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In many educational settings, count data arise that should not be considered realizations of the Poisson model. School days suspended represents an exemplary case of count data that may be zero-inflated and overdispersed relative to the Poisson model after controlling for explanatory variables. This study examined the performance of two models of school days suspended - the zero-inflated negative binomial and the negative binomial hurdle. This study aimed to understand whether the conditions considered would elicit comparable and/or disparate performance between these models. Additionally, this study aimed to understand the consequences of model misspecification when the data-generating mechanism was improperly specified. This study found that the negative binomial hurdle performed better in both simulation studies. Based on the conditions considered here, it is recommend that researchers consider the negative binomial hurdle model over the zero-inflated negative binomial model especially if the structural zero/zero parameters are to be treated as nuisance parameters or the presence of structural zeros is unknown. If structural zeros are expected, and interest is in these parameters, then the zero-inflated negative binomial should still be considered. Additionally, if interest is in the non-structural zero/count parameters, the results here suggest model misspecification has little effect on these parameters, and a researcher may select a model based on the parameters they are interested in interpreting.