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Logical Inconsistency in EI‐Based Second‐Stage Regressions
Abstract
The statistical procedure EI–R, in which point estimates produced by the King (1997) ecological inference technique are used as dependent variables in a linear regression, can be logically inconsistent insofar as the assumptions necessary to support EI–R's first stage (ecological inference via King's technique) can be incompatible with the assumptions supporting its second stage (linear regression). In light of this problem, we develop a specification test for logical consistency of EI–R and describe options available to a researcher who confronts test rejection. We then apply our test to the implementation of EI–R in Burden and Kimball's (1998) study of ticket splitting and find that this implementation is logically inconsistent. In correcting for this problem we show that Burden and Kimball's substantive results are artifacts of a self-contradictory statistical technique.
... ''Is it true that the double-regression method has 'no scientific justification of continued application' (Zax 2002:85)?'' 2 Finally, the data sets adopted here have not only the major variables at the precinct level needed to do traditional ecological regressions, neighborhood models, and King's EI procedures, but they also have other important contextual information that can serve as the covariates in the extended King's EI model. 3 Therefore, we can also test the validity of the suggestion that only King's EI extended model may avoid the problem of ecological inconsistency in a second-stage analysis (Herron and Shotts 2004). ...
... Some scholars suggested that combining King's EI with other statistical techniques, such as a geographically weighted approach, may help resolve some of the assumption violation problems, especially spatial aggregation bias (see Calvo and Escolar 2003). Others indicated that using King's EI estimates blindly in a second-stage regression analysis may cause serious logical inconsistency problem (Herron and Shotts 2004; see below for a discussion of this problem). It is interesting that the King's EI extended model, rather than its basic model, which King himself argues as ''robust'' and has been widely used in academic research and voting rights litigations, may actually provide the best hope to save King's EI from the violations of model assumptions, especially the existence of contextual effect and logical inconsistency (Herron and Shotts 2004). ...
... Others indicated that using King's EI estimates blindly in a second-stage regression analysis may cause serious logical inconsistency problem (Herron and Shotts 2004; see below for a discussion of this problem). It is interesting that the King's EI extended model, rather than its basic model, which King himself argues as ''robust'' and has been widely used in academic research and voting rights litigations, may actually provide the best hope to save King's EI from the violations of model assumptions, especially the existence of contextual effect and logical inconsistency (Herron and Shotts 2004). ...
Most existing models of ecological inference are based on the assumption that there is no aggregation bias. Few studies have focused on how to correct/ model aggregation bias. This article takes advantage of a unique opportunity to compare the controversial ecological inference methods by using aggregate as well as individual-level data from an actual election. Furthermore, the true quantities of interest are also available, which guarantees the accuracy of the empirical tests. Our mean squared error analyses show that King's Ecological Inference (EI) basic model does not always outperform the traditional ecological regression and neighborhood methods when aggregation bias does exist. However, using an appropriate covariate in the King's EI extended model to correct the aggregation bias problem can drastically improve the estimation accuracy at both the precinct and district levels. This article also makes suggestions on how to use a covariate in a King's extended model.
... Therefore I need to include all independent variables from this regression as covariates in the first estimation (see Herron and Shotts, 2004). For the other sectors I also tried covariates, but the results did not perceptibly vary. ...
... First, I exclude any quantities not originally included as covariates in the first-stage estimation as independent variables in EI-R. Second, I apply weighted least squares using the estimated standard errors from the first-stage estimation as weights, as recommended by Herron and Shotts (2004). ...
Mexican immigrants were historically clustered in a few cities, mainly in California and Texas. During the past 15 years, however, arrivals from Mexico established sizeable immigrant communities in many “new” cities. We explore the causes and consequences of the widening geographic diffusion of Mexican immigrants. A combination of demand-pull and supply push factors explains most of the inter-city variation in inflows of Mexican immigrants over the 1990s, and also illuminates the most important trend in the destination choices of new Mexican immigrants – the move away from Los Angeles. Mexican inflows raise the relative supply of low-education labor in a city, leading to the question of how cities adapt to these shifts. One mechanism, suggested by the Hecksher Olin model, is shifting industry composition. We find limited evidence of this mechanism: most of the increases in the relative supply of loweducation labor are absorbed by changes in skill intensity within narrowly defined industries. Such adjustments could be readily explained if Mexican immigrant inflows had large effects on the relative wage structures of different cities. As has been found in previous studies of the local impacts of immigration, however, our analysis suggests that relative wage adjustments are small.
