The dependent variables of crime counts are significantly skewed and overdispersed (i.e., the variance exceeds the mean). Thus, we analyze the spatial distribution of crime using negative binomial regression in Stata 17; a Poisson-based regression that effectively accounts for overdispersion via its alpha parameter [49 , 50 ]. While the Poisson distribution can be appropriately used to model certain count variables, for the present study, we find that Stata’s likelihood-ratio test, which tests the null hypothesis that the dispersion parameter (alpha) is equal to zero, is significant for all our models (
p < 0.05). Negative binomial regression is therefore needed to account for overdispersion [49 , 50 ]. Yet at the same time, we acknowledge that ordinary least squares regression (OLS) is a viable alternative for modeling the spatial distribution of crime, especially given that a large majority of block groups do not have zero crime incidents, and therefore we have estimated ancillary models using OLS. To be clear, we are concerned with using the appropriate model(s) to analyze the spatial distribution of crime, however, it should be noted that negative binomial and OLS regression models are not representative of spatial regression. Therefore, we estimate ancillary spatial error models as a final robustness check (described in more detail below).
Geographic units such as block groups are not islands unto themselves [51 ], in fact, the conditions of spatially contiguous/adjacent units can very well shape what occurs in the focal unit—what is often referred to as a spillover effect. What this means for the current study is that crime in the focal block group is likely impacted by the amount of crime in nearby block groups [52 –54 (
link)]. To account for this spatial dependence, we constructed a spatially lagged measure for each crime outcome using GeoDa software with first-order queen contiguity. Such a measure captures the average number of crime incidents among contiguous block groups in relation to the focal block group. We include a spatially lagged measure of crime (as a predictor) in our full models.
A general expression of the (full) negative binomial regression models that we estimate is as follows:
where
y is the number of crime incidents, POW is the number of places of worship,
SD is a matrix of the sociodemographic characteristic measures,
CF is a matrix of the criminogenic facility measures, SLy is the average number of crime incidents in block groups adjacent to the focal block group (a spatially lagged measure), and α is an intercept.
While one approach for modeling crime across geographic units is to specify the population count as an exposure term (thereby estimating the outcome as a crime rate), we have instead modeled crime counts by including the population count as a predictor, given growing concerns over population count being the denominator of a calculated crime rate [e.g., see 18 , 55 (
link)–58 (
link)]. As anticipated, we detected minimal evidence of spatial autocorrelation in our full models as a result of including the spatially lagged measure of crime. Although the Moran’s I value was statistically significant in all instances, the maximum value was .08 (which is rather weak given that positive spatial autocorrelation ranges from 0 to 1). Furthermore, we assessed and found no evidence of multicollinearity issues based on variance inflation factors (VIF). The maximum VIF was 4.68, which does not exceed the commonly used cutoff of 10 [59 , 60 (
link)].
In the results section, we present two models for both the violent and property crime outcomes (
Table 2). We first estimate a
baseline model that features our places of worship measure along with the sociodemographic characteristic measures, consistent with the modeling approach undertaken by certain prior studies [for example, see 6 (
link), 8 (
link), 12 ]. We then estimate a
full model that additionally includes the measures of well-established criminogenic facilities and the spatially lagged measure of crime in order to determine the extent to which places of worship maintains a significant effect on crime (if at all). Crime and place researchers have called for analyses to integrate measures associated with social disorganization and routine activities theories simultaneously [for example see, 33 , 61 (
link)]; therefore, our full model is consistent with this call.
In addition to discussing the observed effects in terms of their direction and statistical significance, we highlight the magnitude of these effects in relation to one another. We draw on an approach that determines the percent change in the expected crime count
for a one standard deviation increase in the variable of interest using the following formula: (exp(β× SD)– 1) *100. This is a preferred approach because some of our independent variables drastically differ in terms of their scales [49: 492–493, 514–516.], most notably, the POW and facility measures are counts whereas the sociodemographic characteristic measures are percentages. Similar to previous crime and place studies [62 (
link)–65 (
link)] we utilize this approach to effectively compare the effect sizes of variables with substantively different scales.
On the other hand, we recognize that another common approach is to assess the magnitude of the effects using incident rate ratios (IRR). Specifically, an IRR denotes the percent increase or decrease
for every one-unit increase in a predictor by multiplying the difference between the IRR and one by 100 where positive values yield a percent increase and negative values yield a percent decrease [49 ]. In
Table 3, we compute the effect sizes using both approaches, although we base our inferences on the first approach because for the second approach, a one-unit increase may represent a very large increase for one predictor (e.g., DC Metro Station) and a very small increase for another predictor (e.g., population).
, & Wo J.C. (2023). Crime generators or social capital organizations? Examining the effects of places of worship on neighborhood crime. PLOS ONE, 18(3), e0282196.