Evaluation of Methods for Ecological Inference

Abstract

SUMMARY In ecological inference one uses data which are aggregated by areal units to investigate the behaviour of the individuals comprising those units. Aggregated data are readily available in many fields and within a wide variety of data structures. In the structures considered, the aggregate data are characterized by the absence of available data in the internal cells of a cross‐classification. The aim of the ecological methods is to estimate the expected frequencies of such internal cells, which may be conditional on chosen covariates. Four methods of ecological inference are reviewed and their properties and appropriateness considered. These methods are then applied to data for which the internal cells are known and their performances compared.

Combining Incompatible Spatial Data

“…Cleave, Brown, and Payne (1995) and King (1997) have provided critical discussions of some of these in the context of contingency table analysis where individuals are divided into areal units (e.g., census tracts, voting districts), and then cross-classi ed by other variables (e.g., sex, race). Often the cause of specication bias is the failure to incorporate relevant spatial information about individuals (e.g., Klein and Freedman 1993).…”

Ecological inference under unfavorable conditions: Straight and split-ticket voting in diverse settings and small samples

“…The Thomsen model is non-linear in its specification, which guards against these concerns and prevents the estimates of voting probabilities from falling outside of the logical range (0e1), a problem with other methods such as ecological regression (Goodman, 1953(Goodman, , 1959. The estimator has been demonstrated to provide favorable (Cleave et al, 1995) or superior estimates to other existing strategies, such as King's (1997) ecological inference method (Park, 2008a). Though the comparison of estimators is not our objective here, our analyses confirm that the Thomsen estimator consistently outperforms King's EI in estimating the outcomes of interest here (see more below, including Appendix Tables A and B, for a comparison of these estimates).…”

“…While collecting individual-level data would present a more straight-forward manner of addressing the relationship in question, the cost or availability of such data sets often leaves scholars with no choice but to use ecological inference techniques. This realization has spurred significant discussion and advances in the field (Achen and Shivley, 1995;Brown and Payne, 1986;Calvo and Escolar, 2003;Cleave et al, 1995;Elff et al, 2008;Greiner and Quinn, 2009;Shotts, 2003a,b, 2004;Johnston and Pattie, 2000;King, 1997;Rosen et al, 2001;Tam Cho, 1998;Tam Cho and Gaines, 2004;Thomsen, 1987;Wakefield, 2004), with a number of statistical techniques suggested to address the problem of ecological inference.…”

Simple Methods for Ecological Inference in 2×2 Tables

“…Both of these approaches can utilize group level covariates. The potential bene®t of using group level information about covariates is discussed by Cleave et al (1995) and King (1997). In both cases the covariates are used at the group level to explain some of the variation in the random coecients characterizing the relationship between the variables across the groups.…”

“…., G? Various methods of inference in this situation were evaluated by Cleave et al (1995). These included linear ecological regression as originally suggested by Goodman (1953Goodman ( , 1959) and a method based on an aggregated compound multinomial (ACM) model.…”