... There are several limitations in the particular data used in the study that potentially circumscribe the interpretation of the findings. First, despite efforts to overcome the ecological problem, the use of ecological inference models to estimate racial group vote choice in the Oakland and San Francisco elections may cast doubt on the precision of the vote choice data (Achen and 20 Shively 1995;Calvo and Escolar 2003;Cho and Manski 2008;Herron and Shotts 2004). Studies have also suggested that exit poll surveys can be biased when it comes to estimating vote by racial group (Barreto et al. 2006). ...
... Since Robinson's critique, however, new and more sophisticated statistical techniques and methods have been developed to analyze aggregate level data, greatly aided by the increased power of computers. As a result, we have witnessed an increased interest in these models and in debates over the appropriateness of the different models (see Freedman et al., 1991;Grofman, 1991;Achen and Shively, 1995;King, 1997;Cho, 1998, Cho andGaines, 2004;Herron and Shotts, 2004;King et al., 2004;Wakefield, 2004;Imai et al., 2008). These new statistical techniques allow the use of 'ecological regressions' to make ecological inferences while avoiding the ecological fallacy. ...
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.
... In these cases, the researcher must be fully aware of the numerous pitfalls that may ensue (p.169). (See also Herron and Shotts, 2004.) Elsewhere, in a review of Burden and Kimball's (2002) book on the same subject, they have again questioned the validity of the splitticket voting estimates, concluding that because of the 'shaky statistical foundations of EI …decomposing aggregate data may eventually shed new light on ticketsplitting . ...
... A more recent literature exists which links incumbency advantages with increases in split ticket voting (Burden and Kimball 1998, Herron and Shotts 2004). Estimates of incumbency advantage show that it was both quite small (e.g. ...
Existing theories of partisanship do not extend particularly smoothly to the case of costly actions taken on behalf of a party. To address this difficulty we model partisan and nonpartisan actions as alternative norms or conventions of behavior. Evolutionary game theoretic techniques are used to analyze the selection of partisanship or nonpartisanship by a population interacting over time. Equilibrium selection in the model is driven by the varying observability of partisan behavior introduced by electoral institutions. The model suggests that institutions which increase the observability of partisan actions also increase the likelihood that those actions will be taken. Conversely, institutions which decrease the observability of partisan actions thereby decrease the likelihood that such actions will be taken. We test the theoretical results from our model on aggregate levels of split ticket voting across U.S. states between 1880 and 1940. We find considerable support for the model in endogeneity-corrected TSCS estimates of the effects of party registration, direct primaries, and secret ballots.
... Although it was first studied by sociologists in the 1950's (Robinson, 1950;Goodman, 1953;Duncan and Davis, 1953), recent years have witnessed resurgent interest in ecological inference among political methodologists and statisticians (see e.g., Achen and Shively, 1995;King, 1997;King et al., 2004;Wakefield, 2004a, and references therein). Much of the existing research, however, has focused on the development of new parametric models and the criticism of existing models, and has generated numerous debates over the appropriateness of proposed methods and their use (see e.g., Freedman et al., 1991;Grofman, 1991;Cho, 1998;Cho and Gaines, 2004;Herron and Shotts, 2004, and many others). ...
Ecological inference is a statistical problem where aggregate-level data are used to make inferences about individual-level behavior. Recent years have witnessed resurgent interest in ecological inference among political methodologists and statisticians. In this paper, we conduct a theoretical and empirical study of Bayesian and likelihood inference for 2 × 2 ecological ta-bles by applying the general statistical framework of incomplete data. We first show that the ecological inference problem can be decomposed into three factors: distributional effects which address the possible misspecification of parametric modeling assumptions about the unknown distribution of missing data, contextual effects which represent the possible correlation between missing data and observed variables, and aggregation effects which are directly related to the loss of information caused by data aggregation. We then examine how these three factors affect inference and offer new statistical methods to address each of them. To deal with distributional effects, we propose a nonparametric Bayesian model based on a Dirichlet process prior which relaxes common parametric assumptions. We also specify the statistical adjustments necessary to account for contextual effects. Finally, while little can be done to cope with aggregation effects, we offer a method to quantify the magnitude of such effects in order to formally assess its severity. We use simulated and real data sets to empirically investigate the consequences of these three factors and to evaluate the performance of our proposed methods. C code, along with an easy-to-use R interface, is publicly available for implementing our proposed methods.
