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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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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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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 �t 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 �t four longitudinal item response models that include dynamic speci�cations for the ideal points and the case-speci�c 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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Heterogeneity and Individual Party Identification Box-Steffensmeier, Janet M. Smith, Renee M. Uploaded 05-01-1997 Keywords heterogeneity party identification macropartisanship panel data Wiley-Wiley Monte Carlo beta-logistic Markov Abstract Box-Steffensmeier and Smith (1996) suggest that heterogeneity in individual-level party identification accounts for aggregate dynamics in macropartisanship. Wiley-Wiley estimates of partisan persistence suggesting a very high degree of individual-level partisan persistence have been made under the assumption of no heterogeneity. Stratifying panel data by subgroups based on information, interest, and age, shows some heterogeneity in persistence even when the Wiley-Wiley estimator is used. Analytical and Monte Carlo results show, however, that the Wiley-Wiley estimator is biased upward when heterogeneity is present. Given these problems, we estimate a beta-logistic model of heterogeneity and persistence in individual-level party identification and show (a) heterogeneity in the probabilities of persistent response does exist and (b) a portion of that heterogeneity is systematically explained by interest in political campaigns in the 1990-91-92 ANES panel three-wave panel. Our estimates indicate Markov models assuming true state dependence may not be needed. Further, we find that our estimate of one of the parameters of the beta distribution is consistent with the estimate of that parameter that would be derived from our previous aggregate-level analysis.

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The-Stage Estimation of Stochastic Truncation Models with Limited Dependent Variables Boehmke, Frederick Uploaded 04-13-2000 Keywords selection bias stochastic truncation maximum likelihood simulation monte carlo initiative interest groups Abstract Recent work has made progress in estimating models involving selection bias of a par� ticularly strong nature: all nonrespondents are unit nonresponders, meaning that no data is available for them. These models are reasonable successful in circumstances where the dependent variable of interest is continuous, but they are less practical empirically when it is latent and only discrete outcomes or choices are observed. I develop a method in this paper to estimate these models that is much more practical in terms of estimation. The model uses a small amount of auxiliary information to estimate the selection equation and these parameters are then used to estimate the equation of interest in a maximum likelihood setting. After presenting monte carlo analysis to support the model, I apply the technique to a substantive problem: which interest groups are likely to turn to the initiative process to achieve their policy goals.

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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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Time Series Models for Compositional Data Brandt, Patrick T. Monroe, Burt L. Williams, John T. Uploaded 07-09-1999 Keywords compositional data VAR time series analysis bootstrap Monte Carlo simulation macropartisanship Abstract Who gets what? When? How? Data that tell us who got what are compositional data - they are proportions that sum to one. Political science is, unsurprisingly, replete with examples: vote shares, seat shares, budget shares, survey marginals, and so on. Data that also tell us when and how are compositional time series data. Standard time series models are often used, to detrimental consequence, to model compositional time series. We examine methods for modeling compositional data generating processes using vector autoregression (VAR). We then use such a method to reanalyze aggregate partisanship in the United States.

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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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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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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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Coordination, Moderation and Institutional Balancing in American House Elections at Midterm Mebane, Walter R. Wand, Jonathan Uploaded 09-02-1999 Keywords campaign finance itemized contributions congressional elections generalized linear mixed model Monte Carlo EM random effects conditional compound Poisson process Abstract We use Federal Election Commission itemized contributions data from 1984 to estimate a model of campaign contributions in U.S. House elections. The model is a dynamic system of conditional compound Poisson processes in which there are contributions from both individuals and political action committees (PACs). The model includes random effects to allow for unobserved heterogeneity among districts and candidates. The dynamic effects measure how contributions to one candidate react to contributions to other candidates, as well as how contributions from individuals interact with contributions from PACs. We test the hypothesis that some candidates received higher contributions because of PAC endorsements. We also test whether national expectations about presidential election outcomes affect contributions to House candidates, as predicted by a policy moderating model. We use a Monte Carlo EM algorithm to optimize the likelihood of the model in specifications that include more than one random effect.

