Simon Jackman

Bayesian analysis for the social sciences

List of Figures. List of Tables. Preface. Acknowledgments. Introduction. Part I: Introducing Bayesian Analysis. 1. The foundations of Bayesian inference. 1.1 What is probability? 1.2 Subjective probability in Bayesian statistics. 1.3 Bayes theorem, discrete case. 1.4 Bayes theorem, continuous parameter. 1.5 Parameters as random variables, beliefs as distributions. 1.6 Communicating the results of a Bayesian analysis. 1.7 Asymptotic properties of posterior distributions. 1.8 Bayesian hypothesis testing. 1.9 From subjective beliefs to parameters and models. 1.10 Historical note. 2. Getting started: Bayesian analysis for simple models. 2.1 Learning about probabilities, rates and proportions. 2.2 Associations between binary variables. 2.3 Learning from counts. 2.4 Learning about a normal mean and variance. 2.5 Regression models. 2.6 Further reading. Part II: Simulation Based Bayesian Analysis. 3. Monte Carlo methods. 3.1 Simulation consistency. 3.2 Inference for functions of parameters. 3.3 Marginalization via Monte Carlo integration. 3.4 Sampling algorithms. 3.5 Further reading. 4. Markov chains. 4.1 Notation and definitions. 4.2 Properties of Markov chains. 4.3 Convergence of Markov chains. 4.4 Limit theorems for Markov chains. 4.5 Further reading. 5. Markov chain Monte Carlo. 5.1 Metropolis-Hastings algorithm. 5.2 Gibbs sampling. 6. Implementing Markov chain Monte Carlo. 6.1 Software for Markov chain Monte Carlo. 6.2 Assessing convergence and run-length. 6.3 Working with BUGS/JAGS from R. 6.4 Tricks of the trade. 6.5 Other examples. 6.6 Further reading. Part III: Advanced Applications in the Social Sciences. 7. Hierarchical Statistical Models. 7.1 Data and parameters that vary by groups: the case for hierarchical modeling. 7.2 ANOVA as a hierarchical model. 7.3 Hierarchical models for longitudinal data. 7.4 Hierarchical models for non-normal data. 7.5 Multi-level models. 8. Bayesian analysis of choice making. 8.1 Regression models for binary responses. 8.2 Ordered outcomes. 8.3 Multinomial outcomes. 8.4 Multinomial probit. 9. Bayesian approaches to measurement. 9.1 Bayesian inference for latent states. 9.2 Factor analysis. 9.3 Item-response models. 9.4 Dynamic measurement models. Part IV: Appendices. Appendix A: Working with vectors and matrices. Appendix B: Probability review. B.1 Foundations of probability. B.2 Probability densities and mass functions. B.3 Convergence of sequences of random variabales. Appendix C: Proofs of selected propositions. C.1 Products of normal densities. C.2 Conjugate analysis of normal data. C.3 Asymptotic normality of the posterior density. References. Topic index. Author index.

Beyond linearity by default: Generalized additive models

Social scientists almost always use statistical models positing the dependent variable as a global, linear function of X, despite suspicions that the social and political world is not so simple, or that our theories are so strong. Generalized additive models (GAMs) let researchers fit each independent variable with arbitrary nonparametric functions, but subject to the constraint that the nonparametric effects combine additively. In this way GAMs strike a sensible balance between the flexibility of nonparametric techniques and the ease of interpretation and familiarity of linear regression. GAMs thus offer social scientists a practical methodology for improving on the extant practice of global linearity by default. We reanalyze published work from several subfields of political science, highlighting the strengths (and limitations) of GAMs. We estimate non-linear marginal effects in a regression analysis of incumbent reelection, nonparametric duration dependence in an analysis of cabinet duration, and within-dyad interaction effects in a reconsideration of the democratic peace hypothesis. We conclude with a more general consideration of the circumstances in which GAMs are likely to be of use to political scientists, as well as some apparent limitations of the technique.

Pooling the polls over an election campaign

Poll results vary over the course of a campaign election and across polling organisations, making it difficult to track genuine changes in voter support. I present a statistical model that tracks changes in voter support over time by pooling the polls, and corrects for variation across polling organisations due to biases known as ‘house effects’. The result is a less biased and more precise estimate of vote intentions than is possible from any one poll alone. I use five series of polls fielded over the 2004 Australian federal election campaign (ACNielsen, the ANU/ninemsn online poll, Galaxy, Newspoll, and Roy Morgan) to generate daily estimates of the Coalitions share of two-party preferred (2PP) and first preference vote intentions. Over the course of the campaign there is about a 4 percentage point swing to the Coalition in first preference vote share (and a smaller swing in 2PP terms), that begins prior to the formal announcement of the election, but is complete shortly after the leader debates. The ANU/ninemsn online poll and Morgan are found to have large and statistically significant biases, while, generally, the three phone polls have small and/or statistically insignificant biases, with ACNielsen and (in particular) Galaxy performing quite well in 2004. * An earlier version of this paper was prepared for the annual meeting of the Australasian Political Studies Association, University of Adelaide, 29 September–1 October 2004.

Measuring District-Level Partisanship with Implications for the Analysis of U.S. Elections*

Studies of American politics, particularly legislative politics, rely heavily on measures of the partisanship of a district. We develop a measurement model for this concept, estimating partisanship in the absence of election-specific, short-term factors, such as national-level swings specific to particular elections, incumbency advantage, and home-state effects in presidential elections. We estimate the measurement model using electoral returns and district-level demographic characteristics spanning five decades (1952–2000), letting us assess how the distribution of district partisanship has changed over time, in response to population movements and redistricting, particularly via the creation of majority-minority districts. We validate the partisanship measure with an analysis of congressional roll-call data. The model is easily extended to incorporate other indicators of district partisanship, such as survey data.