... Since El generally does not outperform OLS (Cho 1998), it is difficult to justify the additional overhead. El does supply district-level estimates, but these estimates do not possess desirable statistical properties (Herron and Shotts 2003Shotts , 2004). There are instances when one needs to make ecological inferences, and so one will choose to use an ecological inference model such as El. ...
We examine the limits of ecological inference methods by focusing on the case of split-ticket voting. Burden and Kimball (1998) report that, by using the King estimation procedure for inferring individual-level behavior from aggregate data, they are the first to produce accurate estimates of split-ticket voting rates in congressional districts. However, a closer examination of their data reveals that a satisfactory analysis of this problem is more complex than may initially appear. We show that the estimation technique is highly suspect in general and especially unhelpful with their particular data.
... Furthermore, as King (1999) notes, in some cases the bounds will be sufficiently informative, diagnostics will detect some violations of the modeling assumptions, and qualitative information may be included to improve the analysis. (The difficulties of ecological inference may become compounded in the EI-R framework, where ecological estimates are used as the dependent variable in second stage analyses in (Herron and Shotts, 2003b), and although extensions to the EI can alleviate some of these problems Herron and Shotts, 2003a;, there are still concerns over the use of the technique (Herron and Shotts, 2004;Cho and Gaines, 2004).) ...
Ecological inference is a problem of partial identification, and therefore reliable precise conclusions are rarely possible without the collection of individual level (identifying) data. Without such data, sensitivity analyses provide the only recourse. In this paper we review and critique approaches to ecological inference in the social sciences, and describe in detail hierarchical models, which allow both sensitivity analysis and the incorporation of individual level data into an ecological analysis. A crucial element of a sensitivity analysis in such models is prior specification, and we detail how this may be carried out. Furthermore, we demonstrate how the inclusion of a small amount of individual level data can dramatically improve the properties of such estimates.
Forecasting has always been at the forefront of decision making and planning. The uncertainty that surrounds the future is both exciting and challenging, with individuals and organisations seeking to minimise risks and maximise utilities. The large number of forecasting applications calls for a diverse set of forecasting methods to tackle real-life challenges. This article provides a non-systematic review of the theory and the practice of forecasting. We provide an overview of a wide range of theoretical, state-of-the-art models, methods, principles, and approaches to prepare, produce, organise, and evaluate forecasts. We then demonstrate how such theoretical concepts are applied in a variety of real-life contexts.
We do not claim that this review is an exhaustive list of methods and applications. However, we wish that our encyclopedic presentation will offer a point of reference for the rich work that has been undertaken over the last decades, with some key insights for the future of forecasting theory and practice. Given its encyclopedic nature, the intended mode of reading is non-linear. We offer cross-references to allow the readers to navigate through the various topics. We complement the theoretical concepts and applications covered by large lists of free or open-source software implementations and publicly-available databases.
Daten bilden die Grundlage für die empirische Wahlforschung. Der vorliegende Beitrag stellt verschiedene Datenarten vor und analysiert deren Vor- und Nachteile für die Forschung. Es werden für Forschungszwecke erhobene Individualdaten, z.B. Umfragedaten, prozeßproduzierte Aggregatdaten, z.B. Wahlergebnisse, sowie die Daten der repräsentativen Wahlstatistik ausführlich vorgestellt und in ihren Stärken und Schwächen diskutiert.
Schlagworte: Aggregatdaten; Individualdaten; prozeßproduzierte Daten; Umfragedaten; Querschnitt- und Paneldaten; repräsentative Wahlstatistik; ökologischer Fehlschluß.