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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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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.

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Potential Ambiguities in a Directed Dyad Approach to State Policy Emulation Boehmke, Frederick Uploaded 07-10-2007 Keywords state politics state policy diffusion emulation monte carlo health policy dyadic Abstract In this paper I discuss circumstances under which the dyadic model of policy diffusion can produce misleading estimates in favor of policy emulation. These circumstances arise in the context of state pain management policy, and correspond generally to policies that states are uniformly expanding. When this happens, dyadic models of policy diffusion conflate policy emulation and policy adoption: since early adopters are policy leaders, later adopters will appear to emulate them, even if they are merely stragglers acting on their own accord. I demonstrate the possibility of this ambiguity analytically and through Monte Carlo simulation. Both start with the assumption that the data are generated according to a standard, monadic model of policy adoption and then converted to a dyadic model, which can incorrectly produce evidence of emulation. I propose a simple modification of the dyadic emulation model --- conditioning on the opportunity to emulate --- and show that it is much less likely to produce inaccurate findings. I then return to the study of pain management policy and find substantial differences between the dyadic emulation model and the conditional emulation model.

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Cointegration Tests when Data are Near-Integrated De Boef, Suzanna Granato, Jim Uploaded 04-22-1998 Keywords time series near-integration ECMs DickeyFuller tests Monte Carlo Abstract Testing theories about political change requires analysts to make assumptions about the nature of the memory of their time series. Applied analyses are often based on inferences that the time series of interest are integrated and cointegrated. Typically these analyses rest on Dickey-Fuller pretests for unit roots and tests for cointegration based on the residuals from a cointegrating regression in the context of the Engle-Granger two-step methodology. We argue that this approach is not a good one and use Monte Carlo results to show that these tests can lead analysts to falsely conclude that the data are cointegrated (or nearly- cointegrated) when the data is near-integrated and not cointegrating. Further, analysts are likely to falsely conclude the relationship is not cointegrating when it is. We show how inferences are highly sensitive to sample size and the signal to noise ratio in the data. We suggest that analysts use the single equation error correction test for cointegrating relationships, and that caution be used in all cases where near-integration is a reasonable alternative to unit roots. Finally, we suggest that in many cases analysts can drop the language of cointegration and adopt single equation error correction models when the theory of error correction is relevant.

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Estimating Binary Dependent Variable Models Under Conditions of Specification Uncertainty Berry, William DeMeritt, Jacqueline Esarey, Justin Uploaded 01-25-2007 Keywords logit probit binary dependent variable specification uncertainty interaction Monte Carlo analysis Abstract Political scientists routinely use logit or probit models when their data involve binary dependent variables (BDVs). Yet the hypotheses we test with logit and probit are rarely specific enough to justify that one of these models is the correct functional form for the process (or true model) generating the data. In this situation of specification uncertainty, it is reasonable to assume that the model being estimated is misspecified. The only issue is the severity of the resulting distortion in results, i.e., whether logit or probit approximates the true model well enough to yield estimated effects that are acceptably close to the true ones. To study estimation in the presence of specification uncertainty, we conduct Monte Carlo analysis using a strategy of purposeful misspecification: we use various logit and probit models with different terms on data sets generated from a wide range of known true models involving a BDV, none of which takes the exact form of a logit or probit model. We find that a widely-employed approach for using logit or probit to test the hypothesis that an independent variable has a positive (or negative) effect on the probability that some event will occur-­by estimating the effect of the variable at central values of the independent variables­-is highly forgiving of specification uncertainty, yielding reasonably accurate inferences even when the true model is not logit or probit. Unfortunately, other applications of logit and probit­-including a common approach to testing a hypothesis that independent variables interact in influencing the probability of event occurrence­-are not nearly as forgiving of the uncertainty. In some situations of specification uncertainty, we can improve the quality of estimated effects by relying on the Akaike Information Criterion [AIC] to choose the terms to be included in a model, but even these improved estimates leave much to be desired.

