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

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.