Ecological studies arise within many different disciplines. This chapter describes common approaches to ecological inference in an environmental epidemiology setting, and compares these with traditional approaches in political science and sociology. These approaches vary considerably, both in their use of terminology and notation, and in the relative importance of the various issues that make ecological analyses problematic. The aims of this chapter are twofold. Firstly, we describe ecological inference in an epidemiology setting, where the interest is in the relationship between disease status and exposure to some potential risk factor. We concentrate on those issues which are of particular concern in epidemiology, for example the presence of additional (possibly unmeasured) covariates, termed confounders. Secondly, we seek to unite the current work in epidemiology, political science, and sociology by clarifying differences in terminology, by describing commonly used approaches within a common statistical framework, and by highlighting similarities and differences between these approaches. Often different models can be attributed to different sets of underlying assumptions; we emphasize that such assumptions are crucial in the conclusions drawn from ecological data, and their appropriateness should be carefully considered in any specific situation. Combining approaches from all three disciplines gives a broad range of possible assumptions and available techniques from which to choose.
Ecological inference is a statistical problem where aggregate-level data are used to make inferences about individual-level
behavior. In this article, we conduct a theoretical and empirical study of Bayesian and likelihood inference for 2 × 2 ecological
tables by applying the general statistical framework of incomplete data. We first show that the ecological inference problem
can be decomposed into three factors: distributional effects, which address the possible misspecification of parametric modeling assumptions about the unknown distribution of missing
data; contextual effects, which represent the possible correlation between missing data and observed variables; and aggregation effects, which are directly related to the loss of information caused by data aggregation. We then examine how these three factors
affect inference and offer new statistical methods to address each of them. To deal with distributional effects, we propose
a nonparametric Bayesian model based on a Dirichlet process prior, which relaxes common parametric assumptions. We also identify
the statistical adjustments necessary to account for contextual effects. Finally, although little can be done to cope with
aggregation effects, we offer a method to quantify the magnitude of such effects in order to formally assess its severity.
We use simulated and real data sets to empirically investigate the consequences of these three factors and to evaluate the
performance of our proposed methods. C code, along with an easy-to-use R interface, is publicly available for implementing
our proposed methods (Imai, Lu, and Strauss, forthcoming).
Instant-Runoff Voting (IRV/RCV) is a relatively new reform to the rules of voting and elections that has been adopted by several cities. The impact of IRV/RCV balloting on racial group voter turnout in urban elections has not been subject to rigorous empirical analysis. In order to evaluate the relationship between IRV/RCV and voter turnout, I analyze precinct-level racial group voter turnout rates in five San Francisco mayoral elections from 1995 to 2011. I find significant declines in turnout under IRV/RCV rules, especially among Black voters. Variation in racial group turnout is best explained by factors related to candidate race and racial group competition. In addition, I find that IRV/RCV exacerbates turnout disparities between older and younger groups in the population and between those with high education compared to those with low education.
All statistical techniques place limitations on the types of data and the range of inferences that can be accomodated. All computional implementations of these statistical techniques impose further limitations due to algorithmic and low-level computational implementations. Failure to understand these issues can lead to gross misperceptions and seriously incorrect inferences. In this work we examine the numerical accuracy of King's (1997) approach, to ecological inference by using data perturbation, error analysis, and comparative reliability assessment.
Mixed-member electoral systems require voters simultaneously to cast ballots in single-member districts (SMD) and multimember, proportional representation (PR) constituencies. It may be that not all parties offer candidates in both electoral contexts, however. In this event would-be voters for some parties may find themselves ‘frustrated’ by the restricted choice menu on offer in the SMD, being effectively forced to split their vote between different parties. Here we explore the different behaviours of frustrated voters in the 1996 mixed-member election to Italy's Chamber of Deputies, characterizing these as being either in some sense non-strategic (concerned above all with the relative policy platforms of candidates) or strategic (concerned above all to influence the eventual composition of government). Using an extended method for ecological inference, we parameterize and estimate rates of different types of ticket-splitting at the district level, and link the degree of what we characterize as strategic voting to the relative policy distance between the respective local representatives of the Italian pre-electoral coalitions.