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A Monte Carlo Comparison of Methods for Compositional Data Analysis Brehm, John Gates, Scott Gomez, Brad Uploaded 07-08-1998 Keywords Compositional data Dirichlet Additive Logistic Monte Carlo Police Behavior Abstract This paper offers an explication of two techniques for compositional data analysis, which involve non-negative data belonging to mutually exclusive and exhaustive categories. The Dirichlet distribution is a multivariate generalization of the beta distribution that offers considerable flexibility, and ease of use, but requires a strong form of an ``independence of irrelevant alternatives'' (IIA) assumption. The second application, proposed by Aitchison (1986) and applied to political data by Katz and King (1997), is the additive logistic method. This approach addresses the strong IIA assumption, but cannot handle strong forms of independence (Rayens and Srinivasen 1994). Monte Carlo simulations are employed on compositional data to explore the limits of applications of the two methods. Data on police officers' allocation of time across a variety of tasks (Ostrom et al. 1988) is used in this analysis. Comparing both common covariates and unique covariates. When the composites are influenced by common covariates, there appears to be no advantage in the use of additive logistic methods over the Dirichlet. Similarly, the additive logistic and Dirichlet methods appear to be equally successful at estimating the effects of the unique covariates on composites. From these simulation results we conclude that the additive logistic method offers little advantage over the Dirichlet, and suffers from several disadvantages.

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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 re�?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 �??bourgeois�?? 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 �??New Politics�??) parties can be distinguished from the positions of other party families.

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Rational Expectations Coordinating Voting in American Presidential and House Elections Mebane, Walter R. Uploaded 07-08-1998 Keywords coordinating voting probabilistic voting spatial voting retrospective voting policy moderation presidential elections congressional elections ticket splitting rational expectations voter equilibrium Bayesian-Nash equilibrium generalized extreme value model nonparametric Monte Carlo integration maximum likelihood Abstract I define a probabilistic model of individuals' presidential-year vote choices for President and for the House of Representatives in which there is a coordinating (Bayesian Nash) equilibrium among voters based on rational expectations each voter has about the election outcomes. I estimate the model using data from the six American National Election Study Pre-/Post-Election Surveys of years 1976--1996. The coordinating model passes a variety of tests, including a test against a majoritarian model in which there is rational ticket splitting but no coordination. The results give strong individual-level support to Alesina and Rosenthal's theory that voters balance institutions in order to moderate policy. The estimates describe vote choices that strongly emphasize the presidential candidates. I also find that a voter who says economic conditions have improved puts more weight on a discrepancy between the voter's ideal point and government policy with a Democratic President than on a discrepancy of the same size with a Republican President.

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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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A Method-Matching Approach to Maximum Likelihood Estimation of the Beta Distribution Paolino, Philip Uploaded 07-11-1998 Keywords maximum-likelihood beta distribution Monte Carlo Abstract The beta distribution is a flexible distribution that can produce a uniform, unimodal, or bimodal distribution of points that can be either symmetric or skewed, but because the two shape parameters in a standard beta distribution do not correspond to the mean and the variance of the distribution, it it not obvious how one tests for the statistical significance of independent variables upon the mean or variance. In this paper, I will first discuss a "standard" approach to this problem as well as develop a "moment-matching" approach. Second, I will use Monte Carlo simulations to examine how well these approaches reproduce the true values of the function given different sample sizes and conditions. Third, I will present some empirical results using the moment-matching approach and compare these results with those obtained from the "standard" approach. From this work, I conclude that while the "moment-matching" approach produces reasonable estimates under the most common situations, the "standard" approach, using a Wald test to evaluate statistical significance, generally outperforms the "moment-matching" approach. As such, while the "moment-matching" approach has the attractive feature of allowing the researcher to estimate a variable's effect upon the mean or variance directly, its use is probably limited to instances where the researcher has a very good reason for wanting to constrain certain parameters to having zero effect upon either the mean or varianc

