Ecological Inference Methods Research Articles

An ecological inference approach to the origins of proportional representation

Facing a prospective majority of socialists during the early third of the 20th century, some secular conservative and liberal parties pooled their votes to raise the majority threshold for the left, while others raised it by enacting some form of proportional representation. We use vote transfers, estimated by a new method of ecological inference, to explain those far-reaching choices. We provide a new conceptualization and measurement of the segmentation of the electoral market to test a proposition within the Boix-Rokkan framework: proportional representation reform was chosen when vote transfers foretold coalition failure. To substantiate our claim, we investigate two most similar cases, Denmark during 1910–1918 and New Zealand during 1928–1931, that diverged in the explanatory variable and in the response.

Validating the Applicability of Bayesian Inference with Surname and Geocoding to Congressional Redistricting

AbstractEnsuring descriptive representation of racial minorities without packing minorities too heavily into districts is a perpetual difficulty, especially in states lacking voter file race data. One advance since the 2010 redistricting cycle is the advent of Bayesian Improved Surname Geocoding (BISG), which greatly improves upon previous ecological inference methods in identifying voter race. In this article, we test the viability of employing BISG to redistricting under two posterior allocation methods for race assignment: plurality versus probabilistic. We validate these methods through 10,000 redistricting simulations of North Carolina and Georgia’s congressional districts and compare BISG estimates to actual voter file racial data. We find that probabilistic summing of the BISG posteriors significantly reduces error rates at the precinct and district level relative to plurality racial assignment, and therefore should be the preferred method when using BISG for redistricting. Our results suggest that BISG can aid in the construction of majority-minority districts during the redistricting process.

On the Radical Views of Coal Miners in the Early Twentieth Century in Southern Illinois

There has been great interest in the Southern Illinois mine war by historians. An explanation has been that this war was caused by miners who had radical political beliefs. We examine this view by applying four methods of ecological inference to estimate the proportion of coal miners who were socialist voters in this time period. Based on these results (especially considering the assumptions of the methods) we conclude that miners were politically less radical than previously thought.

On the Radical Views of Coal Miners in the Early Twentieth Century in Southern Illinois

There has been great interest in the Southern Illinois mine war by historians. An explanation has been that this war was caused by miners who had radical political beliefs. We examine this view by applying four methods of ecological inference to estimate the proportion of coal miners who were socialist voters in this time period. Based on these results (especially considering the assumptions of the methods) we conclude that miners were politically less radical than previously thought.

Global and localized neighborhood effects on public transit ridership in Baton Rouge, Louisiana

This study examines what socio-demographic and spatial factors explain the variation of public transit ridership in a medium-size city in southern U.S. – Baton Rouge, Louisiana. In order to gain a sharper spatial resolution in the analysis, the ecological inference method is used to disaggregate socio-demographic data from the census block group level to the census block level. Monte Carlo simulation and transit schedule data are used to improve the estimation of travel time by private vehicle and public transit, respectively, also at the census block level. The semi-parametric geographically-weighted regression (SGWR) is used to identify, among significant variables, what are global factors and what are local factors. The results indicate that neighborhoods with higher concentrations of non-White minorities, recent immigrants and carless households have positive global effects on public transit ridership. The effects by neighborhood median income, public transit to private vehicle commuting time ratio, and accessibility to employment via public transit are localized or vary across the study area, and some of these variables even show opposite effects in specific pockets in contrast to their area-wide average effects.

Analyzing Grouped Administrative Data for RCTs Using Design-Based Methods

This article discusses estimation of average treatment effects for randomized controlled trials (RCTs) using grouped administrative data to help improve data access. The focus is on design-based estimators, derived using the building blocks of experiments, that are conducive to grouped data for a wide range of RCT designs, including clustered and blocked designs, and models with weights and covariates. Because of the linearity of the regression model underlying RCTs, the asymptotic properties of design-based estimators using group-level averages—formed randomly or by covariates for nonclustered designs and as cluster-level averages for clustered designs—match those using individual data. Furthermore, design effects from aggregation are tolerable with moderate numbers of groups and few covariates, suggesting little information is lost in these cases. Ecological inference methods for subgroup analyses, however, yield large design effects. Several empirical examples using real-world education RCT data demonstrate the theory.

