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Covariate Functional Form in Cox Models Keele, Luke Uploaded 10-25-2005 Keywords Cox model event history survival models splines semi-parametric duration models Abstract In most event history models, the effect of a covariate on the hazard is assumed to have a log-linear functional form. For continuous covariates, this assumption is often violated as the effect is highly nonlinear. Assuming a log-linear functional form when the nonlinear form applies causes specification errors leading to erroneous statistical conclusions. Scholars can, instead of ignoring the presence of nonlinear effects, test for such nonlinearity and incorporate it into the model. I review methods to test for and model nonlinear functional forms for covariates in the Cox model. Testing for such nonlinear effects is important since such nonlinearity can appear as nonproportional hazards, but time varying terms will not correct the misspecification. I investigate the consequences of nonlinear function forms using data on international conflicts from 1950-1985. I demonstrate that the conclusions drawn from this data depend on fitting the correct functional form for the covariates.

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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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Signals, Models, and Congressional Overrides of the Supreme Court Zorn, Christopher Hettinger, Virginia Uploaded 04-05-1999 Keywords event history models split-population duration models Congress Supreme Court statutory decisions overrides Abstract Sparked by interest in game-theoretic representations of the separation of powers, empirical work examining congressional overrides of Supreme Court statutory decisions has burgeoned in recent years. Much of this work has been hampered, however, by the relative rarity of such events; as has long been noted, congressional attention to the Court is limited, and most Court decisions represent the last word on statutory interpretation. With this fact foremost in our minds, we examine empirically a number of theories regarding such reversals. We apply a split-population duration model to the survival of Supreme Court statutory interpretation decisions. This approach allows us to separate the factors which lead to the event itself (i.e., the presence or absence of an override in a particular case) from those which influence the timing of the event. We find that case-specific factors relating to the salience of a case are an important influence in the incidence of overrides, while Congress- and Court-specific political influences dominate the timing at which those overrides occur. By separating the incidence and timing of overrides, our results yield a more accurate and nuanced understanding of this aspect of the separation of powers system.

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Cosponsorship Coalitions in the U.S. House of Representatives Grant, J. Tobin Pellegrini, Pasquale (Pat) A. Uploaded 04-22-1998 Keywords clustering coalitions cosponsorship duration models hazard models heterogeneity spatial models Abstract urrent theories and methods for studying of cosponsorship assume that the decision to cosponsor is identical to decision to vote. In this paper we develop a new theory of cosponsorship that identifies where along the ideological spectrum cosponsors of a bill are more likely to be. Moreover, we predict that members with organizational ties to the sponsor are more likely to cosponsor than other members. To test this theory, we employ a spatial duration model. This method has recently been used by geographers to estimate areas that are more likely to experience an "event." Using this technique permits a statistical test that supports our substantive hypotheses that cosponsorship coalitions are shaped by the characteristics of the location of the bill, the shared ties to the sponsor, and the policy area. In addition, more active sponsors are associated with wider and less clustered coalitions. These findings demonstrate that theories of the voting decision are not applicable to cosponsorship.

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Strategic Position-Taking and the Timing of Voting Decisions in Congress Box-Steffensmeier, Janet M. Zorn, Christopher Arnold, Laura W. Uploaded 01-01-1995 Keywords timing Congressional voting duration models proportional hazards survival rate Abstract Voting behavior is intimately linked with many of the most prominent questions of concern to students of legislatures, including the strength of legislative parties and factions, the parameters of individual decision making, and the nature of representation (Collie 1985). One critical element of voting in legislatures is the timing of various choices legislators make. The study of strategic position taking and the timing of voting decisions is important for three major reasons: it adds information about the context and sequence of decision making; the analysis more closely approximates members' strategic considerations; and finally, in contrast to most of the literature on legislative roll call voting, the process is examined rather than strictly the result. Yet, despite the importance of position taking and timing, no one has examined comprehensively this crucial aspect of timing. Research on the timing of voting decisions provides insight into theoretical questions regarding the strategic behavior of legislators, institutional constraints on member behavior, and strategies of interest group influence. The project examines the vote to ratify the North American Free Trade Agreement, which has been called ". . . the most important vote on Capital Hill since the Berlin Wall came down" (Frenzel 1994, 3).

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Beyond Ordinary Logit: Taking Time Seriously in Binary Time-Series--Cross-Section Models Beck, Nathaniel Katz, Jonathan Tucker, Richard Uploaded 08-22-1997 Keywords binary time-series--cross-section data logit/probit temporal dependence grouped duration models complementary log-log cubic spline economic interdependence democratic peace war Abstract Researchers typically analyze time-series--cross-section data with a binary dependent variable (BTSCS) using ordinary logit or probit. However, BTSCS observations are likely to violate the independence assumption of the ordinary logit or probit statistical model. It is well known that if the observations are temporally related that the results of an ordinary logit or probit analysis may be misleading. In this paper, we provide a simple diagnostic for temporal dependence and a simple remedy. Our remedy is based on the idea that BTSCS data is identical to grouped duration data. This remedy does not require the BTSCS analyst to acquire any further methodological skills and it can be easily implemented in any standard statistical software package. While our approach is suitable for any type of BTSCS data, we provide examples and applications from the field of International Relations, where BTSCS data is frequently used. We use our methodology to re-assess Oneal and Russett's (1997) findings regarding the relationship between economic interdependence, democracy, and peace. Our analyses show that 1) their finding that economic interdependence is associated with peace is an artifact of their failure to account for temporal dependence and 2) their finding that democracy inhibits conflict is upheld even taking duration dependence into account.