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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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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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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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The Estimation of Time-Invariant Variables in Panel Analyses with Unit Fixed Effects Pluemper, Thomas Troeger, Vera E. Uploaded 07-23-2004 Keywords Time Invariant Variables Unit effects Monte Carlo Hausman-Taylor Abstract This paper analyzes the estimation of time-invariant variables in panel data models with unit-effects. We compare three procedures that have frequently been employed in comparative politics, namely pooled-OLS, random effects and the Hausman-Taylor model, to a vector decomposition procedure that allows estimating time-invariant variables in an augmented fixed effects approach. The procedure we suggest consists of three stages: the first stage runs a fixed-effects model without time-invariant variables, the second stage decomposes the unit-effects vector into a part explained by the time-invariant variables and an error term, and the third stage re-estimates the first stage by pooled-OLS including the time invariant variables plus the error term of stage 2. We use Monte Carlo simulations to demonstrate that this method works better than its alternatives in estimating typical models in comparative politics. Specifically, the unit fixed effects vector decomposition technique performs better than both pooled OLS and random effects in the estimation of time-invariant variables correlated with the unit effects and better than Hausman-Taylor in estimating the time-invariant variables correlated with the unit effects. Finally, we re-analyze recent work by Huber and Stephens (2001) as well as by Beramendi and Cusack (2004). These analyses seek to cope with the problem of time-invariant variables in panel data.

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The Robustness of Normal-theory LISREL Models: Tests Using a New Optimizer, the Bootstrap, and Sampling Experiments, with Applications Mebane, Walter R. Sekhon, Jasjeet Wells, Martin T. Uploaded 01-01-1995 Keywords statistics estimation covariance structures linear structural relations LISREL bootstrap confidence intervals BCa specification tests goodness-of-fit hypothesis tests optimization evolutionary programming genetic algorithms monte carlo sampling experiment Abstract Asymptotic results from theoretical statistics show that the linear structural relations (LISREL) covariance structure model is robust to many kinds of departures from multivariate normality in the observed data. But close examination of the statistical theory suggests that the kinds of hypotheses about alternative models that are most often of interest in political science research are not covered by the nice robustness results. The typical size of political science data samples also raises questions about the applicability of the asymptotic normal theory. We present results from a Monte Carlo sampling experiment and from analysis of two real data sets both to illustrate the robustness results and to demonstrate how it is unwise to rely on them in substantive political science research. We propose new methods using the bootstrap to assess more accurately the distributions of parameter estimates and test statistics for the LISREL model. To implement the bootstrap we use optimization software two of us have developed, incorporating the quasi-Newton BFGS method in an evolutionary programming algorithm. We describe methods for drawing inferences about LISREL models that are much more reliable than the asymptotic normal-theory techniques. The methods we propose are implemented using the new software we have developed. Our bootstrap and optimization methods allow model assessment and model selection to use well understood statistical principles such as classical hypothesis testing.

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The “Unfriending” Problem: The Consequences of Homophily in Friendship Retention for Causal Estimates of Social Influence Noel, Hans Nyhan, Brendan Uploaded 07-08-2010 Keywords peer effects social networks monte carlo homophily contagion simulation Abstract Christakis, Fowler, and their colleagues have recently published numerous articles estimating “contagion” effects in social networks. In response to concerns that their results are driven by homophily, Christakis and Fowler describe Monte Carlo results showing no evidence of homophily-induced bias in their statistical model’s estimates of peer effects. However, their simulations do not address the role of homophily in friendship retention, which may cause significant problems in longitudinal social network data. We investigate the effects of this mechanism using Monte Carlo simulations and demonstrate that homophily in friendship retention induces significant upward bias and decreased coverage levels in the Christakis and Fowler model if there is non-negligible attrition over time.

