A Generation of Ecological Regression: A Survey and Synthesis

Much of this material was later incorporated into the published paper “Ecological Inference from Goodman to King.” After discussing the essential problem of inferring individual behavior from statistics on aggregate quantities, such as precincts or counties, the paper lays out Leo Goodman’s 1959 method in detail. It then moves on to two alternatives to Goodman’s technique: “homogeneous areas” and the “method of bounds.” Focusing only on homogeneous areas leaves out places in which the demography of the population was more complex, and in any event, there may be too few such segregated areas to generalize from in a particular data set.
The method of bounds usually does not, by itself, constrain estimates enough to be very useful, and it is usually difficult to justify further constraining assumptions. I then take up two alternative interpretations of the Goodman’s statistics, the “linear neighborhood model” and the “nonlinear neighborhood model,” both of which represented efforts in voting rights cases to deny the possibility of proving racially polarized voting. Instead of assuming, as Goodman’s model (ER) does that, for example, all white people have the same tendency to vote Republican, whatever county they live in, the bivariate neighborhood model (BLN) assumes that all people in each county have the same tendency to vote Republican, whatever their racial identities. It seems strange that under BLN, race, for instance, explains everything about voting behavior on
the county level, but has no influence on how individuals of different races vote. Because the estimating equations for BER and BLN are identical, the only ways to choose between them are to use other information, such as polls or a sequence of elections or qualitative information or theories of political behavior, or to examine patterns in the aggregate data, perhaps leading to the estimation of different models for subsets of the data or the inclusion of other variables in the estimating equations. Is it plausible to believe that Black and white people voted identically in each county or precinct in elections suffused with racial issues? Close examination of patterns in
the data, especially scatterplots, may suggest that other equations, perhaps involving further variables, should be estimated. In some cases, these other equations may eliminate seeming anomalies in the original estimates and explain much more of the variation in the dependent variables, such as political parties. But a discussion of more complicated models and their substantive interpretations supports the position of Justice William J. Brennan, Jr. in the Gingles case that the proper measure of racially polarized voting is one without controls for partisanship, incumbency, campaign resources, or other variables that are themselves usually correlated with race.