Models of ecological inference (EI) have to rely on crucial assumptions about the individual-level data-generating process, which cannot be tested because of the unavailability of these data. However, these assumptions may be violated by the unknown data and this may lead to serious bias of estimates and predictions. The amount of bias, however, cannot be assessed without information that is unavailable in typical applications of EI. We therefore construct a model that at least approximately accounts for the additional, nonsampling error that may result from possible bias incurred by an EI procedure, a model that builds on the Principle of Maximum Entropy. By means of a systematic simulation experiment, we examine the performance of prediction intervals based on this second-stage Maximum Entropy model. The results of this simulation study suggest that these prediction intervals are at least approximately correct if all possible configurations of the unknown data are taken into account. Finally, we apply our method to a real-world example, where we actually know the true values and are able to assess the performance of our method: the prediction of district-level percentages of split-ticket voting in the 1996 General Election of New Zealand. It turns out that in 95.5% of the New Zealand voting districts, the actual percentage of split-ticket votes lies inside the 95% prediction intervals constructed by our method.
Many observers expected new women voters to respond to their political context in distinctive ways. Some scholars anticipated that newly-enfranchised women—lacking political interest and experience—would be volatile and highly responsive to context. Others expected political isolation and norms proscribing political activity would insulate women from political stimuli. We test these competing predictions with a Bayesian approach to ecological inference and a unique set of aggregate data. We find that the responsiveness of women's turnout is strikingly similar to that of men. However, the lesser impact of electoral competition, and the greater effect of electoral laws and prior suffrage activism, suggest that the experience of and response to disenfranchisement shaped women's turnout after the vote was won.
Many observers suggest that white evangelical Protestant churches serve to mobilize their members into politics, while others argue that they encourage withdrawal from political life. This paper reconciles these two claims. I hypothesize that the time members of evangelical Protestant denominations spend in service to their church comes at the expense of participation in the wider community, contrary to the way mainline Protestant and Catholic churches foster civic activity among their members. However, I further hypothesize that the tight social networks formed through this intensive church activity can at times facilitate rapid and intense political mobilization. Data from the Citizen Participation Study supports the first hypothesis, while applying King's method of ecological inference to two elections in Alabama supports the second.
Much of the scholarly interest in critical realignments results from the pivotal role that ordinary citizens play during these
periods. By altering their voting behavior, citizens hold political elites accountable and forge non-incremental change in
policy outputs. A central question regarding realignments is thus how are citizens changing their behavior to hold elites
accountable? Are citizens producing realignments by converting from one party to the opposition? Are previous non-voters becoming
mobilized in response to emerging issues or crises? Or are one party’s supporters disproportionately abstaining from voting
and altering the partisan balance in the process? This article makes four central contributions to our understanding of these
realignment processes, or dynamics. We present a theoretical framework for the analysis of realignment dynamics, based upon
the Michigan model of voting and its conception of the normal vote. Where previous dynamics studies have collectively only
examined two realignments, we examine the dynamics of all presidential realignments in American electoral history. Where previous
studies have often focused on national, sectional, or state levels of analysis, we focus on city- and county-level realignments,
a critical advancement for an inherently local-level phenomenon such as critical realignments. Finally, unlike previous studies,
we identify the factors that promote particular realignment dynamics. We find that the conversion of active partisans has
produced most of the enduring change in voting behavior in the United States, with the relative contribution of different
dynamics varying both across time and space. Political factors such as the strength of state and local parties and demographic
factors such as changes in the size of local immigrant populations have each favored particular realignment dynamics in American
electoral history.
KeywordsRealignments-Voting behavior-Democratic accountability
There was a consensus among earlier students of New England politics that the political influence of European ancestry was fading by the latter half of the 20th century. We examine this proposition in recent times by exploring the role of ethnic ancestry in explaining the political divide in the region's presidential voting in over 1500 New England towns. Contrary to earlier predictions, ethnic origin does retain some explanatory power in models of recent voting behavior, and ethnic cleavages have not been entirely replaced by economic divisions in the electorate. Although the settlement patterns of the more established and numerous nationality groups (i.e. Irish and Italians) are less associated with partisanship than they were 50 years ago, the political salience of white ethnicity persists, suggesting that ethnic groups do not simply dealign or politically “assimilate” over time. Some groups maintain a strong identity in spite of upward mobility because movement from city to suburbs is selected not just on housing, income or school characteristics, as is usually the case, but on ethnicity too. Towns with significant concentrations of specific European ancestry groups lean Republican, even after we have accounted for the presence of other sources of political leaning and past voting tendencies, while Democratic attachments are undeniably strong in towns where the newer immigrant groups have settled. The “new ethnicity” (i.e. racial minorities) and the “old ethnicity” (i.e. white ethnics) clearly carry distinct political implications for this region's presidential politics.
