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Time Series Models for Discrete Data: solutions to a problem with quantitative studies of international conflict Jackman, Simon Uploaded 07-21-1998 Keywords categorical time series dependent binary data Markov regression models latent autoregressive process Markov Chain Monte Carlo international conflict democratic peace Abstract Discrete dependent variables with a time series structure occupy something of a statistical limbo for even well-trained political scientists, prompting awkward methodological compromises and dubious substantive conclusions. An important example is the use of binary response models in the analysis of longitudinal data on international conflict: researchers understand that the data are not independent, but lack any way to model serial dependence in the data. Here I survey methods for modeling categorical data with a serial structure. I consider a number of simple models that enjoy frequent use outside of political science (originating in biostatistics), as well as a logit model with an autoregressive error structure (the latter model is fit via Bayesian simulation using Markov chain Monte Carlo methods). I illustrate these models in the context of international conflict data. Like other re-analyses of these data addressing the issue of serial dependence, citeaffixed{beck:btscs}{e.g.,}, I find economic interdependence does not lessen the chances of international conflict. Other findings include a number of interesting asymmetries in the effects of covariates on transitions from peace to war (and vice versa). Any reasonable model of international conflict should take into account the high levels of persistence in the data; the models I present here suggest a number of methods for doing so.

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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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Testing Theories Involving Strategic Choice: The Example of Crisis Escalation Smith, Alastair Uploaded 07-23-1997 Keywords Strategic choice Bayesian model testing Markov chain Monte Carlo simulation multi-variate probit crisis escalation war Abstract If we believe that politics involves a significant amount of strategic interaction then classical statistical tests, such as Ordinary Least Squares, Probit or Logit, cannot give us the right answers. This is true for two reasons: The dependent variables under observation are interdependent-- that is the essence of game theoretic logic-- and the data is censored -- that is an inherent feature of off the path expectations that leads to selection effects. I explore the consequences of strategic decision making on empirical estimation in the context of international crisis escalation. I show how and why classical estimation techniques fail in strategic settings. I develop a simple strategic model of decision making during crises. I ask what this explanation implies about the distribution of the dependent variable: the level of violence used by each nation. Counterfactuals play a key role in this theoretical explanation. Yet, conventional econometric techniques take no account of unrealized opportunities. For example, suppose a weak nation (B) is threatened by a powerful neighbor (A). If we believe that power strongly influences the use of force then the weak nation realizes that the aggressor's threats are probably credible. Not wishing to fight a more powerful opponent, nation B is likely to acquiesce to the aggressor's demands. Empirically, we observe A threaten B. The actual level of violence that A uses is low. However, the theoretical model suggests that B acquiesced precisely because A would use force. Although the theoretical model assumes a strong relationship between strength and the use of force, traditional techniques find a much weaker relationship. Our ability to observe whether nation A is actually prepared to use force is censored when nation B acquiesces. I develop a Strategically Censored Discrete Choice (SCDC) model which accounts for the interdependent and censored nature of strategic decision making. I use this model to test existing theories of dispute escalation. Specifically, I analyze Bueno de Mesquita and Lalman's (1992) dyadically coded version of the Militarized Interstate Dispute data (Gochman and Moaz 1984). I estimate this model using a Bayesian Markov chain Monte Carlo simulation method. Using Bayesian model testing, I compare the explanatory power of a variety of theories. I conclude that strategic choice explanations of crisis escalation far out-perform non-strategic ones.

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Validation of software for Bayesian models using posterior quantiles Cook, Samantha Gelman, Andrew Rubin, Donald Uploaded 08-16-2005 Keywords Bayesian inference Markov chain Monte Carlo simulation computation hierarchical models Abstract We present a simulation-based method designed to establish the computational correctness of software developed to fit a specific Bayesian model, capitalizing on properties of Bayesian posterior distributions. We illustrate the validation technique with two examples. The validation method is shown to find errors in software when they exist and, moreover, the validation output can be informative about the nature and location of such errors.

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Democracy as a Latent Variable Treier, Shawn Jackman, Simon Uploaded 07-16-2003 Keywords democracy Polity measurement latent variables Bayesian statistics item-response model ordinal data latent class analysis democratic peace Markov chain Monte Carlo Abstract Measurement is critical to the social scientific enterprise. Many key concepts in social-scientific theories are not observed directly, and researchers rely on assumptions (tacitly or explicitly, via formal measurement models) to operationalize these concepts in empirical work. In this paper we apply formal, statistical measurement models to the Polity indicators of democracy and autocracy, used widely in studies of international relations. In so doing, we make explicit the hitherto implicit assumptions underlying scales built using the Polity indicators. We discuss two models: one in which democracy is operationalized as a latent continuous variable, and another in which democracy is operationalized as a latent class. Our modeling approaches allow us to assess the measurement error in the resulting measure of democracy. We show that this measurement error is considerable, and has substantive consequences when using a measure of democracy as an independent variable in cross-national statistical analysis. Our analysis suggests that skepticism as to the precision of the Polity democracy scale is well-founded, and that many researchers have been overly sanguine about the properties of the Polity democracy scale in applied statistical work.

