuous, linear model, but in reality it is a count
relationship that should be modeled as such. For massive galaxies, a negative
binomial (NB) model has been shown to describe the data well, but it is unclear
how the scaling relation behaves at low galaxy masses where a substantial
portion of galaxies have $N_{GC}=0$. In this work, we test the utility of
Poisson and NB models for describing the low-mass end of the $N_{GC}-M_*$
scaling relation. We introduce the use of zero-inflated versions of these
models, which allow for larger zero populations (e.g. galaxies without GCs)
than would otherwise be predicted. We evaluate our models with a variety of
predictive model comparison methods, including predictive intervals,
leave-one-out cross-validation criterion, and posterior predictive comparisons.
We find that the NB model is consistent with our data, but the naive Poisson is
not. Moreover, we find that zero inflation of the models is not necessary to
describe the population of low-mass galaxies that lack GCs, suggesting that a
single formation and evolutionary process acts over all galaxy masses. Under
the NB model, there does not appear to be anything unique about the lack of GCs
in many low-mass galaxies; they are simply the low-mass extension of the larger
$N_{GC}-M_*$ scaling relation.
