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When analyzing data, researchers are often less interested in the parameters of statistical models than in functions of these parameters such as predicted values. Here we show that Bayesian simulation with Markov-Chain Monte Carlo tools makes it easy to compute these quantities of interest with their uncertainty. We illustrate how to produce customary and relatively new quantities of interest such as variable importance ranking, posterior predictive data, difficult marginal effects, and model comparison statistics to allow researchers to report more informative results.
In this article, we develop and make available measures of public ideology in 2010 for the 50 American states, 435 congressional districts, and state legislative districts. We do this using the geospatial statistical technique of Bayesian universal kriging, which uses the locations of survey respondents, as well as population covariate values, to predict ideology for simulated citizens in districts across the country. In doing this, we improve on past research that uses the kriging technique for forecasting public opinion by incorporating Alaska and Hawaii, making the important distinction between ZIP codes and ZIP Code Tabulation Areas, and introducing more precise data from the 2010 Census. We show that our estimates of ideology at the state, congressional district, and state legislative district levels appropriately predict the ideology of legislators elected from these districts, serving as an external validity check.
Multimodal, high-dimension posterior distributions are well known to cause mixing problems for standard Markov chain Monte Carlo (MCMC) procedures; unfortunately such functional forms readily occur in empirical political science. This is a particularly important problem in applied Bayesian work because inferences are made from finite intervals of the Markov chain path. To address this issue, we develop and apply a new MCMC algorithm based on tempered transitions of simulated annealing, adding a dynamic element that allows the chain to self-tune its annealing schedule in response to current posterior features. This important feature prevents the Markov chain from getting trapped in minor modal areas for long periods of time. The algorithm is applied to a probabilistic spatial model of voting in which the objective function of interest is the candidate's expected return. We first show that such models can lead to complex target forms and then demonstrate that the dynamic algorithm easily handles even large problems of this kind.
Welcome to the special issue of Political Analysis dedicated to Bayesian methods. We hope that you enjoy the varied and interesting contributions herein featuring Bayesian statistical methods. For many people in empirical political science, Bayesian statistics seems like a weird offshoot of probability that surfaces occasionally in journals and books but does not occupy a particularly central role. This perception appears to be changing. In fact, it appears to be changing quite rapidly. The purpose of this issue is to support and accelerate this momentum by further demonstrating the full flexibility and power of Bayesian methodology.
We develop a new approach for modeling public sentiment by micro-level geographic region based on Bayesian hierarchical spatial modeling. Recent production of detailed geospatial political data means that modeling and measurement lag behind available information. The output of the models gives not only nuanced regional differences and relationships between states, but more robust state-level aggregations that update past research on measuring constituency opinion. We rely here on the spatial relationships among observations and units of measurement in order to extract measurements of ideology as geographically narrow as measured covariates. We present an application in which we measure state and district ideology in the United States in 2008.
We apply a specialized Bayesian method that helps us deal with the methodological challenge of unobserved heterogeneity among immigrant voters. Our approach is based on generalized linear mixed Dirichlet models (GLMDMs) where random effects are specified semiparametrically using a Dirichlet process mixture prior that has been shown to account for unobserved grouping in the data. Such models are drawn from Bayesian nonparametrics to help overcome objections handling latent effects with strongly informed prior distributions. Using 2009 German voting data of immigrants, we show that for difficult problems of missing key covariates and unexplained heterogeneity this approach provides (1) overall improved model fit, (2) smaller standard errors on average, and (3) less bias from omitted variables. As a result, the GLMDM changed our substantive understanding of the factors affecting immigrants' turnout and vote choice. Once we account for unobserved heterogeneity among immigrant voters, whether a voter belongs to the first immigrant generation or not is much less important than the extant literature suggests. When looking at vote choice, we also found that an immigrant's degree of structural integration does not affect the vote in favor of the CDU/CSU, a party that is traditionally associated with restrictive immigration policy.
The study of covert networks is plagued by the fact that individuals conceal their attributes and associations. To address this problem, we develop a technology for eliciting this information from qualitative subject-matter experts to inform statistical social network analysis. We show how the information from the subjective probability distributions can be used as input to Bayesian hierarchical models for network data. In the spirit of “proof of concept,” the results of a test of the technology are reported. Our findings show that human subjects can use the elicitation tool effectively, supplying attribute and edge information to update a network indicative of a covert one.
Missing values are a frequent problem in empirical political science research. Surprisingly, the match between the measurement of the missing values and the correcting algorithms applied is seldom studied. While multiple imputation is a vast improvement over the deletion of cases with missing values, it is often unsuitable for imputing highly non-granular discrete data. We develop a simple technique for imputing missing values in such situations, which is a variant of hot deck imputation, drawing from the conditional distribution of the variable with missing values to preserve the discrete measure of the variable. This method is tested against existing techniques using Monte Carlo analysis and then applied to real data on democratization and modernization theory. Software for our imputation technique is provided in a free, easy-to-use package for the R statistical environment.
