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Estimating King's ecological inference normal model via the EM algorithm Mattos, Rogerio Veiga, Alvaro Uploaded 04-20-2000 Keywords ecological inference disaggregate data exponential families truncated normal EM Algorithm Abstract Recently, Gary King introduced a new model for ecological inference, based on a truncated bivariate normal, which he estimates by maximum probability and uses to simulate the predictive densities of the disaggregate data. This paper reviews King's model and its assumption of truncated normality, with the aim to implement maximum probability estimation of his model and disaggregate data prediction in an alternative fashion via the EM Algorithm. In addition, we highlight and discuss important modeling issues related to the chance of non-existence of maximum likelihood estimates, and to the degree that corrections for this non-existence by means of suitably chosen priors are effective. At the end, a Monte Carlo simulation study is run in order to compare the two approaches.

2

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A Random Effects Approach to Legislative Ideal Point Estimation Bailey, Michael Uploaded 04-21-1998 Keywords ideal points random effects models Bayesian estimation em algorithm Abstract Conventionally, scholars use either standard probit/logit techniques or fixed-effect methods to estimate legislative ideal points. However, these methods are unsatisfactory when a limited number of votes are available: standard probit/logit methods are poorly equipped to handle multiple votes and fixed-effect models disregard serious ``incidental parameter'' problems. In this paper I present an alternative approach that moves beyond single-vote probit/logit analysis without requiring the large number of votes needed for fixed-effects models. The method is based on a random effects, panel logit framework that models ideal points as stochastic functions of legislator characteristics. Monte Carlo results and an application to trade politics demonstrate the practical usefulness of the method.

3

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Estimating voter preference distributions from individual-level voting data (with application to split-ticket voting Lewis, Jeffrey B. Uploaded 09-15-1998 Keywords split ticket voting ideal point estimation spatial voting models EM algorithm Abstract In the last decade a great deal of progress has been made in estimating spatial models of legislative roll-call voting. There are now several well-known and effective methods of estimating the ideal points of legislators from their roll-call votes. Similar progress has not been made in the empirical modeling of the distribution of preferences in the electorate. Progress has been slower, not because the question is less important, but because of limitations of data and a lack of tractable methods. In this paper, I present a method for inferring the distribution of voter ideal points on a single dimension from individual-level voting returns on ballot propositions. The statistical model and estimation technique draw heavily on the psychometric literature on test taking and, in particular, on the work of Bock and Aitkin (1981}. The method yields semi-parametric estimates of the distribution of voters along an unobserved spatial dimension. The model is applied to data from the 1992 general election in Los Angeles County. I present the distribution of voter ideal points of each of 17 Congressional districts. Finally, I consider the issue of split-ticket voting estimating for two Congressional districts the distribution of voters that split their tickets and of those that did not.

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Bayesian and Likelihood Inference for 2 x 2 Ecological Tables: An Incomplete Data Approach Imai, Kosuke Lu, Ying Strauss, Aaron Uploaded 12-16-2006 Keywords Coarse data Contextual effects Data augmentation EM algorithm Missing information principle Nonparametric Bayesian Modeling. Abstract 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 x 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 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.

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A Spatial Model of Electoral Platforms Elff, Martin Uploaded 07-01-2008 Keywords Parties party families electoral platforms party manifestos spatial models unobserved data latent trait models EM algorithm Monte Carlo integration Monte Carlo EM importance sampling SIR algorithm ideological dimensions Abstract The reconstruction of political positions of parties, candidates and governments has made considerable headway during the last decades, not the least due to the efforts of the Manifesto Research Group the and Comparative Manifestos Project, which compiled and published a data set on the electoral platforms of political parties from most major democracies for most of the post-war era. A central assumption underlying the coding of electoral platforms into quantitative data as done by the MRG/CMP is that parties take positions by selective emphases of policy objectives, which put their accomplishments in a most positive light (Budge 2001) or are representative for their current polital/ideological positions. Consequently, the MRG/CMP data consist of percentages of the respective manifesto texts that refer to various policy objectives. As a consequence both of this underlying assumption and of the structure of the CMP data, methods of classical multivariate analysis are not well suited to these data, due to the requirements to the data for an appropriate application of these methods (van der Brug 2001; Elff 2002). The paper offers an alternative method for reconstructing positions in political spaces based on latent trait modelling, which both reï¬?ects the assumptions underlying the coding of the texts and the peculiar structure of the data. Finally, the validity of the proposed method is demonstrated with respect to the average position of party families within reconstructed policy spaces. It turns out that communist, socialist, and social democrat parties differ clearly from â??bourgeoisâ?? parties with regards to their positions on an economic left/right dimension, while British and Scandinavian conservative parties can be distinguished from Christian democratic parties by their respective positions on a libertarian/authoritarian and a traditionalist/modernist dimension. Similarly, the typical political positions of green (or â??New Politicsâ??) parties can be distinguished from the positions of other party families.

6

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A Statistical Method for Empirical Testing of Competing Theories Imai, Kosuke Tingley, Dustin Uploaded 08-24-2010 Keywords EITM finite mixture model Bayesian statistics multiple testing false discovery rate EM algorithm Abstract Empirical testing of competing theories lies at the heart of social science research. We demonstrate that a very general and well-known class of statistical models, called finite mixture models, provides an effective way of rival theory testing. In the proposed framework, each observation is assumed to be generated from a statistical model implied by one of the theories under consideration. Researchers can then estimate the probability that a specific observation is consistent with either of the competing theories. By directly modeling this probability with the characteristics of observations, one can also determine the conditions under which a particular theory applies. We discuss a principled way to identify a list of observations that are statistically significantly consistent with each theory. Finally, we propose several measures of the overall performance of a particular theory. We illustrate the advantages of our method by applying it to an influential study on trade policy preferences.