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Parameterization and Bayesian Modeling Gelman, Andrew Uploaded 06-15-2004 Keywords censored data data augmentation Gibbs sampler hierarchical model missing data imputation parameter expansion prior distribution truncated data Abstract Progress in statistical computation often leads to advances in statistical modeling. For example, it is surprisingly common that an existing model is reparameterized, solely for computational purposes, but then this new configuration motivates a new family of models that is useful in applied statistics. One reason this phenomenon may not have been noticed in statistics is that reparameterizations do not change the likelihood. In a Bayesian framework, however, a transformation of parameters typically suggests a new family of prior distributions. We discuss examples in censored and truncated data, mixture modeling, multivariate imputation, stochastic processes, and multilevel models.

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A Bayesian Method for the Analysis of Dyadic Crisis Data Smith, Alastair Uploaded 11-04-1996 Keywords Bayesian model testing Censored data Crisis data Gibbs sampling Markov chain Monte Carlo Ordered discrete choice model Strategic choice Abstract his paper examines the level of force that nations use during disputes. Suppose that two nations, A and B, are involved in a dispute. Each nation chooses the level of violence that it is prepared to use in order to achieve its objectives. Since there are two opponents making decisions, the outcome of the crisis is determined by a bivariate rather than univariate process. I propose a bivariate ordered discrete choice model to examine the relationship between nation A's decision to use force, nation B's decision to use force, and a series of explanatory variables. The model is estimated in the Bayesian context using a Markov chain Monte Carlo simulation technique. I analyze Bueno de Mesquita and Lalman's (1992) dyadically coded version of the Militarized Interstate Dispute data (Gochman and Moaz 1984). Various models are compared using Bayes Factors. The results indicate that nation A's and nation B's decisions to use force can not be regarded as independent. Bayesian model comparison show that variables derived from Bueno de Mesquita's expected utility theory (1982, 1985; Bueno de Mesquita and Lalman 1986, 1992) provide the best explanatory variables for decision making in crises.

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The Trouble with Tobit: A District-Level Sample Selection Model of Voting for Extreme Right Parties in Europe, 1980-2004 Bowyer, Benjamin Uploaded 07-07-2008 Keywords Tobit Heckman sample selection censored data aggregate data extreme right parties Abstract The growing electoral success of extreme right parties (ERPs) in many European countries has sparked academic interest in explaining variation in extreme right success. However, much of the extant research on the electoral success of extreme right parties suffers from at least two types of selection bias. The first involves the selection of cases and occurs when only those national elections that were contested by extreme right parties are included in the cross-national analysis. To address this problem, a growing number of scholars of ERP electoral support employ Tobit models to analyze national-level election results pooled across countries and election years. However, this approach conceals a second source of selection bias: ERPs are extremely selective about which election districts within a country they choose to contest. The correct specification of this process of self-selection requires the recognition of two fundamental points. First, the causal factors that determine whether an extreme right party contests an election are not identical to those that influence its share of the vote if it does appear on the ballot. Second, this decision about when and where to field candidates is one that is observable at the level of the election district. This paper argues that the appropriate way to model is as a Heckman sample selection model estimated at the level of electoral district. I present a preliminary analysis of a dataset that pools district-level election results for eighteen European countries from 1980-2004 (N=12,050), the results of which demonstrate the value of this approach.