Ecological inference is a statistical technique used to infer individual behavior from aggregate data. A particularly relevant instance of ecological inference involves the estimation of the inner cells of a set of R × C related contingency tables when only their aggregate margins are known. This problem spans multiple disciplines, including quantitative history, epidemiology, political science, marketing, and sociology. This paper proposes new models for solving the problem using the latent structure theory, and presents the ecolRxC package, an R implementation of this methodology. This article exemplifies, explains, and statistically documents the new extensions and, using real inner cell election data, shows how the new models in ecolRxC lead to significantly more accurate solutions than ecol and VTR, two Stata routines suggested within this framework. ecolRxC also holds its own against ei.MD.bayes and nslphom, the two algorithms currently identified in the literature as the most accurate to solve this problem. ecolRxC records accuracies as good as those reported for ei.MD.bayes and nslphom. Besides, from a theoretical perspective, ecolRxC stands up for modeling a causal theory of political behavior to build its algorithm. This distinguishes it from other procedures proposed from different frameworks (such as ei.MD.bayes and nslphom) which model expected behaviors, instead of modeling how voters make choices based on their underlying preferences as ecolRxC does.

The link between objective facts and politically relevant beliefs is an essential mechanism for democratic accountability. Yet the bulk of empirical work on this topic measures objective facts at whatever geographic units are readily available. We investigate the implications of these largely arbitrary choices for predicting individual-level opinions. We show that varying the geographic resolution—namely aggregating economic data to different geographic units—influences the strength of the relationship between economic evaluations and local economic conditions. Finding that unemployment claims are the best predictor of economic evaluations, especially when aggregated at the commuting zone or media market level, we underscore the importance of the modifiable areal unit problem. Our methods provide an example of how applied scholars might investigate the importance of geography in their own research going forward.

Ecological inference (EI) is the process of learning about individual behavior from aggregate data. We relax assumptions by allowing for “linear contextual effects,” which previous works have regarded as plausible but avoided due to nonidentification, a problem we sidestep by deriving bounds instead of point estimates. In this way, we offer a conceptual framework to improve on the Duncan–Davis bound, derived more than 65 years ago. To study the effectiveness of our approach, we collect and analyze 8,430 $2\times 2$ EI datasets with known ground truth from several sources—thus bringing considerably more data to bear on the problem than the existing dozen or so datasets available in the literature for evaluating EI estimators. For the 88% of real data sets in our collection that fit a proposed rule, our approach reduces the width of the Duncan–Davis bound, on average, by about 44%, while still capturing the true district-level parameter about 99% of the time. The remaining 12% revert to the Duncan–Davis bound.

Social scientists are frequently interested in how populations evolve over time. Creating poststratification weights for surveys, for example, requires information on the weighting variables’ joint distribution in the target population. Typically, however, population data are sparsely available across time periods. Even when population data are observed, the content and structure of the data—which variables are observed and whether their marginal or joint distributions are known—differ across time, in ways that preclude straightforward interpolation. As a consequence, survey weights are often based only on the small subset of auxiliary variables whose joint population distribution is observed regularly over time, and thus fail to take full advantage of auxiliary information. To address this problem, we develop a dynamic Bayesian ecological inference model for estimating multivariate categorical distributions from sparse, irregular, and noisy data on their marginal (or partially joint) distributions. Our approach combines (1) a Dirichlet sampling model for the observed margins conditional on the unobserved cell proportions; (2) a set of equations encoding the logical relationships among different population quantities; and (3) a Dirichlet transition model for the period-specific proportions that pools information across time periods. We illustrate this method by estimating annual U.S. phone-ownership rates by race and region based on population data irregularly available between 1930 and 1960. This approach may be useful in a wide variety of contexts where scholars wish to make dynamic ecological inferences about interior cells from marginal data. A new R package estsubpop implements the method.

Political scientists are increasingly interested in the geographic distribution of political and economic phenomena. Unlike distribution measures at the individual level, geographic distributions depend on the “unit question” in which researchers choose the appropriate political subdivision to analyze, such as nations, subnational regions, urban and rural areas, or electoral districts. We identify concerns with measuring geographic distribution and comparing distributions within and across political units. In particular, we highlight the potential for threats to inference based on the modifiable areal unit problem (MAUP), whereby measuring concepts at different unit aggregations alters the observed value. We offer tangible options for researchers to improve their research design and data analysis to limit the MAUP. To help manage the measurement error when the unit of observation is unclear or appropriate data are not available, we introduce a new measure of geographic distribution that accounts for fluctuations in the scale and number of political units considered. We demonstrate using Monte Carlo simulations that our measure is more reliable and stable across political units than commonly used indicators because it reduces measurement fluctuations associated with the MAUP.