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Modeling Structural Changes: Bayesian Estimation of Multiple Changepoint Models and State Space Models Park, Jong Hee Uploaded 07-17-2006 Keywords Multiple changepoint model State space model Markov chain Monte Carlo methods Bayes factors Data augmentation. Abstract While theoretical models in political science are inspired by structural changes in politics, most empirical methods assume stable patterns of causal relationships. Static models with constant parameters do not properly capture dynamic changes in the data and lead to incorrect parameter estimates. In this paper, I introduce two Bayesian time series models, which can detect and estimate possible structural changes in temporal data: multiple changepoint models and state space models. To emphasize the utility of the models to political scientists, I show some examples in the context of discrete dependent variables. Then, I apply these models to an important debate in international politics over U.S. use of force abroad. The findings of the multiple changepoint and state space models demonstrate that the predictors of presidential use of force have shifted dramatically.

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Presidential Approval: the case of George W. Bush Beck, Nathaniel Jackman, Simon Rosenthal, Howard Uploaded 07-19-2006 Keywords presidential approval public opinion polls house effects dynamic linear model Bayesian statistics Markov chain Monte Carlo state space pages of killer graphs Abstract We use a Bayesian dynamic linear model to track approval for George W. Bush over time. Our analysis deals with several issues that have been usually addressed separately in the extant literature. First, our analysis uses polling data collected at a higher frequency than is typical, using over 1,100 published national polls, and data on macro-economic conditions collected at the weekly level. By combining this much poll information, we are much better poised to examine the public's reactions to events over shorter time scales than can the typical analysis of approval that utilizes monthly or quarterly approval. Second, our statistical modeling explicitly deals with the sampling error of these polls, as well as the possibility of bias in the polls due to house effects. Indeed, quite aside from the question of ``what drives approval?'', there is considerable interest in the extent to which polling organizations systematically diverge from one another in assessing approval for the president. These bias parameters are not only necessary parts of any realistic model of approval that utilizes data from multiple polling organizations, but easily estimated via the Bayesian dynamics linear model.

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Binary and Ordinal Time Series with AR(p) Errors: Bayesian Model Determination for Latent High-Order Markovian Processes Pang, Xun Uploaded 07-06-2008 Keywords Autoregressive Errors Auxiliary Particle Filter Fixed-lag Smoothing Markov Chain Monte Carlo (MCMC) Political Science Sampling Importance Resampling(SIR) Abstract To directly and adequately correct serial correlation in binary and ordinal response data, this paper proposes a probit model with errors following a pth-order autoregressive process, and develops simulation-based methods in the Bayesian context to handle computational challenges of posterior estimation, model comparison, and lag order determination. Compared to the extant methods, such as quasi-ML, GCM, and and simulation-based ML estimators, the current method does not rely on the properties of the big variance-covariance matrix or the shape of the likelihood function. In addition, the present model efficiently handles high-order autocorrelated errors that raise computationally formidable difficulties to the conventional methods. By applying a mixed sampler of the Gibbs and Metropolis-Hastings algorithm, the posterior distributions of the parameters do not depend on initial observations. The auxiliary particle filter, complemented by the fixed-lag smoothing, is extended to approximate Bayes Factors for models with latent high-order Markov processes. Computational methods are tested with empirical data. Energy cooperation policies of the International Energy Agency are analyzed in terms of their effects on global oil-supply security. The current model with different lag orders, together with other competitive models, is estimated and compared.

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Sampling Schemes for Generalized Linear Dirichlet Random Effects Models Kyung, Minjung Gill, Jeff Casella, George Uploaded 02-18-2009 Keywords generalized linear mixed Dirchlet model Markov chain Monte Carlo Dirichlet process priors for random effects precision parameters Scottish Social Attitudes Survey terrorism targeting Abstract We evaluate MCMC sampling schemes for a variety of link functions in generalized linear models with Dirichlet random effects. We find that models using Dirichlet process priors for the random effects tend to capture information in the data in a nonparametric fashion. In fitting the the Dirichlet process, dealing with the precision parameter has troubled model specifications in the past. Here we find that incorporating this parameter into the MCMC sampling scheme is not only computationally feasible, but also results in a more robust set of estimates, in that they are marginalized-over rather than conditioned-upon. Applications are provided with social science problems in areas where the data can be difficult to model. In all, we find that these models provide superior Bayesian posterior results in theory, simulation, and application.

