Political scientists presenting binary dependent variable (BDV) models often hypothesize that variables interact to influence the probability of an event, Pr (Y ). The current typical approach to testing such hypotheses is (1) estimate a logit or probit model with a product term, (2) test the hypothesis by determining whether the coefficient for this term is statistically significant, and (3) characterize the nature of any interaction detected by describing how the estimated effect of one variable on Pr(Y ) varies with the value of another. This approach makes a statistically significant product term necessary to support the interaction hypothesis. We show that a statistically significant product term is neither necessary nor sufficient for variables to interact meaningfully in influencing Pr(Y ). Indeed, even when a logit or probit model contains no product term, the effect of one variable on Pr(Y ) may be strongly related to the value of another. We present a strategy for testing for interaction in a BDV model, including guidance on when to include a product term. M any phenomena important to political scientists are binary outcomes: an event occurs (Y = 1), or it does not (Y = 0). 1 Political scientists studying binary dependent variables (BDVs) frequently hypothesize that two independent variables interact in influencing the probability that the event will occur, 2 i.e., that the effect of one independent variable William D. journals published 77 quantitative articles analyzing binary dependent variables, representing 41% of all the empirical articles in these journals.2 Indeed, of the 77 articles presenting BDV models in the journals referenced in note 1, 26-over one-third-test hypotheses that one or more variables interact. 3 To be more precise, X 1 is said to interact with X 2 in influencing the probability that the event will occur [i.e., Prob(Y = 1)] if given an increment in X 1 [from X 1(lo) to X 1(hi) ] and an increment in X 2 [from X 2(lo) to X 2(hi) ],When both increments are infinitesimal, this requires that the second derivative, ∂ 2 Prob(Y = 1)/∂X 1 ∂X 2 , be different from zero. When the difference in X 1 is infinitesimal, but the difference in X 2 is discrete, this requires that the marginal effect of X 1 on Prob(Y = 1) [i.e., the first derivative, ∂Prob(Y = 1)/∂X 1 ] has different values at X 2(lo) and X 2(hi) . When both increments are discrete, this requires that a second difference in probabilities be nonzero.(X 1 ) on this probability is conditional on the value of the other (X 2 ). 3 Typically, current practice is to test this hypothesis using logit or probit, being guided by two recommendations from the political methodology literature.First, scholars have wisely been urged to focus on the presentation and interpretation of substantively relevant quantities-in the BDV context, the probability

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At the turn of the twenty-first century, an important pair of studies established that greater female representation in government is associated with lower levels of perceived corruption in that government. But recent research finds that this relationship is not universal and questions why it exists. This article presents a new theory explaining why women’s representation is only sometimes related to lower corruption levels and provides evidence in support of that theory. The study finds that the women’s representation–corruption link is strongest when the risk of corruption being detected and punished by voters is high – in other words, when officials can be held electorally accountable. Two primary mechanisms underlie this theory: prior evidence shows that (1) women are more risk-averse than men and (2) voters hold women to a higher standard at the polls. This suggests that gender differences in corrupt behavior are proportional to the strength of electoral accountability. Consequently, the hypotheses predict that the empirical relationship between greater women’s representation and lower perceived corruption will be strongest in democracies with high electoral accountability, specifically: (1) where corruption is not the norm, (2) where press freedom is respected, (3) in parliamentary systems and (4) under personalistic electoral rules. The article presents observational evidence that electoral accountability moderates the link between women’s representation and corruption in a time-series, cross-sectional dataset of seventy-six democratic-leaning countries.

When a researcher suspects that the marginal effect of [Formula: see text] on [Formula: see text] varies with [Formula: see text], a common approach is to plot [Formula: see text] at different values of [Formula: see text] along with a pointwise confidence interval generated using the procedure described in Brambor, Clark, and Golder to assess the magnitude and statistical significance of the relationship. Our article makes three contributions. First, we demonstrate that the Brambor, Clark, and Golder approach produces statistically significant findings when [Formula: see text] at a rate that can be many times larger or smaller than the nominal false positive rate of the test. Second, we introduce the interactionTest software package for R to implement procedures that allow easy control of the false positive rate. Finally, we illustrate our findings by replicating an empirical analysis of the relationship between ethnic heterogeneity and the number of political parties from Comparative Political Studies.

Cluster-robust standard errors (as implemented by the eponymous cluster option in Stata) can produce misleading inferences when the number of clusters G is small, even if the model is consistent and there are many observations in each cluster. Nevertheless, political scientists commonly employ this method in data sets with few clusters. The contributions of this paper are: (a) developing new and easy-to-use Stata and R packages that implement alternative uncertainty measures robust to small G, and (b) explaining and providing evidence for the advantages of these alternatives, especially cluster-adjusted t-statistics based on Ibragimov and Müller. To illustrate these advantages, we reanalyze recent work where results are based on cluster-robust standard errors.