Ecological Fallacy and Covariates: New Insights based on Multilevel Modelling of Individual Data

SummaryThe paper provides a new and more explicit formulation of the assumptions needed by the ordinary ecological regression to provide unbiased estimates and clarifies why violations of these assumptions will affect any method of ecological inference. Empirical evidence is obtained by showing that estimates provided by three main ecological inference methods are heavily biased when compared with multilevel logistic regression applied to a unique set of individual data on voting behaviour. The main findings of our paper have two important implications that can be extended to all situations where the assumptions needed to apply ecological inference are violated in the data: (i) only ecological inference methods that allow one to model the effect of covariates have a chance to produce unbiased estimates, and (ii) there are certain data generating mechanisms producing a kind of bias in ecological estimates that cannot be corrected by modelling the effect of covariates.

An evaluation of the performance and suitability of R\xa0\xd7\xa0C methods for ecological inference with known true values

Ecological inference refers to the study of individuals using aggregate data and it is used in an impressive number of studies; it is well known, however, that the study of individuals using group data suffers from an ecological fallacy problem (Robinson in Am Sociol Rev 15:351–357, 1950). This paper evaluates the accuracy of two recent methods, the Rosen et al. (Stat Neerl 55:134–156, 2001) and the Greiner and Quinn (J R Stat Soc Ser A (Statistics in Society) 172:67–81, 2009) and the long-standing Goodman’s (Am Sociol Rev 18:663–664, 1953; Am J Sociol 64:610–625, 1959) method designed to estimate all cells of R × C tables simultaneously by employing exclusively aggregate data. To conduct these tests we leverage on extensive electoral data for which the true quantities of interest are known. In particular, we focus on examining the extent to which the confidence intervals provided by the three methods contain the true values. The paper also provides important guidelines regarding the appropriate contexts for employing these models.

Tracing the electorate of the MoVimento Cinque Stelle: an ecological inference analysis

The 2013 Italian parliamentary election was characterized by the outstanding performance of the MoVimento Cinque Stelle, which in its first participation in a general election obtained a remarkable 25% of the national vote. Where did these votes come from? Furthermore, is it possible to observe different electoral dynamics across geographical areas of Italy? In order to address these questions, we first estimate the flow of votes between the 2008 and 2013 general elections by applying an ecological inference method – the Goodman model – to the entire Italian voting population, and then we take a closer look at the differences in the four geopolitical areas in which Italy is traditionally divided. We find that the extraordinary performance of the MoVimento 5 Stelle was largely due to its capacity of attracting similar amounts of former Partito Democratico and Popolo della Libertà supporters, as well as a considerable amount of voters from their traditional allies: Lega Nord and Italia dei Valori. The MoVimento 5 Stelle was also able to mobilize previous non-voters. We shed light on the territorial features of these dynamics.

Evidence in Voting Rights Act Litigation: Producing Accurate Estimates of Racial Voting Patterns

Abstract Voting Rights Act litigation, even in the wake of Shelby County v. Holder, requires estimates of racial bloc voting, or the extent to which members of different racial groups vote differently. Although there are a variety of methods to make these estimates, direct evaluation and comparison of these methods is lacking. I examine these alternate methods in the way that they might be used in litigation using a large dataset of partisanship and racial information at the precinct level in five states. Additionally, I extend the application of these methods to estimation of racial group preferences in locations with more than one racial minority and assess the contextual determinants of larger and smaller errors in ecological regression estimates. I conclude that the ecological inference method developed by King (1997), which incorporates the deterministic precinct-level bounds on the quantities of interest and is easily implemented using open-source software, provides the best estimates for precinct-s...

Using Experiments to Estimate Racially Polarized Voting

“Racial polarization,” the linchpin issue in so-called vote dilution cases, has traditionally been measured using observational data and methods of ecological inference. However, strategic behavior by voters, potential candidates, and other political actors can make it difficult to infer polarization in political preferences from polarization in vote shares. We present a conjoint stated-preference experiment for investigating racial polarization and associated questions about disparate treatment of minority candidates. The design yields measures of racial polarization and disparate treatment, and can guide courts in their use of observational data.

