1

Paper

Candidate Viability and Voter Learning in the Presidential Nomination Process Paolino, Philip Uploaded 08-30-1999 Keywords beta distribution maximum likelihood heterogeneity Bayesian Abstract Candidates' viability and momentum are important features of the presidential nomination process in the United States, and much work has examined how both influence the outcome of the nomination campaign (e.g. Aldrich 1980a, Aldrich 1980b, Bartels 1988, Brady and Johnston 1987) Previous treatments, however, have focused upon candidates' expectations of winning or losing the nomination. A critical feature that has been mentioned, but not addressed directly is the volatility of these expectations. In this paper, I use a view of viability and momentum that considers both expectations and the variance of the public's perceptions about candidates' viability which allows us to examine how voters use new information to update their beliefs about both elements of candidates' viability and provides a basis for assessing candidates' potential momentum.

2

Paper

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.

3

Paper

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

4

Paper

A Statistical Assessment of The Spatial Model of Ideology Ghobarah, Hazen Uploaded 07-20-1998 Keywords spatial theory macroµ-stability ideology maximum likelihood multi-dimensional scaling Abstract The spatial model of ideology (Hinich and Munger, 1994) specifies a formal framework for linking positions of the electorate, the parties, and the candidates on a plethora of issues to positions on a few ideological dimensions- perhaps just one or two dimensions. While extant tests of this model have relied on cross-sectional survey data, this study utilizes a panel. The panel format allows a direct examination of the stability, and indeed the reality, of the parameters and the cognitive processes that are posited by the formal model. Given the available variables in the panel, I operationalize one model for party competition and another for presidential candidates. The results of both are supportive of the linkage model. The statistical methodology used in this study is no more complex than the model requires; it includes maximum likelihood factor analysis and a customized multi-dimensional scaling procedure.

5

Paper

Intrainstitutional Mobility in the Postreform House of Representatives Wawro, Gregory Uploaded 08-26-1998 Keywords legislative entrepreneurship legislative organization maximum likelihood methods mobility analysis career concerns vacancy competition Abstract Theory: When deciding whom to promote to prestigious positions within the House, members will favor those individuals who are the most likely to use the resources associated with prestigious positions to produce legislation when there is substantial demand for it. Members will select those individuals who have demonstrated a propensity for engaging in legislative entrepreneurship because they are the most qualified in this regard. Hypothesis: "The job ladders hypothesis": Members who engage in legislative entrepreneurship are more likely to move up the job ladder to prestigious positions within the committee and party hierarchies in the House. Method: I develop measures of legislative entrepreneurship using data on the characteristics of bills sponsored by members and members' testimony before committees. I develop a statistical model that addresses the problems of analyzing intrainstitutional mobility and the problems with assessing entrepreneurial ability. With this model I perform a multivariate analysis to assess the effects of legislative entrepreneurship while accounting for other variables that previous studies have found to affect intrainstitutional mobility. Results: Engaging in legislative entrepreneurship increases the probability that members of the majority party will advance to full committee, subcommittee, and party leadership positions.

6

Paper

Precise, Second-Order Correct Estimates of the Natural Rate of Unemployment via Bootstrap Calibration Sekhon, Jasjeet Uploaded 09-11-1997 Keywords Natural Rate of Unemployment NAIRU Unemployment Bootstrap Calibration Confidence Interval Likelihood Marginal Likelihood Conditional Likelihood Profile Likelihood Abstract The natural rate of unemployment, which is usually considered to be the nonaccelerating inflation rate of unemployment (NAIRU), is an important and often used economic variable (Gordon 1997). In this paper I present second-order correct $O_{p}(n^{-2})$ confidence regions for estimates of the NAIRU, obtained via bootstrap calibration. These confidence regions are three times smaller than those provided in recent econometric work (Staiger, Stock and Watson 1997a, 1997b). The confidence regions are sufficiently precise to support use of the NAIRU for a variety of analytical and policy purposes, including monetary policy, as determined by a criterion suggested by Krueger (1997).

7

Paper

Measuring Party Cohesion on Roll Call Votes with an Application to the Labor Committee of the Chilean Senate Londregan, John B. Uploaded 08-22-1997 Keywords Maximum Likelihood Roll Call Voting Chile Abstract I introduce measures of two forms of party cohesion, affinity, in which members of the same party share a similar ideological outlook, and would vote alike in any event, and discipline, in which legislators of the same party compromise their basic ideological positions on party votes. These measures are based on maximum likelihood estimates of a spatial model of voting. Applied to the Labor Committee of the Chilean Senate the analysis identifies substantial affinity among elected Senators from the ruing Concertacion coalition, while the Institutional Senators exhibit marked differences in their ideological affinities. Neither of the discipline measures exceeds the threshold of tatistical significance.