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Joint Modeling of Dynamic and Cross-Sectional Heterogeneity: Introducing Hidden Markov Panel Models Park, Jong Hee Uploaded 07-14-2009 Keywords Bayesian statistics Fixed-effects Hidden Markov models Markov chain Monte Carlo methods Random-effects Reversible jump Markov chain Monte Carlo Abstract Researchers working with panel data sets often face situations where changes in unobserved factors have produced changes in the cross-sectional heterogeneity across time periods. Unfortunately, conventional statistical methods for panel data are based on the assumption that the unobserved cross-sectional heterogeneity is time constant. In this paper, I introduce statistical methods to diagnose and model changes in the unobserved heterogeneity. First, I develop three combinations of a hidden Markov model with panel data models using the Bayesian framework; (1) a baseline hidden Markov panel model with varying fixed effects and varying random effects; (2) a hidden Markov panel model with varying fixed effects; and (3) a hidden Markov panel model with varying intercepts. Second, I present model selection methods to diagnose the dynamic heterogeneity using the marginal likelihood method and the reversible jump Markov chain Monte Carlo method. I illustrate the utility of these methods using two important ongoing political economy debates; the relationship between income inequality and economic growth and the effect of institutions on income inequality.

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Modeling History Dependence in Network-Behavior Coevolution Franzese, Robert Hays, Jude Kachi, Aya Uploaded 07-21-2010 Keywords path dependence history dependence network coevolution spatial econometrics selection homophily SIENA RSIENA markov chain logit p-star military alliance conflict behavior Abstract Spatial interdependence--the dependence of outcomes in some units on those in others--is substantively and theoretically ubiquitous and central across the social sciences. Spatial association is also omnipresent empirically. However, spatial association may arise from three importantly distinct processes: common exposure of actors to exogenous external and internal stimuli, interdependence of outcomes/behaviors across actors (contagion), and/or the putative outcomes may affect the variable along which the clustering occurs (selection). Accurate inference about any of these processes generally requires an empirical strategy that addresses all three well. From a spatial-econometric perspective, this suggests spatiotemporal empirical models with exogenous covariates (common exposure) and spatial lags (contagion), with the spatial weights being endogenous (selection). From a longitudinal network-analytic perspective, we can identify the same three processes as potential sources of network effects and network formation. From that perspective, actors' self-selection into networks (by, e.g., behavioral homophily) and actors' behavior that is contagious through those network connections likewise demands theoretical and empirical models in which networks and behavior coevolve over time. This paper begins building such modeling by, on the theoretical side, extending a Markov type-interaction model to allow endogenous tie-formation, and, on the empirical side, merging a simple spatial-lag logit model of contagious behavior with a simple p-star logit model of network formation, building this synthetic discrete-time empirical model from the theoretical base of the modified Markov type-interaction model. One interesting consequence of network-behavior coevolution--identically: endogenous patterns of spatial interdependence--emphasized here is how it can produce history-dependent political dynamics, including equilibrium phat and path dependence (Page 2006). The paper explores these implications, and then concludes with a preliminary demonstration of the strategy applied to alliance formation and conflict behavior among the great powers in the first half of the twentieth century.

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Degeneracy and Inference for Social Networks Handcock, Mark S. Uploaded 07-15-2002 Keywords Random graph models log-linear network model Markov fields Markov Chain Monte Carlo Abstract Networks are a form of "relational data". Relational data arise in many social science fields and graph models are a natural approach to representing the structure of these relations. This framework has many applications including, for example, the structure of social networks, the behavior of epidemics, the interconnectedness of the WWW, and long-distance telephone calling patterns. We review stochastic models for such graphs, with particular focus on sexual and drug use networks. Commonly used Markov models were introduced by Frank and Strauss (1986) and were derived from developments in spatial statistics (Besag 1974). These models recognize the complex dependencies within relational data structures. To date, the use of graph models for networks has been limited by three interrelated factors: the complexity of realistic models, lack of use of simulation studies, and a poor understanding of the properties of inferential methods. In this talk we discuss these factors and the degeneracy of commonly promoted models. We also review the role of Markov Chain Monte Carlo (MCMC) algorithms for simulation and likelihood-based inference. These ideas are applied to a sexual relations network from Colorado Springs with the objective of understanding the social determinants of HIV spread. In this talk we focus on stochastic models for such graphs that can be used to represent the structural characteristics of the networks. In our applications, the nodes usually represent people, and the edges represent a specified relationship between the people.

