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Estimation in Dirichlet Random Effects Models Kyung, Minjung Gill, Jeff Casella, George Uploaded 04-28-2009 Keywords generalized linear mixed model Dirichlet process random effects model precision parameter likelihood Gibbs sampling importance sampling probit mixed Dirichlet random effects model Abstract We develop a new Gibbs sampler for a linear mixed model with a Dirichlet process random effect term, which is easily extended to a generalized linear mixed model with a probit link function. Our Gibbs sampler exploits the properties of the multinomial and Dirichlet distribution, and is shown to be an improvement, in terms of operator norm and efficiency, over other commonly used MCMC algorithms. We also investigate methods for the estimation of the precision parameter of the Dirichlet process, finding that maximum likelihood may not be desirable, but a posterior mode is a reasonable approach. Examples are given to show how these models perform on real data. Our results complement both the theoretical basis of the Dirichlet process nonparametric prior and the computational work that has been done to date. Forthcoming: Annals of Statistics.

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What to do When Your Hessian is Not Invertible: Alternatives to Model Respecification in Nonlinear Estimation Gill, Jeff King, Gary Uploaded 05-14-2002 Keywords Hessian Cholesky generalized inverse maximum likelihood statistical computing importance sampling pseudo-variance generalized linear model singular normal Abstract What should a researcher do when statistical analysis software terminates before completion with a message that the Hessian is not invertable? The standard textbook advice is to respecify the model, but this is another way of saying that the researcher should change the question being asked. Obviously, however, computer programs should not be in the business of deciding what questions are worthy of study. Although noninvertable Hessians are sometimes signals of poorly posed questions, nonsensical models, or inappropriate estimators, they also frequently occur when information about the quantities of interest does exist in the data, through the likelihood function. We explain the problem in some detail and lay out two preliminary proposals for ways of dealing with noninvertable Hessians without changing the question asked.

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Listwise Deletion is Evil: What to Do About Missing Data in Political Science King, Gary Honaker, James Joseph, Anne Scheve, Kenneth Uploaded 07-13-1998 Keywords missing data imputation IP EM EMs EMis data augmentation MCMC importance sampling item nonresponse Abstract We address a substantial discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. With a few notable exceptions, statisticians and methodologists have agreed on a widely applicable approach to many missing data problems based on the concept of ``multiple imputation,'' but most researchers in our field and other social sciences still use far inferior methods. Indeed, we demonstrate that the threats to validity from current missing data practices rival the biases from the much better known omitted variable problem. This discrepancy is not entirely our fault, as the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise on the part of the user (indeed, even experts disagree on how to use them). In this paper, we adapt an existing algorithm, and use it to implement a general-purpose, multiple imputation model for missing data. This algorithm is between 20 and 100 times faster than the leading method recommended in the statistics literature and is very easy to use. We also quantify the considerable risks of current political science missing data practices, illustrate how to use the new procedure, and demonstrate the advantages of our approach to multiple imputation through simulated data as well as via replications of existing research.

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Listwise Deletion is Evil: What to Do About Missing Data in Political Science (revised) King, Gary Honaker, James Joseph, Anne Scheve, Kenneth Uploaded 08-19-1998 Keywords missing data imputation IP EM EMs EMis data augmentation MCMC importance sampling item nonresponse Abstract We propose a remedy to the substantial discrepancy between the way political scientists analyze data with missing values and the recommendations of the statistics community. With a few notable exceptions, statisticians and methodologists have agreed on a widely applicable approach to many missing data problems based on the concept of ``multiple imputation,'' but most researchers in our field and other social sciences still use far inferior methods. Indeed, we demonstrate that the threats to validity from current missing data practices rival the biases from the much better known omitted variable problem. As it turns out, this discrepancy is not entirely our fault, as the computational algorithms used to apply the best multiple imputation models have been slow, difficult to implement, impossible to run with existing commercial statistical packages, and demanding of considerable expertise on the part of the user (even experts disagree on how to use them). In this paper, we adapt an existing algorithm, and use it to implement a general-purpose, multiple imputation model for missing data. This algorithm is between 65 and 726 times faster than the leading method recommended in the statistics literature and is very easy to use. We also quantify the considerable risks of current political science missing data practices, illustrate how to use the new procedure, and demonstrate the advantages of our approach to multiple imputation through simulated data as well as via replications of existing research. We also offer easy-to-use public domain software that implements our approach.

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The Spatial Probit Model of Interdependent Binary Outcomes: Estimation, Interpretation, and Presentation Franzese, Robert Hays, Jude Uploaded 07-20-2007 Keywords Spatial Probit Bayesian Gibbs-Sampler Estimator Recursive Importance-Sampling Estimator Interdependence Diffusion Contagion Emulation Abstract We have argued and shown elsewhere the ubiquity and prominence of spatial interdependence in political science research and noted that much previous practice has neglected this interdependence or treated it solely as nuisance to the serious detriment of sound inference. Previously, we considered only linear-regression models of spatial and/or spatio-temporal interdependence. In this paper, we turn to binary-outcome models. We start by stressing the ubiquity and centrality of interdependence in binary outcomes of interest to political and social scientists and note that, again, this interdependence has been ignored in most contexts where it likely arises and that, in the few contexts where it has been acknowledged, the endogeneity of the spatial lag has not be recognized. Next, we explain some of the severe challenges for empirical analysis posed by spatial interdependence in binary-outcome models, and then we follow recent advances in the spatial-econometric literature to suggest Bayesian or recursive-importance-sampling (RIS) approaches for tackling estimation. In brief and in general, the estimation complications arise because among the RHS variables is an endogenous weighted spatial-lag of the unobserved latent outcome, y*, in the other units; Bayesian or RIS techniques facilitate the complicated nested optimization exercise that follows from that fact. We also advance that literature by showing how to calculate estimated spatial effects (as opposed to parameter estimates) in such models, how to construct confidence regions for those (adopting a simulation strategy for the purpose), and how to present such estimates effectively.

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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.