Suchergebnisse

AbstractSeparation commonly occurs in political science, usually when a binary explanatory variable perfectly predicts a binary outcome. In these situations, methodologists often recommend penalized maximum likelihood or Bayesian estimation. But researchers might struggle to identify an appropriate penalty or prior distribution. Fortunately, I show that researchers can easily test hypotheses about the model coefficients with standard frequentist tools. While the popular Wald test produces misleading (even nonsensical) p-values under separation, I show that likelihood ratio tests and score tests behave in the usual manner. Therefore, researchers can produce meaningful p-values with standard frequentist tools under separation without the use of penalties or prior information.

Political scientists commonly focus on quantities of interest computed from model coefficients rather than on the coefficients themselves. However, the quantities of interest, such as predicted probabilities, first differences, and marginal effects, do not necessarily inherit the small-sample properties of the coefficient estimates. Indeed, unbiased coefficient estimates are neither necessary nor sufficient for unbiased estimates of the quantities of interest. I characterize this transformation-induced bias, calculate an approximation, illustrate its importance with two simulation studies, and discuss its relevance to methodological research.

When facing small numbers of observations or rare events, political scientists often encounter separation, in which explanatory variables perfectly predict binary events or nonevents. In this situation, maximum likelihood provides implausible estimates and the researcher might want incorporate some form of prior information into the model. The most sophisticated research uses Jeffreys' invariant prior to stabilize the estimates. While Jeffreys' prior has the advantage of being automatic, I show that it often provides too much prior information, producing smaller point estimates and narrower confidence intervals than even highly skeptical priors. To help researchers assess the amount of information injected by the prior distribution, I introduce the concept of a partial prior distribution and develop the tools required to compute the partial prior distribution of quantities of interest, estimate the subsequent model, and summarize the results.

Previous research in political methodology argues that researchers do not need to include a product term in a logistic regression model to test for interaction if they suspect interaction due to compression alone. I disagree with this claim and offer analytical arguments and simulation evidence that when researchers incorrectly theorize interaction due to compression, models without a product term bias the researcher, sometimes heavily, toward finding interaction. However, simulation studies also show that models with a product term fit a broad range of non-interactive relationships surprisingly well, enabling analysts to remove most of the bias toward finding interaction by simply including a product term.

Many scholars suggest that proportional representation increases party mobilization by creating nationally competitive districts that give parties an incentive to mobilize everywhere. This paper provides theoretical and empirical arguments that bring this claim into question. I propose, unlike earlier scholars, that the positive effect of district competitiveness on party mobilization efforts increases as electoral districts become more disproportional, arguing that disproportionality itself encourages mobilization by exaggerating the impact of competitiveness on mobilization. Individual-level survey data from national legislative elections show that competitiveness has a much larger positive effect on parties' mobilization efforts in single-member districts than in proportional districts. Contrary to prior literature, these results suggest proportional electoral rules give parties no strong incentive to mobilize anywhere. [Copyright Elsevier Ltd.]

Political scientists often theorize that an explanatory variable should have "no effect" and support this claim by demonstrating that its coefficient's estimate is not statistically significant. This empirical argument is quite weak, but I introduce applied researchers to simple, powerful tools that can strengthen their arguments for this hypothesis. With several supporting examples, I illustrate that researchers can use 90% confidence intervals to argue against meaningful effects and provide persuasive evidence for their hypothesis.

AbstractIn small samples, maximum likelihood (ML) estimates of logit model coefficients have substantial bias away from zero. As a solution, we remind political scientists of Firth's (1993, Biometrika, 80, 27–38) penalized maximum likelihood (PML) estimator. Prior research has described and used PML, especially in the context of separation, but its small sample properties remain under-appreciated. The PML estimator eliminates most of the bias and, perhaps more importantly, greatly reduces the variance of the usual ML estimator. Thus, researchers do not face a bias-variance tradeoff when choosing between the ML and PML estimators—the PML estimator has a smaller bias and a smaller variance. We use Monte Carlo simulations and a re-analysis of George and Epstein (1992, American Political Science Review, 86, 323–337) to show that the PML estimator offers a substantial improvement in small samples (e.g., 50 observations) and noticeable improvement even in larger samples (e.g., 1000 observations).

Methodologists and econometricians advocate the partial observability model as a tool that enables researchers to estimate the distinct effects of a single explanatory variable on two partially observable outcome variables. However, we show that when the explanatory variable of interest influences both partially observable outcomes, the partial observability model estimates are extremely sensitive to misspecification. We use Monte Carlo simulations to show that, under partial observability, minor, unavoidable misspecification of the functional form can lead to substantial large-sample bias, even though the same misspecification leads to little or no bias under full observability.

AbstractPolitical science is gradually moving away from an exclusive focus on statistical significance and toward an emphasis on the magnitude and importance of effects. While we welcome this change, we argue that the current practice of "magnitude-and-significance," in which researchers only interpret the magnitude of a statistically significant point estimate, barely improves the much-maligned "sign-and-significance" approach, in which researchers focus only on the statistical significance of an estimate. This exclusive focus on the point estimate hides the uncertainty behind a veil of statistical significance. Instead, we encourage researchers to explicitly account for uncertainty by interpreting the range of values contained in the confidence interval. Especially when making judgments about the importance of estimated effects, we advise researchers to make empirical claims if and only if those claims hold for the entire confidence interval.