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. Copyright (c) 2009 Royal Statistical Society.
A new solution to the ecological inference problem is used to examine split-ticket voting patterns across states and congressional districts in the 1988 elections. Earlier studies of ticket splitting used either aggregate data, which suffer from the "ecological fallacy" and threaten individual-level inferences, or survey data from small, unrepresentative samples. We produce more accurate estimates of the proportions of voters splitting their ballots in each state and district which enables us to examine variations across geographical units. We also clarify the connection between ticket splitting and divided government and test several competing theories about the causes of both. We find contrary to balancing arguments, that voters are not intentionally splitting tickets to produce divided government and moderate policies. In most cases split outcomes are a by-product of lopsided congressional campaigns that feature well-funded, high-quality candidates versus unknown competitors.
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We address in Herron and Shotts (2003; hereinafter HS) an increasingly common statistical practice called EI-R, in which point estimates generated by the King (1997) ecological inference technique are used as dependent variables in second-stage linear regressions. Although HS argue that EI-R slope estimates are inconsistent and suffer from attenuation bias, this characterization of EI-R is excessively conservative. Indeed, we show here that EI-R estimates can suffer from sign reversals, attenuation bias, and augmentation bias, that inference based on these estimates can be misleading, and that EI-R is unfixable and should not be used.
Between 1880 and 1912, voting rates of white southerners declined dramatically and black voters were substantially disfranchised, as is well known. Scholarly efforts to understand the processes that produced these patterns have been hampered by the paucity of reliable data on voter turnout by race (Kousser 1974). Although counts of the number of black and white voters are not available, substantial information on electoral demography is known. How can estimates of the racial components of the electorate be estimated from decennial census data and aggregated electoral returns? Gary King (1997) provided a new solution to this old problem (Achen and Shively 1995) and opened new avenues for historical research. This research has three purposes. First, it provides an evaluation from a practitioner's perspective of the statistical software used to implement King's method. The program, named EzI-A(n Easy) Program for Ecological Inference-is described in King (1997) and provided free via his Web site (http://gking.harvard.edu). EzI is a Windows-compatible shell for the GAUSS program EI, which is the calculation engine that implements the computer-intensive iterative solution King described. EzI is undoubtedly easier to use than EI, but its ease of use is misleading. EzI can readily produce poor estimates if model diagnostics and sources of independent validation information are ignored. We provide some suggestions for using EzI based on our experience and show that it can produce reasonable estimates of voter turnout by race. Second, we report estimates of black and white voter turnout for 1880, 1892, 1900, and 1912 for the eleven southern states calculated from averages of our county-level EzI estimation results. The estimates are broadly consistent with expectations derived from previous research (Kousser 1974). Estimates of black and white turnout rates are informative in their own right, but many researchers would like to evaluate the relative strength of various plausible determinants of racial differences in turnout. The third contribution of this research is to show how one can use the county-level estimates produced by King's technique to evaluate the importance of various factors that produce racial differences in turnout. We show how the turnout estimates obtained from EzI can be used as dependent variables in a second-stage mobilization model in which the black and white voting rates are allowed to affect each other. We describe some solutions for common problems in regression-model specifications often used to estimate the determinants of voter turnouts. Preliminary results reported indicate that other factors may have been as important as the poll tax and the literacy tests in restricting the turnout of black voters during the late nineteenth and early twentieth centuries in the South. Beyond the substance of the voter-turnout analyses, the methodological discussions developed below should prove useful for solving other ecological inference problems.
Using ecological inference methods and a dataset that combines results from the 1995 Québec referendum, the federal and provincial elections of 1997 and 1998, and data from the Canadian census, this article considers the relationship between the local linguistic environment and francophone support for Québec sovereignty. Outside of Montréal, we find that the linguistic composition of the population has little direct influence on support for sovereignty but that support for sovereignty declines as the proportion of francophones who know English rises. In Montréal, we find that support for sovereignty rises as the non-francophone portion of the population declines, but knowledge of a second language does not influence support for sovereignty.
