Since Beck, Katz, and Tucker (1998), the standard method for modeling time dependence in binary data has been to incorporate time dummies or splined time in logistic regressions. Although we agree with the need for modeling time dependence, we demonstrate that time dummies can induce estimation problems due to separation. Splines do not suffer from these problems. However, the complexity of splines has led substantive researchers (1) to use knot values that may be inappropriate for their data and (2) to ignore any substantive discussion concerning temporal dependence. We propose a relatively simple alternative: including t, t2, and t3 in the regression. This cubic polynomial approximation is trivial to implement—and, therefore, interpret—and it avoids problems such as quasi-complete separation. Monte Carlo analysis demonstrates that, for the types of hazards one often sees in substantive research, the polynomial approximation always outperforms time dummies and generally performs as well as splines or even more flexible autosmoothing procedures. Due to its simplicity, this method also accommodates nonproportional hazards in a straightforward way. We reanalyze Crowley and Skocpol (2001) using nonproportional hazards and find new empirical support for the historical-institutionalist perspective.

Carter and Signorino (2010) (hereinafter “CS”) add another arrow, a simple cubic polynomial in time, to the quiver of the binary time series—cross-section data analyst; it is always good to have more arrows in one's quiver. Since comments are meant to be brief, I will discuss here only two important issues where I disagree: are cubic duration polynomials the best way to model duration dependence and whether we can substantively interpret duration dependence.

We thank Neal Beck for his comments. In general, there is little difference in our theoretical and practical positions. We all agree that in some applications, time dummies can be problematic; controlling for temporal dependence is important for less-biased estimation of the coefficients on our substantive regressors; a smoothed function of time (whether via a cubic polynomial or spline) is a useful way to model temporal dependence in grouped binary data; and viewing the graph of the hazard can be informative.

Randomized experiments commonly compare subjects receiving a treatment to subjects receiving a placebo. An alternative design, frequently used in field experimentation, compares subjects assigned to an untreated baseline group to subjects assigned to a treatment group, adjusting statistically for the fact that some members of the treatment group may fail to receive the treatment. This article shows the potential advantages of a three-group design (baseline, placebo, and treatment). We present a maximum likelihood estimator of the treatment effect for this three-group design and illustrate its use with a field experiment that gauges the effect of prerecorded phone calls on voter turnout. The three-group design offers efficiency advantages over two-group designs while at the same time guarding against unanticipated placebo effects (which would undermine the placebo-treatment comparison) and unexpectedly low rates of compliance with the treatment assignment (which would undermine the baseline-treatment comparison).

There has been no attention to circular (purely cyclical) data in political science research. We show that such data exist and are mishandled by models that do not take into account the inherently recycling nature of some phenomenon. Clock and calendar effects are the obvious cases, but directional data are observed as well. We describe a standard maximum likelihood regression modeling framework based on the von Mises distribution, then develop a general Bayesian regression procedure for the first time, providing an easy-to-use Metropolis-Hastings sampler for this approach. Applications include a chronographic analysis of U.S. domestic terrorism and directional party preferences in a two-dimensional ideological space for German Bundestag elections. The results demonstrate the importance of circular models to handle periodic and directional data in political science.

A wide range of potentially useful data are available for election forecasting: the results of previous elections, a multitude of preelection polls, and predictors such as measures of national and statewide economic performance. How accurate are different forecasts? We estimate predictive uncertainty via analysis of data collected from past elections (actual outcomes, preelection polls, and model estimates). With these estimated uncertainties, we use Bayesian inference to integrate the various sources of data to form posterior distributions for the state and national two-party Democratic vote shares for the 2008 election. Our key idea is to separately forecast the national popular vote shares and the relative positions of the states. More generally, such an approach could be applied to study changes in public opinion and other phenomena with wide national swings and fairly stable spatial distributions relative to the national average.

This study presents a survey-based method for conducting inference into the determinants of sensitive political behavior. The approach combines two well-established literatures in statistical methods in the social sciences: the randomized response (RR) methodology utilized to reduce evasive answer bias and the generalized propensity score methodology utilized to draw inferences about causal effects in observational studies. The approach permits one to estimate the causal impact of a multivalued predictor variable of interest on a given sensitive behavior in the face of unknown interaction effects between the predictor and the confounders as well as nonlinearities in the relationship between the confounders and the sensitive behavior. Simulation results point to the superior performance of the RR relative to direct survey questioning using this method for samples of moderate to large size. The utility of the approach is illustrated through an application to corruption in the public bureaucracy in three countries in South America.

Signaling models are ubiquitous in political science. An essential characteristic of these models is that actors can update their beliefs about their opponents. An actor observes the behavior of his opponent, and this behavior functions as a signal that allows the actor to learn more about his opponent's true “type.” As a result, the actor is able to adapt his own behavior. Current statistical models of strategic choice based on perfect Bayesian equilibrium, however, allow for very little, if any, belief updating. I explain why current models allow for little updating and offer in their stead a new, fully strategic choice estimator that calculates the correct amount of belief updating.