A New Twist on an Old Approach: A Random-Interaction Approach for Estimating Rates of Inter-Group Interaction

Abstract

There are numerous instances in which researchers wish to measure the rate of intra-or inter-group interactions (whether positive or negative). When computing such measures as rates there is great uncertainty regarding the appropriate denominator: we analytically illustrate how the choice of the denominator when calculating such rates is not trivial and that some existing strategies create a built-in relationship between the computed rate and the group composition within the entity. Another strand of prior work only focused on the relative occurrence of intra-versus inter-group events, which does not account for the important theoretical possibility that both types of events might increase in certain social contexts. Our approach provides an advance over these earlier strategies as it allows one to take into account the relative frequency of interaction between members of different groups, but then translates this into per capita rates. We also provide an empirical example using data on inter-and intra-group robbery and aggravated assault events for block groups in a section of the city of Los Angeles to illustrate how our procedure works and to illustrate how other approaches can lead to dramatically different conclusions.

Hispanic Immigration and Black Violence at the Macro‐Level: Examining the Conditioning Effect of Victim Race/Ethnicity

“…In particular, racial/ethnicity diversity stands out for its negative association with black intragroup and (to a lesser extent) intergroup violence, consistent with other recent research (e.g., Hipp et al. , ). This finding may reflect improved externalities or enhanced bridging social capital that strengthen community social control and create opportunities for black advancement.…”

“…) as the denominator in computing crime rates. As Hipp, Tita, and Boggess () demonstrate, this method produces inconsistent rates because the rates are a function of the size of the two groups: in places that are predominantly black (or white or Hispanic), the correlation between the group size and the denominator introduces bias in the estimation of intergroup rates and can create built‐in relationships with the racial/ethnic composition of the place (e.g., between Hispanic immigration and black‐on‐Hispanic violence rates). As such, we follow Hipp et al.…”

“…As such, we follow Hipp et al. (, ) and calculate intra‐ and intergroup rates of violence that are adjusted to account for the different sizes of each racial/ethnic group and their likelihood of randomly interacting with each other in geographic space. Specifically, we calculate the conditional probabilities of random interaction for black‐on‐black offending as follows: where N B is the size of the black population in a given census place and N T is the total at‐risk population (ages 10–64; but see our supplemental models).…”

Living on the Edge: Neighborhood Boundaries and the Spatial Dynamics of Violent Crime

“…The negative binomial regressions model the number of crimes but do not standardize for a baseline (Hipp et al 2011;Osgood 2000). To account for variations in the size of the population across areas, I include population size (in 100s) as a control variable and in supplementary analysis as an offset.…”

The Transmission of Historical Racial Violence

“…Recognizing that interracial contact may be an important, but insufficient, catalyst of intergroup conflict, we include a ''random-interaction'' term in the logistic portion of the SEM (Jacobs & Wood, 1999). We calculate the random-interaction term using Hipp, Tita, and Boggess' (2011) …”