Racially Polarized Voting in a Southern U.S. Election: How Urbanization and Residential Segregation Shape Voting Patterns

This paper advances a model of racially polarized voting that captures the intervening effects of urbanization and residential segregation on white voters’ political behavior. The model is tested for a 2011 referendum election in the U.S. state of Mississippi. Using King’s method of ecological inference and weighted least squares regression, we find that regional minority population size impacts white opposition to minority-preferred political alternatives both directly and indirectly through an effect on residential racial segregation. Importantly, these influences hinge on intra-regional patterns of urbanization. The findings have important implications for understanding spatial variation in regional political behavior and intergroup relations.

Racial Voting and Geography in the United States

Voters express varied levels of support for the parties’ candidates depending on where they live, be it in the South (Aldrich 1995; Carmines and Stimson 1989) or rural and urban sub-regions (Gimple and Karns 2006; McKee 2008). This difference is especially pronounced among Whites, leading to varying levels of polarization based on race depending on region and sub-region of the country. To investigate this variation, we develop a new national dataset of 2008 presidential election results within 169,304 precincts merged with census demographic data. We apply methods of ecological inference to these data to estimate voting patterns among racial and ethnic groups nationally, within sections of the country, and ultimately at the precinct level. We then use these estimates to derive a measure of racial polarization at the congressional district level, and use it to predict behavior among members of the U.S. House on roll call votes identified by the NAACP as being related to civil rights. We find that polarization especially affects Democratic members in these cases, as they may need to bring together coalitions of minority voters who have favorable opinions on these issues and White voters who do not.

Ecological Inference and Spatial Variation of Individual Behavior: National Divide and Elections inCatalonia

When in geography one reconstructs individual behavior starting from aggregated data through ecological inference, a crucial aspect is the spatial variation of individual behavior. Basic ecological inference methods treat areas as if they were all exchangeable, which in geographical applications is questionable due to the existence of contextual effects that relate to area location and induce spatial dependence. Here that assumption is avoided by basing ecological inference on a model that simultaneously does a cluster analysis, grouping together areas with similar individual behavior, and an ecological inference analysis in each cluster, estimating the individual behavior in the areas of each group. That allows one to capture most of the spatial dependence and summarize the individual behavior at a local level through the behavior estimated for each cluster. This approach is used to investigate vote switching inCatalonia, where voters split across a national allegiance divide on top of the ideological divide. That leads toCatalans having a lot of options to choose from, and to them voting differently depending on whether the election is for theCatalan parliament or for theSpanish parliament. To investigate that, the results in the two most recent pairs of such elections are analyzed by simultaneously clustering areas based on the similarity of their vote and vote switch patterns, and estimating one vote switch pattern for each cluster. As a result,Catalonia is partitioned into four clusters that have a strong spatial structure, with all the areas in the same cluster having similar demographic composition. The estimated vote switch patterns are quite different across clusters but very similar across pairs of elections, and they help assess how the differential voter turnout and the strategic dual vote effects vary in space.

A cluster analysis of vote transitions

To help settle the debate triggered the day after any election around the origin and destination of the vote of winners and losers, a Bayesian analysis of the results in a pair of consecutive elections is proposed. It is based on a model that simultaneously carries out a cluster analysis of the areas in which the results are broken into and links the results in the two elections of areas in a given cluster through a vote switch matrix. The number of clusters is chosen both through predictive checks as well as by testing whether the residuals are spatially correlated or not. The analysis is tried on the results in Barcelona of a pair of consecutive elections held just four months apart, in 2003 for the Catalan parliament and in 2004 for the Spanish parliament. The proposed approach, which reconstructs individual behavior from aggregated data, can be exported to be a solution for any ecological inference problem where one cannot assume that all the areas are exchangeable the way typically assumed by other ecological inference methods.