8

Paper

The Consequences of Majority-Minority Districts for Representation: Evidence of Partisan Mobilization, Countermobilization and Demobilization Brandt, Patrick T. Bailey, Michael Uploaded 08-21-1997 Keywords Multinomial probit panel data methods simulated maximum likelihood probability simulation redistricting Abstract Few analyses of the effects of race-based congressional redistricting have used survey data to analyze the implications of redistricting. This type of micro-level data can add significant intuition to aggregate data analysis. This paper looks at whether voters respond to redistricting by mobilizing, demobilizing, or countermobilizing using panel data from the 1990-1992 National Election Study. A 2-period vote choice model is estimated using a multiperiod multinomial probit model, and controlling for the effects of redistricting. Results show that the presence of black Democratic candidates in majority-minority districts after redistricting reduces turnout by white voters for the Democratic candidates.

9

Paper

Congressional Campaign Contributions, District Service and Electoral Outcomes in the United States: Statistical Tests of a Formal Game Model with Nonlinear Dynamics Mebane, Walter R. Uploaded 07-22-1997 Keywords congressional elections campaign contributions campaign finance district service intergovernmental transfers formal model game theory Cournot-Nash equilibrium Nash equilibrium differential equations dynamical system nonlinear dynamics Hopf bifurcation normal form Whitney embedding theorem divergence theorem Liouville's theorem multivariate normal distribution maximum likelihood Wald test stability asymptotic stability Abstract Using a two-stage game model of congressional campaigns, the second stage being a system of ordinary differential equations, I argue that candidates, political parties and financial contributors interact strategically in American congressional elections in a way that is inherently nonlinear. Congressional races in which the incumbent faces a challenge are generated by dynamical systems that have Hopf bifurcations: a small change in the challenger's quality or in the type of district service can change a stable incumbent advantage into an oscillating race in which the incumbent's chances are uncertain. The normal form equations for such a system inspire a statistical model that can recover qualitative features of the dynamics from cross-sectional data. I estimate and test the model using data from the 1984 and 1986 election periods for political action committee campaign contributions, intergovernmental transfers and general election vote shares.

10

Paper

Coordinating Voting in American Presidential and House Elections Mebane, Walter R. Uploaded 07-21-1997 Keywords coordinating voting moderating voting probabilistic voting spatial voting retrospective voting presidential elections congressional elections split-ticket voting pivotal voter theorem beta distribution multinomial logit maximum likelihood Abstract I describe and estimate a probabilistic voting model designed to test whether individuals' votes for President and for the House of Representatives are coordinated with respect to two cutpoints on a single spatial dimension, in the way that Alesina and Rosenthal's pivotal voter theorem suggests they should be. In my model the cutpoints are random variables about which each individual has a subjective probability distribution. Each person's probabilistic coordinating voting behavior occurs relative to the cutpoints' expected values under the distribution. The model implements the idea the pattern of coordination depends on an individual's evaluation of the economy. The economic bias in the coordinating pattern implies that voters punish a Democratic President for success in improving the economy. The economically successful Democratic President can avoid losses only if the voters who rate the economy as having improved also believe that the policy position of the Democratic party has shifted to the right.

11

Paper

A Simulated Maximum Likelihood application to the 1988 Democratic Primary Lawrence, Eric D. Uploaded 03-28-1997 Keywords simulated maximum likelihood multinomial probit vote choice models Abstract The multinomial probit model has some appealing advantages over models that do not allow for correlated errors, such as multinomial logit and conditional logit. With a few exceptions, however, multinomial probit models have not been estimated for vote choice models because of the computational costs inherent in evaluating high dimensional integrals. This paper explains one recently developed approach, simulated maximum likelihood combined with the GHK simulator, that makes it feasible to accurately estimate multinomial probit models. The method is demonstrated on a model of the 1988 Democratic Super Tuesday primary.

12

Paper

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

13

Paper

Power-law distributions in empirical data Clauset, Aaron Shalizi, Cosma Newman, Mark Uploaded 06-11-2007 Keywords Power-law distributions Pareto Zipf maximum likelihood heavy-tailed distributions likelihood ratio test model selection Abstract Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the empirical detection and characterization of power laws is made difficult by the large fluctuations that occur in the tail of the distribution. In particular, standard methods such as least-squares fitting are known to produce systematically biased estimates of parameters for power-law distributions and should not be used in most circumstances. Here we describe statistical techniques for making accurate parameter estimates for power-law data, based on maximum likelihood methods and the Kolmogorov-Smirnov statistic. We also show how to tell whether the data follow a power-law distribution at all, defining quantitative measures that indicate when the power law is a reasonable fit to the data and when it is not. We demonstrate these methods by applying them to twenty-four real-world data sets from a range of different disciplines. Each of the data sets has been conjectured previously to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data while in others the power law is ruled out.

