A Spatial Negative Binomial Regression of Individual-level Count Data with Regional and Person-Specific Covariates

The relationship between conditions in the local environment and individual-level behavior is of general interest to many fields of research. Unfortunately, researchers often encounter situations where individuals’ locations are reported at the region-level, and modeling individual-level outcomes as a function of region-level data introduces the potential for biased estimates. We show analytically, via simulation, and through an empirical illustration that using region-level covariates in the popular Negative Binomial Regression with count outcomes leads to biased coefficients, which may also be statistically significant. To overcome this problem, we develop a new hierarchical Bayesian spatial model that extends the standard Negative Binomial Regression. The proposed model of individual-level count outcomes properly accounts for observed region-level covariates and unobserved spatial autocorrelation. The model is illustrated on Internet retailing data from Philadelphia and Manhattan.