The practice of using point estimates produced by the King ecological inference technique as dependent variables in second-stage linear regressions leads to second-stage results that, in general, are inconsistent. This conclusion holds even when all assumptions behind King's ecological technique are satisfied. Second-stage inconsistency is a consequence of the fact that King-based point estimates of disaggregated quantities contain errors correlated with the true quantities the estimates measure. Our findings on second-stage inconsistency, as well as a fix that we propose, follow from econometric theory in conjunction with an analysis of simulated and real ecological data sets.
In his 1997 book, King announced "A Solution to the Ecological Inference Problem". This review discusses King's method, and tests it on data where truth is known. In the test data, his method produces results that are far from truth, and diagnostics are unreliable. Ecological regression makes estimates that are similar to King's, while the neighborhood model is more accurate. His announcement is premature.
The election of African Americans to Congress is a primary achievement of the post-civil rights transition from protest to politics. I evaluate the link between black congressional representation and political engagement, as measured by voting participation. There are two related objectives: Construct a broader model of participation that takes into account a key component of the political environment since the civil rights era, and more fully appreciate the political significance of minority officeholding by considering its nonpolicy consequences. Using precinct data from eight midterm elections, I demonstrate that the election of blacks to Congress negatively affects white political involvement and only rarely increases political engagement among African Americans.
New techniques of ecological inference are utilized to estimate with confidence intervals francophone support in each federal electoral district in Quebec for the pro-sovereignty side in the 1993 and 1997 Canadian general elections and the 1992 and 1995 referenda. Analyzing the link between demographic and political contextual variables and support for the sovereignty of Quebec suggests that demographic factors, such as the proportion of farmers and government workers, influence francophone voting behaviour more often than political factors such as incumbency. Unlike in many other countries with ethnically based movements, francophone support for sovereignty actually rises as the francophone portion of the population rises. This finding indicates that the contact hypothesis probably applies to the Quebec sovereignty movement.
We examine the limits of ecological inference methods by focusing on the case of split-ticket voting. Burden and Kimball (1998) report that, by using the King estimation procedure for inferring individual-level behavior from aggregate data, they are the first to produce accurate estimates of split-ticket voting rates in congressional districts. However, a closer examination of their data reveals that a satisfactory analysis of this problem is more complex than may initially appear. We show that the estimation technique is highly suspect in general and especially unhelpful with their particular data.
Why do some voters split their ballots, selecting a Republican for one office and a Democrat for another? Why do voters often choose one party to control the White House while the other controls the Congress? Barry Burden and David Kimball address these fundamental puzzles of American elections by explaining the causes of divided government and debunking the myth that voters prefer the division of power over one-party control. Why Americans Split Their Tickets links recent declines in ticket-splitting to sharpening policy differences between parties and demonstrates why candidates' ideological positions still matter in American elections. "Burden and Kimball have given us the most careful and thorough analysis of split-ticket voting yet. It won't settle all of the arguments about the origins of ticket splitting and divided government, but these arguments will now be much better informed. Why Americans Split Their Tickets is essential reading for anyone interested in understanding the major trends in U.S. electoral politics of the past several decades." -Gary Jacobson, University of California, San Diego "When voters split their tickets or produce divided government, it is common to attribute the outcome as a strategic verdict or a demand for partisan balance. Burden and Kimball strongly challenge such claims. With a thorough and deft use of statistics, they portray ticket-splitting as a by-product of the separate circumstances that drive the outcomes of the different electoral contests. This will be the book to be reckoned with on the matter of ticket splitting." -Robert Erikson, Columbia University "[Burden and Kimball] offset the expansive statistical analysis by delving into the historical circumstances and results of recent campaigns and elections. ... [They] make a scholarly and informative contribution to the understanding of the voting habits of the American electorate-and the resulting composition of American government." -Shant Mesrobian, NationalJournal.com
In the last several years, new disputes have erupted over the use of group averages from census areas or voting districts to draw inferences about individual social behavior. Social scientists, policy analysts, and historians often have little choice about using this kind of data, but statistical analysis of them is fraught with pitfalls. The recent debates have led to a new menu of choices for the applied researcher. This volume explains why older methods like ecological regression so often fail, and it gives the most comprehensive treatment available of the promising new techniques for cross-level inference. Experts in statistical analysis of aggregate data, Christopher H. Achen and W. Philips Shively contend that cross-level inference makes unusually strong demands on substantive knowledge, so that no one method, such as Goodman's ecological regression, will fit all situations. Criticizing Goodman's model and some recent attempts to replace it, the authors argue for a range of alternate techniques, including estensions of cross-tabular, regression analysis, and unobservable variable estimators.