The susceptibility of Colorado potato beetle [Leptinotarsa decemlineata (Say), Coleoptera: Chrysomelidae] to entomopathogenic nematodes (Steinernema carpocapsae, ’All’ strain, Nematoda: Heterorhabditae) was tested in the laboratory and the field in 1992 and 1993. Under laboratory conditions, applications of 5.0 × 105S. carpocapsae per square metre to larvae, pupae, and (or) adults resulted in 100% mortality in all experimental groups. Steinernema carpocapsae persisted through the larval–pupal and pupal–adult transitions. A single application of nematodes was sufficient to control the Colorado potato beetle. The following treatments were tested at field sites in New Brunswick and Prince Edward Island: (i) untreated check, (ii) application of nematodes, or (iii) application of insecticides. Straw mulch was either present or absent in each treatment. In 1992 in New Brunswick, nematodes and fenvalerate reduced Colorado potato beetle populations by 31% compared with the untreated check. However, in 1993, differences among treatments were not significant. The results from the field trials in Prince Edward Island were variable; the life expectancy of nematodes is likely shorter in the field than under laboratory conditions. Further investigation into the benefits of repeated applications of nematodes, higher rates, or improvements in application technology are required to achieve consistent control of the Colorado potato beetle.
There has been no attention to circular (purely cyclical) data in political science research. We show that such data exist and are mishandled by models that do not take into account the inherently recycling nature of some phenomenon. Clock and calendar effects are the obvious cases, but directional data are observed as well. We describe a standard maximum likelihood regression modeling framework based on the von Mises distribution, then develop a general Bayesian regression procedure for the first time, providing an easy-to-use Metropolis-Hastings sampler for this approach. Applications include a chronographic analysis of U.S. domestic terrorism and directional party preferences in a two-dimensional ideological space for German Bundestag elections. The results demonstrate the importance of circular models to handle periodic and directional data in political science.
Increasingly, political science researchers are turning to Markov chain Monte Carlo methods to solve inferential problems with complex models and problematic data. This is an enormously powerful set of tools based on replacing difficult or impossible analytical work with simulated empirical draws from the distributions of interest. Although practitioners are generally aware of the importance of convergence of the Markov chain, many are not fully aware of the difficulties in fully assessing convergence across multiple dimensions. In most applied circumstances, every parameter dimension must be converged for the others to converge. The usual culprit is slow mixing of the Markov chain and therefore slow convergence towards the target distribution. This work demonstrates the partial convergence problem for the two dominant algorithms and illustrates these issues with empirical examples.
In this study, a novel method is explored for improving the electromigration lifetime of Cu wires, using Ta implantation into Cu. For high implant doses (2E15 cm−2), the electromigration lifetime is improved by over 5X using this method. An increase in lifetime is achieved, even for an average surface concentration of Ta on the order of 0.1 atm%. We propose that the improvement in electromigration lifetime is due to the reduction of defects at the SiN/Cu interface due to the presence of Ta. The line-to-line leakage at high voltages (> 5V) increases with the Ta implant, with higher leakage at higher Ta concentrations, so the Ta dose must be limited to avoid excessive leakage.
The recent decline in electoral turnout in Canada has attracted the concern of scholars and public officials, but the partisan consequences of this decline have received only scant attention. We begin to address that question with a simulation based on the 1997 Canadian Election Study. Based on estimated probabilities of individual behaviour derived from multinomial logit models of voter choice, we find that higher turnout would have likely hurt the Liberal party in Quebec, but slightly helped the Liberals outside of Quebec. We interpret this pattern as evidence that generational politics plays a role in shaping the relationship between electoral turnout and partisan support.
This chapter describes the means by which we label and treat known and unknown values. Basically there are two types of observable data, and the abstract terminology for yet-to-be observed values should also reflect this distinction. We first talk here about the levels of measurement for observed values where the primary distinction is discrete versus continuous. We will then see that the probability functions used to describe the distribution of such variables preserves this distinction. Many of the topics here lead to the use of statistical analysis in the social sciences.
Levels of Measurement
It is important to classify data by the precision of measurement. Usually in the social sciences this is an inflexible condition because many times we must take data “as is” from some collecting source. The key distinction is between discrete data, which take on a set of categorical values, and continuous data, which take on values over the real number line (or some bounded subset of it). The difference can be subtle. While discreteness requires countability, it can be infinitely countable, such as the set of positive integers. In contrast, a continuous random variable takes on uncountably infinite values, even if only in some range of the real number line, like [0 :1], because any interval of the real line, finitely bounded or otherwise, contains an infinite number of rational and irrational numbers.
To see why this is an uncountably infinite set, consider any two points on the real number line. It is always possible to find a third point between them. Now consider finding a point that lies between the first point and this new point; another easy task.