This is an example of a sampling zero.Ī logistic model is used model the state of sampling versus structural zeros, which contains an intercept and regressors for camera, race, and the interaction term between them (Zeileis, Kleiber, & Jackman). Randolph County, in North Carolina, had one shooting in 2015 and zero in 2016. In the context of this study, we assume that the sampling zeros can be explained by the fact that in certain counties, there is a natural fluctuation to the rate of officer-involved shootings from year to year. The sampling zeros are modeled with a Poisson or negative binomial distribution, and we assume that those zero observations happened by chance. The figure below shows a zero-inflated Poisson model with the zero observations split between structural zeros and sampling zeros. Zero-inflated models, in which the outcome can assume either a Poisson or negative binomial distribution, have been developed to express two different origins of zero observations: “structural” and “sampling” (Hu, Pavlicova, & Nunes). This characteristic of the data results in the variance exceeding the mean in the observed distribution, resulting in what is referred to as “overdispersion.” A few analytical methods have been developed to address overdispersion in social science inquiry, and in this report I explore one such method, the zero-inflated model. However, when considering the count of officer-involved shootings in each county, there is a large frequency of zero-count observations. To refresh, when estimating a Poisson regression, we assume that the mean is equal to the variance. Up until now, I have discussed the presence of overdispersion in these data, but failed to analytically address the issue.
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