The Limits of Deliberative Discussion: A Model of Everyday Political Arguments

Can citizens learn from talking politics with one another? To bring out the logic of deliberation, we focus on a simplified model of political discussion: a one-exchange argument. Our model rests on three conditions, all commonly satisfied in real life: (1) that only two alternatives are open for choice—support or opposition to a policy; (2) that as political sophistication increases, so too does the probability that citizens will choose the policy alternative more consonant with their most thoroughly considered view of the matter; and (3) that arguments on opposing sides of an issue are of equal quality. Taking advantage of a specially designed experiment embedded in a large public opinion survey in France, we find that the proportion of citizens choosing policy alternatives consonant with their more general ideological orientations does not increase over the course of our experiment. In the aggregate, we find that deliberation leads at least as many people to ideologically inconsistent positions as it helps people find their way to ideologically consistent positions. In this sense, we find that deliberation is for naught.

Alternative Models of Dynamics in Binary Time-Series-Cross-Section Models: The Example of State Failure 1

This paper investigates a variety of dynamic probit models for time-series– cross-section data in the context of explaining state failure. It shows that ordinary probit, which ignores dynamics, is misleading. Alternatives that seem to produce sensible results are the transition model and a model which includes a lagged latent dependent variable. It is argued that the use of a lagged latent variable is often superior to the use of a lagged realized dependent variable. It is also shown that the latter is a special case of the transition model. The relationship between the transition model and event history methods is also considered: the transition model estimates an event history model for both values of the dependent variable, yielding estimates that are identical to those produced by the two event history models. Furthermore, one can incorporate the insights gleaned from the event history models into the transition analysis, so that researchers do not have to assume duration independence. The conclusion notes that investigations of the various models have been limited to data sets which contain long sequences of zeros; models may perform differently in data sets with shorter bursts of zeros and ones.

To Simulate or NOMINATE

Carroll et al. (2009) summarize the similarities and differences between the NOMINATE and IDEAL methods of fitting spatial voting models to binary roll-call data. As those authors note, for the class of problems with which either NOMINATE and the Bayesian quadratic-normal model can be used, the ideal point estimates almost always coincide, and when they do not, the discrepancy is due to the somewhat arbitrary identification and computational constraints imposed by each method. There are, however, many problems for which the Bayesian quadratic-normal model can be easily generalized, so as to address a broad array of questions and take advantage of additional data. Given the nature and source of the differences between NOMINATE and the Bayesian approach—as well as the fact that both approaches are approximations of the decision-making processes being modeled—we believe that it is preferable to choose the more flexible Bayesian approach.

Primary Politics: Race, Gender, and Age in the 2008 Democratic Primary

Abstract Despite Barack Obama’s momentum in the early phase of the Democratic nomination, the process of selecting a nominee took longer than usual. Obama’s momentum, it seems, got stuck, and the 2008 Democratic presidential nomination was an unusually drawn out affair. Even when it appeared Barack Obama would win the nomination, many Clinton supporters said they would support John McCain in the general election. Why were some Democrats unwilling to join the Obama bandwagon once he emerged as a viable front‐runner – and ultimately the Democratic nominee? In this paper we bring a unique set of panel data from the 2008 Cooperative Campaign Analysis Project (CCAP) to bear on questions about primary vote choice, examining the evolution of preferences over the unusually long and intense 2008 Democratic presidential nomination campaign. Attitudes about race predict vote choice in partisan contests; here we show that (conditional on the presence of a black candidate) these attitudes help explain the dynamics of candidate support over the prolonged intra‐party contest for the 2008 Democratic presidential nomination.

Candidacies and Competitiveness in Multimember Districts

Multimember districts (MMDs) were widespread in U.S. state legislatures as recently as 1970, yet little information is available about them. We provide information about their frequency, distribution, types, and sizes, the degree to which they are contested, and the extent to which incumbents run in them and are reelected. We then indicate how to calculate vote margins in MMDs. The method is to create pseudo-pairs by matching the Democratic candidate who has the highest vote with the Republican candidate who has the lowest vote, the Democratic candidate who has the second highest vote with the Republican who has the second-lowest vote, and so on.

''The Most Liberal Senator''?: Analyzing and Interpreting Congressional Roll Calls

The non-partisan National Journal recently declared Senator John Kerry to be the ‘‘top liberal’’ in the Senate based on analysis of 62 roll calls in 2003. Although widely reported in the media (and the subject of a debate among the Democratic presidential candidates), we argue that this characterization of Kerry is misleading in at least two respects. First, when we account for the ‘‘margin of error’’ in the voting scores -- which is considerable for Kerry given that he missed 60 % of the National Journal’s key votes while campaigning -- we discover that the probability that Kerry is the ‘‘top liberal’’ is only.30, and that we cannot reject the conclusion that Kerry is only the 20 th most liberal senator. Second, we compare the position of the President Bush on these key votes; including the President’s announced positions on these votes reveals the President to be just as conservative as Kerry is liberal (i.e., both candidates are extreme relative to the 108 th Senate). A similar conclusion holds when we replicate the analysis using all votes cast in the 107 th Senate. A more comprehensive analysis than that undertaken by National Journal (including an accounting of the margins of error in voting scores) shows although Kerry belongs to the most liberal quintile of the contemporary Senate, Bush belongs to the most conservative quintile.