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Bayesian Methods: A Social and Behavioral Sciences Approach, ANSWER KEY TO THE SECOND EDITION. Odd Numbers. Park, Hong Min Gill, Jeff Uploaded 09-14-2010 Keywords Bayes modeling simulation Bayesian inference MCMC prior posterior Bayes Factor DIC GLM Markov chain Monte Carlo hierarchical models linear nonlinear Abstract This is the odd-numbered exercise answers to the second edition of Bayesian Methods: A Social and Behavioral Sciences Approach (minus Chapter 13). Course Instructors can get the full set from Chapman & Hall/CRC upon request.

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Stochastic Dependence in Competing Risks Gordon, Sanford C. Uploaded 09-05-2001 Keywords Competing risks duration models survival models event history random effects frailty models unobserved heterogeneity Monte Carlo simulation Congress legislative position-taking cabinet survival numeric integration Markov Chain Monte Carlo Abstract The term "Competing Risks" describes duration models in which spells may terminate via multiple outcomes: The term of a cabinet, for example, may end with or without an election; wars persist until the loss or victory of the aggressor. Analysts typically assume stochastic independence among risks, the duration modeling equivalent of independence of irrelevant alternatives. However, many political examples violate this assumption. I review competing risks as a latent variables approach. After discussing methods for modeling dependence that place restrictions on the nature of association, I introduce a parametric generalized dependent risks model in which inter-risk correlation may be estimated and its significance tested. The method employs risk-specific random effects drawn from a multivariate normal distribution. Estimation is conducted using numerical methods and/or Bayesian simulation. Monte Carlo simulation reveals desirable large sample properties of the estimator. Finally, I examine two applications using data on cabinet survival and legislative position taking.

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Bayesian Learning about Ideal Points of U.S. Supreme Court Justices, 1953-1999 Martin, Andrew D. Quinn, Kevin M. Uploaded 07-09-2001 Keywords item response models dynamic linear models Markov chain Monte Carlo Abstract At the heart of attitudinal and strategic explanations of judicial behavior is the assumption that justices have policy preferences. These preferences have been measured in a handful of ways, including using factor analysis and multidimensional scaling techniques (Schubert, 1965, 1974), looking at past votes in a single policy area (Epstein et al., 1989), content-analyzing newspaper editorials at the time of appointment to the Court (Segal and Cover, 1989), and recording the background characteristics of the justices (Tate and Handberg, 1991). In this manuscript we employ Markov chain Monte Carlo (MCMC) methods to Þt Bayesian measurement models of judicial preferences for all justices serving on the U.S. Supreme Court from 1953 to 1999. We are particularly interested in considering to what extent ideal points of justices change throughout their tenure on the Court, and how the proposals over which they are voting also change across time. To do so, we Þt four longitudinal item response models that include dynamic speciÞcations for the ideal points and the case-speciÞc parameters. Our results suggest that justices do not have constant ideal points, even after controlling for the types of cases that come before the Court.

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Estimation and Inference by Bayesian Simulation: an on-line resource for social scientists Jackman, Simon Uploaded 08-30-1999 Keywords Markov chain Monte Carlo Bayesian statistics how-to BUGS ordinal probit time series Abstract http://tamarama.stanford.edu/mcmc a Web-based on-line resource for Markov chain Monte Carlo, specifically tailored for social scientists. MCMC is probably the most exciting development in statistics in the last ten years. But to date, most applications of MCMC methods are in bio-statistics, making it difficult for social scientists to fully grasp the power of MCMC methods. In providing this on-line resource I aim to overcome this deficiency, helping to put MCMC in the reach of social scientists. The resource comprises: (*) a set of worked examples (*) data and programs (*) links to other relevant web sites (*) notes and papers At the meetings in Atlanta, I will present two of the worked examples, which are part of this document: (*) Cosponsor: computing auxiliary quantities from MCMC output (e.g., percent correctly predicted in a logit/probit model of legislative behavior; cf Herron 1999). (*) Delegation: estimating a time-series model for ordinal data (e.g., changes to the U.S. president's discretionary power in trade policy, 1890-1990; cf Epstein and O'Halloran 1996).

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Campaign Timing and Vote Determinants Peterson, David A.M. Uploaded 09-07-1999 Keywords Campaign effects hierarchical models random coefficient Markov chain Monte Carlo Abstract Questions about the role of campaigns in making different considerations more important for voters have been central to the study of political behavior for fifty years (Lazardsfeld et al 1948). The basic concern is does the information presented during the campaign alter how voters evaluate and choose between candidates. This paper develops a random coefficient or hierarchical logit model to analyze the 1984 NES Continuous Monitoring Survey. The specification treats the effect of partisanship, policy distance and candidate character traits as a function of the campaign timing. Of the theories tested in this paper, the attitude strength model best predicts the changes in vote determinants across the campaign.