14

Paper

Practical Maximum Likelihood Altman, Micah McDonald, Michael P. Uploaded 07-22-2001 Keywords maximum likelihood optimization statistical computation numerical stability accuracy Abstract Maximum likelihood estimation is now widely used in political science, providing a general statistical framework in which we build and test increasingly complex models of politics. The modern development of maximum likelihood is attributable to Fisher, and the approach dominated mathematical statistics during the twentieth century. More attention has been paid to the development of complex statistical models than to the necessary details of their estimation. In this article we discuss some of the art and practice of MLE: -Estimation: We discuss how to choose algorithms for MLE estimations, methods for setting algorithm parameters appropriately, and how to formulate likelihood functions for efficient and accurate estimation. -Tests of Estimation: Methods of statistical inference assume that a global maximum of the likelihood function has been found. There are however, few general guarantees that likelihood functions are single-peaked. Furthermore, no MLE software currently in use by political scientists verifies that global maximum of the likelihood function has been reached. We provide tests of global optimality, drawing from current research in statistics, econometrics, and computer science. -MLE Based Inference: Standard errors produced by MLE's can be misleading, and lead to unreliable inferences, when the likelihood function is not well behaved around its maximum. We illustrate the consequences of unreliable methods, and discuss more robust methods of calculating

15

Paper

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

16

Paper

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.

17

Paper

Two-Stage Estimation of Non-Recursive Choice Models Alvarez, R. Michael Glasgow, Garrett Uploaded 03-02-1999 Keywords two-stage estimation probit endogeneity two-stage probit least squares two-stage conditional maximum likelihood Abstract Questions of causation are important issues in empirical research on political behavior. Most of the discussion of the econometric problems associated with multi-equation models with reciprocal causation has focused on models with continuous dependent variables (e.g. Markus and Converse 1979; Page and Jones 1979). Yet many models of political behavior involve discrete or dichotomous dependent variables; this paper describes two techniques which can consistently estimate reciprocal relationships between dichotomous and continuous dependent variables. The first, two-stage probit least squares (2SPLS), is very similar to two-stage instrumental variable techniques. The second, two-stage conditional maximum likelihood (2SCML), may overcome problems associated with 2SPLS, but has not been used in the political science literature. First, we demonstrate the potential pitfalls of ignoring the problems of reciprocal causation in non-recursive choice models. Then, we show the properties of both techniques using Monte Carlo simulations: both the two-stage models perform well in large samples, but in small samples the 2SPLS model has superior statistical properties. However, the 2SCML model offers an explicit statistical test for endogeneity. Last, we apply these techniques to an empirical example which focuses on the relationship between voter preferences in a presidential election and the voter's uncertainty about the policy positions taken by the candidates. This example demonstrates the importance of these techniques for political science research.

18

Paper

The MAP-B Program with Macro and Micro Applications Hinich, Melvin J. Ghobarah, Hazen Uploaded 07-11-1999 Keywords spatial maps maximum likelihood resampling Abstract We present and apply a general methodology for obtaining a multi-dimensional map of the 'political space' in a given country based on the rating by members of the public of a set candidates or parties. This methodology produces spatial ideology maps of the stimuli (candidates or parties) and the distribution of ideal points of the public. Earlier versions of this methodology, have been applied to American presidential elections (e.g. Enelow and Hinich, 1984:169-216), and to elections in Taiwan (Lin, Chu and Hinich, in World Politics, 1996), Germany (Pappi and Eckstein, in Public Choice, 1998), Ukraine (Hinich, Khmelko and Ordeshook, in Post-Soviet Affairs, 1999), and Russia (Myagkov and Ordeshook, in Public Choice, 1998) among others. This methodology allows for the specification of a valence dimension to capture non-policy characteristics of parties and candidates. The new version (MapB) is capable of recovering the distribution of the estimates of the candidate/party positions in the ideological space through a modified resampling technique. Moreover, it is available as a standalone user-friendly program for the PC/Windows platform.

19

Poster

Robust Estimation of the Cox Proportional Hazards Model Harden, Jeff Uploaded 07-17-2010 Keywords Event History Modeling Cox Proportional Hazards Model Partial Likelihood Maximization Iteratively-Reweighted Robust Estimation Cross-Validation Abstract The Cox proportional hazards model is often used with time-to-event data in political science. However, misspecification issues such as measurement error or omitted covariates can cause substantial coefficient bias when it is estimated via the conventional Partial Likelihood Maximization (PLM). Here we review an iteratively-reweighted robust (IRR) estimator of the Cox model that is proven to reduce this bias under such conditions and propose a cross-validated median fit (CVMF) test to select between PLM and IRR. Then we apply the test to data in political science. We consider several typologies of replications with respect to (1) the test's selection (PLM or IRR) and (2) the implications of IRR for the original hypotheses (less support, more support, or mixed results). Overall, we demonstrate that PLM and IRR can each be optimal, that substantive conclusions can depend on which one is used, and that the CVMF test is effective in choosing between them.