Understanding Interaction Models: Improving Empirical Analyses

Abstract

Multiplicative interaction models are common in the quantitative political science literature. This is so for good reason. Institutional arguments frequently imply that the relationship between political inputs and outcomes varies depending on the institutional context. Models of strategic interaction typically produce conditional hypotheses as well. Although conditional hypotheses are ubiquitous in political science and multiplicative interaction models have been found to capture their intuition quite well, a survey of the top three political science journals from 1998 to 2002 suggests that the execution of these models is often flawed and inferential errors are common. We believe that considerable progress in our understanding of the political world can occur if scholars follow the simple checklist of dos and don'ts for using multiplicative interaction models presented in this article. Only 10% of the articles in our survey followed the checklist.

Explaining rural/non-rural disparities in physical health-related quality of life: a study of United Methodist clergy in North Carolina

“…The interaction term Rural X Years in church is not significant (p =.122), but this obscures the fact that including the interaction term makes both the effect size and its standard error depend on the value of Years in church. Following the technique outlined by Brambor and colleagues [37], we calculate the total marginal effect of rurality on physical HRQL for each value of Years in church and graph the result (Figure 1). This reveals that the negative relationship does strengthen in a statistically significant way as time spent in a rural area increases, but only after clergy have spent more than three years in a rural church (exponentiation of 1.099=3, p =.05).…”

The Autocratic Trust Bias: Politically Sensitive Survey Items and Self-Censorship

“…Because multilevel logistic regression coe cients are somewhat di cult to interpret (even without two-level interaction terms) I proceed by graphing the interaction e↵ects (Brambor, Clark, and Golder, 2006), and then by visualizing the e↵ects in each country expressed in odds ratios.…”

Investing in Legal Advice - What Determines the Costs of Enforcing Intellectual Property Rights?

“…20 Because the marginal effect of the relative forward citations is non-linear, it is not significantly larger than zero anymore if the average relative forward citations exceed roughly 1300 percent (see Brambor et al, 2006). However, this is only the case for less than 3 cases (0.5 percent of my sample).…”