Where did the votes go? Reassessing American party realignments via vote transfers between major parties from 1860 to 2008

Political scientists have long debated theories of electoral party realignments. In this paper, we apply ecological inference methods to statistically analyze the transfer of votes within counties in US presidential elections since 1860. Through this analysis we are able to identify the major periods of party realignment in US history and the counties where these shifts took place. As a result, we are able to provide new insights into American electoral history, and provide strong evidence that the 2008 presidential election did not represent a realigning election as the phrase is generally understood.

The emergence of right-wing radicalism at the local level in Spain: the Catalan case

In spite of being considered an example of failure of the radical right, Spain has seen for the first time since the restoration of democracy how some extreme parties got representation in the last 2003 and 2007 local elections. This article focuses on the most successful among these parties, namely the Plataforma per Catalunya. We suggest that partisan conversion of socialist voters and mobilization of former abstainers are the main origin of radical votes. By contrast, new cohorts of voters and swings from right-wing voters or nationalist voters do not have an influence. The results are triangulated with two methods of ecological inference that allow us to estimate the proportion of individuals who changed their vote in one direction or the other across two consecutive elections.

Ecological Inference Techniques: An Empirical Evaluation Using Data Describing Gender and Voter Turnout at New Zealand Elections, 1893–1919

Summary The difference, if any, between men’s and women’s voting patterns is of particular interest to historians of gender and politics. For elections that were held before the introduction of opinion surveying in the 1940s, little data are available with which to estimate such differences. We apply six methods for ecological inference to estimate men’s and women’s voting rates in New Zealand (NZ), 1893–1919. NZ is an interesting case-study, since it was the first self-governing country where women could vote. Furthermore, NZ officials recorded the voting rates of men and women at elections, making it possible to compare estimates produced by methods for ecological inference with known true values, thus testing the efficacy of different methods for ecological inference for this data set. We find that the most popular methods for ecological inference, namely Goodman’s ecological regression and King’s parametric method, give poor estimates, as does the much debated neighbourhood method. However, King’s non-parametric method, Chambers and Steel’s semiparametric method and the Steel, Beh and Chambers homogeneous approach all gave good estimates that were close to the known values, with the homogeneous approach performing best overall. The success of these methods in this example suggests that ecological inference may be a viable option when investigating gender and voting. Moreover, researchers using ecological inference in other fields may do well to consider a range of statistical methods. This work is a significant NZ contribution to historical politics and the first quantitative contribution, in the area of NZ gender and politics.

The Social Bases of Political Parties in Argentina, 1912–2003

To what extent has the Argentine party system been polarized along class lines? The political historiography gives mixed and contradictory answers to this question. We explore the social bases of Argentina's political parties using an original database, the most comprehensive database of Argentine elections yet assembled, and new methods of ecological inference that yield more reliable results than previous analyses. We identify two distinct party systems, one in place between 1912 and 1940, the other emerging after 1946. The first party system was not consistently class based, but the second was, with the Radical Party representing the middle classes and the Peronists, workers and the poor. Still, there were important exceptions. Lower-class support for the Peronists, as proxied by literacy rates, declined during Perón's exile, which implies that the party had trouble mobilizing lower-class illiterate voters. Since the return to democracy in 1983, class polarization has again found some expression in the party system.

Voting Green*

Objectives. Economics, partisanship, and demographics have all been identified as linked to support for environmental protection. The principal objective of this study is to extend the extant literature by using a larger data set and a variety of methods.Methods. We use variety of statistical methods to test measures of party strength, demographics, and economics against county‐level data from 29 environmental initiative elections in 13 states.Results. Democratic partisanship is the most consistent predictor of aggregate support for environmental measures. This trend holds through pooled, individual‐level, and ecological inference analysis. Median family income and income squared are consistently significant, as is education.Conclusion. Based on these data, we reach three general conclusions. First, while several variables are consistently significant, party strength is the most consistent predictor of pro‐environmental voting across states and initiatives. Second, our analyses suggest that limiting analyses to data from a single state or region may have important implications for statistical inferences. Lastly, a preliminary analysis using methods of ecological inference suggests that the aggregate results are robust to ecological problems.