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A Practical Statistical Model for Multiparty Electoral Data Honaker, James Katz, Jonathan King, Gary Uploaded 08-23-2000 Keywords compositional data multiparty electoral data EM algorithms Abstract Katz and King (1999) develop a model for predicting or explaining aggregate electoral results in multiparty democracies. This model is, in principle, analogous to what least squares regression provides American politics researchers in that two-party system. Katz and King applied this model to three-party elections in England and revealed a variety of new features of incumbency advantage and where each party pulls support from. Although the mathematics of their statistical model covers any number of political parties, it is computationally very demanding, and hence slow and numerically imprecise, with more than three. The original goal of our work was to produce an approximate method that works quicker in practice with many parties without making too many theoretical compromises. As it turns out, the method we offer here improves on Katz and King's (in bias, variance, numerical stability, and computational speed) even when the latter is computationally feasible. We also offer easy-to-use software that implements our suggestions.

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Time Series Models for Compositional Data Brandt, Patrick T. Monroe, Burt L. Williams, John T. Uploaded 04-13-1999 Keywords compositional data vector autoregression macropartisanship Abstract Who gets what? When? How? Data that tell us who got what are compositional data - they are proportions that sum to one. Political science is, unsurprisingly, replete with examples: vote shares, seat shares, budget shares, survey marginals, and so on. Data that also tell us when and how are compositional time series data. Standard time series models are often used, to detrimental consequence, to model compositional time series. We examine methods for modeling compositional data generating processes using vector autoregression (VAR). We then use such a method to reanalyze aggregate partisanship in the United States.

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Time Series Models for Compositional Data Brandt, Patrick T. Monroe, Burt L. Williams, John T. Uploaded 07-09-1999 Keywords compositional data VAR time series analysis bootstrap Monte Carlo simulation macropartisanship Abstract Who gets what? When? How? Data that tell us who got what are compositional data - they are proportions that sum to one. Political science is, unsurprisingly, replete with examples: vote shares, seat shares, budget shares, survey marginals, and so on. Data that also tell us when and how are compositional time series data. Standard time series models are often used, to detrimental consequence, to model compositional time series. We examine methods for modeling compositional data generating processes using vector autoregression (VAR). We then use such a method to reanalyze aggregate partisanship in the United States.

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A Monte Carlo Comparison of Methods for Compositional Data Analysis Brehm, John Gates, Scott Gomez, Brad Uploaded 07-08-1998 Keywords Compositional data Dirichlet Additive Logistic Monte Carlo Police Behavior Abstract This paper offers an explication of two techniques for compositional data analysis, which involve non-negative data belonging to mutually exclusive and exhaustive categories. The Dirichlet distribution is a multivariate generalization of the beta distribution that offers considerable flexibility, and ease of use, but requires a strong form of an ``independence of irrelevant alternatives'' (IIA) assumption. The second application, proposed by Aitchison (1986) and applied to political data by Katz and King (1997), is the additive logistic method. This approach addresses the strong IIA assumption, but cannot handle strong forms of independence (Rayens and Srinivasen 1994). Monte Carlo simulations are employed on compositional data to explore the limits of applications of the two methods. Data on police officers' allocation of time across a variety of tasks (Ostrom et al. 1988) is used in this analysis. Comparing both common covariates and unique covariates. When the composites are influenced by common covariates, there appears to be no advantage in the use of additive logistic methods over the Dirichlet. Similarly, the additive logistic and Dirichlet methods appear to be equally successful at estimating the effects of the unique covariates on composites. From these simulation results we conclude that the additive logistic method offers little advantage over the Dirichlet, and suffers from several disadvantages.

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Bias and Responsiveness in Multiparty and Multigroup Representation Monroe, Burt L. Uploaded 07-21-1998 Keywords partisan bias responsiveness seats and votes electoral systems compositional data JudgeIt Abstract There is an extensive and expanding literature that examines methods for estimating the responsiveness and partisan bias of two-party electoral systems. Attempts to extend these methods into the multiparty domain appropriate for the vast majority of electoral systems, or to the analysis of the representation of other types of groups (e.g., regions, ethnic groups), have been limited. I describe index, multiyear, uniform swing, and variable swing methods -- along with novel graphical displays -- for analyzing seats-votes curves, bias, and responsiveness in multiparty systems. The variable swing method is a multiparty generalization of Gelman and King's "JudgeIt" model. Examples discussed include elections in the UK, Mauritius, and Costa Rica, and geographic representation worldwide. In comparing the various methods it is argued that variable swing is ideal for most applications, that uniform swing and index methods provide useful answers to a limited set of questions despite faulty assumptions, and that multiyear methods are generally not useful.

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A Statistical Model for Multiparty Electoral Data Katz, Jonathan King, Gary Uploaded 07-16-1997 Keywords multiparty elections compositional data multivariate-t Abstract We propose an internally consistent and comprehensive statistical model for analyzing multiparty, district-level aggregate election data. This model can be used to explain or predict how the geographic distribution of electoral results depends upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or characteristics of the aggregate areas. We also provide several new graphical representations for help in data exploration, model evaluation, and substantive interpretation. Although the model applies more generally, we use it to resolve an important controversy over the size of and trend in the electoral advantage of incumbency in Great Britain. Contrary to previous analyses, which are all based on measures now known to be biased, we demonstrate that the incumbency advantage is about 1% for the major parties and 4% for the Liberal party and its successors. Also contrary to previous research, we show that these effects have not grown in recent years. Finally, we are able to estimate from which party each party's incumbency advantage is predominantly drawn.

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A Statistical Model for Multiparty Electoral Data Katz, Jonathan King, Gary Uploaded 04-08-1997 Keywords multiparty elections compositional data multivariate-t Abstract This paper proposes an internally consistent and comprehensive statistical model for analyzing multiparty, district-level aggregate election data. This model can be used to explain or predict how the geographic distribution of electoral results depends upon economic conditions, neighborhood ethnic compositions, campaign spending, and other features of the election campaign or characteristics of the aggregate areas. We also provide several new graphical representations for help in data exploration, model evaluation, and substantive interpretation. The model is more general, but we apply it resolve a controversy over the size of and trend in the electoral advantage of incumbency in Great Britain.

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A Compositional-Hierarchical Model of Abstention under Compulsory Voting (poster) Katz, Gabriel Uploaded 06-18-2008 Keywords compulsory voting abstention compositional data hierarchical modelling MCMC. Abstract Invalid voting and electoral absenteeism are two important sources of abstention in compulsory voting systems. Previous studies in this area have not considered the correlation between both variables and ignored the compositional nature of the data, potentially leading to unfeasible results and discarding helpful information from an inferential standpoint. In order to overcome these problems, this paper develops a statistical model that accounts for the compositional and hierarchical structure of the data and addresses robustness concerns raised by the use of small samples that are typical in the literature. The model is applied to analyze invalid voting and electoral absenteeism in Brazilian legislative elections between 1945 and 2006 via MCMC simulations. The results show considerable differences in the determinants of both forms of non-voting; while invalid voting was strongly positively related both to political protest and to the existence of important informational barriers to voting, the influence of these variables on absenteeism is less evident. Comparisons based on posterior simulations indicate that the model developed in this paper fits the dataset better than several alternative modeling approaches and leads to different substantive conclusions regarding the effect of different predictors on the both sources of abstention.