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Selection Bias and Continuous-Time Duration Models: Consequences and a Proposed Solution Boehmke, Frederick Morey, Daniel Shannon, Megan Uploaded 07-15-2003 Keywords duration selection bias exponential monte carlo Abstract In this paper we explore the consequences of non-random sample selection for continuous time duration analysis. While the consequences of selectivity are reasonably well-understood in linear regression and common discrete choice models, we have little or no understanding of how it affects duration models. In this paper we study this issue by conducting a series of Monte Carlo analyses that estimate common duration models on data that suffer from selectivity. Our findings indicate that the consequences are severe: both coefficients and standard errors may be biased in an unknown direction. In addition, we find that selection bias may create the appearance of (non-existent) duration dependence. Given these difficulties, we develop a solution for self-selectivity bias in duration models and present evidence that demonstrates its superiority to models that ignore the problem.

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Correlated Disturbances in Discrete Choice Models:A Comparison of Multinomial Probit Models Alvarez, R. Michael Nagler, Jonathan Uploaded 01-01-1995 Keywords econometrics logit multinomial probit gev discrete-choice monte-carlo Abstract Correlated Disturbances in Discrete Choice Models: A Comparison of Multinomial Probit Models and Logit Models In political science, there are many cases where individuals make discrete choices from more than two alternatives. This paper uses Monte Carlo analysis to examine several questions about one class of discrete choice models --- those involving both alternative-specific and individual-specific variables on the right-hand side --- and demonstrates several findings. First, the use of estimation techniques assuming uncorrelated disturbances across alternatives in discrete choice models can lead to significantly biased parameter estimates. This point is tempered by the observation that probability estimates based on the full choice set generated from such estimates are not likely to be biased enough to lead to incorrect inferences. However, attempts to infer the impact of altering the choice set -- such as by removing one of the alternatives -- will be less successful. Second, the Generalized Extreme Value (GEV) model is extremely unreliable when the pattern of correlation among the disturbances is not as restricted as the GEV model assumes. GEV estimates may suggest grouping among the choices that is in fact not present in the data. Third, in samples the size of many typical political science applications -- 1000 observations -- Multinomial Probit (MNP) is capable of recovering precise estimates of the parameters of the systemic component of the model, though MNP is not likely to generate precise estimates of the relationship among the disturbances in samples of this size. Paradoxically, MNP's primary benefit is its ability to uncover relationships among alternatives and to correctly estimate the affect of removing an alternative from the choice set. Thus this paper suggests the increased use of MNP by political scientists examining discrete choice problems when the central question of interest is the effect of removing an alternative from the choice set. We demonstrate that for other questions, models positing independent disturbances may be `close enough.'

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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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Lagging the Dog?: The Robustness of Panel Corrected Standard Errors in the Presence of Serial Correlation and Observation Specific Effects Kristensen, Ida Wawro, Gregory Uploaded 07-13-2003 Keywords time-series cross-section data serial correlation fixed effects panel data lag models Monte Carlo experiments Abstract This paper examines the performance of the method of panel corrected standard errors (PCSEs) for time-series cross-section data when a lag of the dependent variable is included as a regressor. The lag specification can be problematic if observation-specific effects are not properly accounted for, leading to biased and inconsistent estimates of coefficients and standard errors. We conduct Monte Carlo studies to assess how problematic the lag specification is, and find that, although the method of PCSEs is robust when there is little to no correlation between unit effects and explanatory variables, the method's performance declines as that correlation increases. A fixed effects estimator with robust standard errors appears to do better in these situations.

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Getting the Mean Right: Generalized Additive Models Beck, Nathaniel Jackman, Simon Uploaded 00-00-0000 Keywords non-parametric regression smoothing loess non-linear egression Monte Carlo analysis interaction effects incumbency cabinet duration violence Abstract We examine the utility of the generalized additive model as an alternative to the common linear model. Generalized additive models are flexible in that they allow the effect of each independent variable to be modelled non-parametrically while requiring that the effect of all the independent variables is additive. GAMs are common in the statistics literature but are conspicuously absent in political science. The paper presents the basic features of the generalized additive model. Through Monte Carlo experimentation we show that there is little danger of the generalized additive model finding spurious structures. We use GAMS to reanalyze several political science data sets. These applications show that generalized additive models can be used to improve standard analyses by guiding researchers as to the parametric shape of response functions. The technique also provides interesting insights about data, particularly in terms of modelling interactions.

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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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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.