A recently proposed statistical model of ecological inference (the inference of individual behavior from observations consisting of aggregated individual-level data), known by its adherents as "EI", has recently gained a great deal of attention both inside and outside the statistical profession. This article shows that EI is in fact an application of the standard statistical theory of prediction, though with many statistical errors, not the least of which is the failure of the author of EI to recognize the relationship between EI and prediction. Although application of the theory of prediction may improve the inference of individual behavior for any observation of the aggregated dataset, it is unlikely to improve the estimate of individual behavior derived from the use of all of the observations, which is the usual goal of ecological inference.
I examine a recently proposed solution to the ecological inference problem (King 1997). It is asserted that the proposed model
is able to reconstruct individual-level behavior from aggregate data. I discuss in detail both the benefits and limitations
of this model. The assumptions of the basic model are often inappropriate for instances of aggregate data. The extended version
of the model is able to correct for some of these limitations. However, it is difficult in most cases to apply the extended
model properly.
Cross-Contamination in EI-R
- Herron
- C Michael
- Kenneth W Shotts
Herron, Michael C., and Kenneth W. Shotts. 2003a. " Cross-Contamination in EI-R. " Political Analysis 11(1):77–85.
Ecological Inference and the Comparative Method APSA-CP: Newsletter of the APS A Organized Section in
- D Voss
- David Stephen
- Lublin
Voss, D. Stephen, and David Lublin. 1998. " Ecological Inference and the Comparative Method. " APSA-CP: Newsletter of the APS A Organized Section in Comparative Politics 9(1):25–31.
Seeing the Forest and the Trees: Explaining Split-Ticket Voting within Districts and States
- Kimball David
- C Burden
Kimball, David C., and Barry C. Burden. 1998. " Seeing the Forest and the Trees: Explaining Split-Ticket Voting within Districts and States. " Presented at the annual meeting of the American Political Science Association, Boston, MA.
Why Americans Split Their Tickets: Campaigns, Competition, and Divided Government Ann Arbor: University of Michigan Press The Limits of Ecological Inference: The Case of Split Ticket Voting
- Burden
- C Barry
- David C Kimball
- Wendy K Cho
- Brain J Tam
- Gaines
Burden, Barry C., and David C. Kimball. 2002. " Why Americans Split Their Tickets: Campaigns, Competition, and Divided Government. " Ann Arbor: University of Michigan Press. Cho, Wendy K. Tam, and Brain J. Gaines. 2004. " The Limits of Ecological Inference: The Case of Split Ticket Voting. " American Journal of Political Science 48(1):151–70.
A Solution to the Ecological Inference Problem
- King
- Gary
King, Gary. 1997. A Solution to the Ecological Inference Problem. Princeton: Princeton University Press.
Comment on McCue's ‘The Statistical Foundations of the El Method.’
- Lewis Jeffrey B.
Lewis, Jeffrey B. 2002a. " Comment on McCue's 'The Statistical Foundations of the El Method.' " The American Statistician 56(3):255.
Sincere Voting, Hedging, and Raiding: Testing a Formal Model of Crossover Voting in Blanket Primaries Presented at the an-nual meeting of the American Political Science Association
- Cohen
- Thad Jonathan
- John Kousser
- Sides
Cohen, Jonathan, Thad Kousser, and John Sides. 1999. " Sincere Voting, Hedging, and Raiding: Testing a Formal Model of Crossover Voting in Blanket Primaries. " Presented at the an-nual meeting of the American Political Science Association, Atlanta, GA.
Gender and the Vote 1920-1932
- Wolbrecht Christin Andj.Kevin
- Corder
Sincere Voting, Hedging, and Raiding: Testing a Formal Model of Crossover Voting in Blanket Primaries
- Jonathan Cohen
- Thad Kousser
- John Sides
Sincere Voting Hedging and Raiding: Testing a Formal Model of Crossover Voting in Blanket Primaries
- Cohen Jonathan Thadkousser Andjohnsides
Ecological Inference and the Comparative Method
- Voss D. Stephen