# More on Product Terms and Interaction in Logistic Regression Models

I noticed that Bill Berry, Justin Esarey, and Jackie DeMeritt's (BDE) long-time R&R'ed paper at AJPS is finally forthcoming. I really like seeing highly applied, but rigorous, work like this being published at top journals. You should definitely have a look at their paper if you use logit or probit models to argue for interaction.

First, the background. BDE published a paper back in 2010 that examines whether researchers need to include a product term in order to argue for interaction.  This first paper examines the situation in which the researcher expects interaction due to compression (when the researcher expects changes in predicted probabilities to be smaller and the probabilities approach zero and one). BDE argue that the logit model with no product term is able to capture this type of interaction and, therefore, no product term is needed in this situation. I've previously discussed this paper here and mentioned that I have a paper arguing that one should include a product term even when interaction is expected on the basis of compression alone. While I disagree with his particular situation, the rest of the paper is fantastic. In particular, I've found their advice about hypothesizing interaction in terms of $Pr(Y)$ or $Y^*$ especially valuable.

In the forthcoming paper, BDE extend their analysis to the situation in which researchers expect effects (i.e., changes in predicted probabilities) to vary, but do not have a theoretically motivated specification. They refer to this as "specification ambiguity." In this situation, I was delighted to read that BDE recommend always include a product term. They find that excluding the product term biases the researcher toward finding interaction. This is the same reason I disagree with their recommendation to exclude product term in the situation of strong theory. With the publication of this new paper, the literature is almost where I'd like it to be, with the exception of the tiny point I mentioned above.

# Creating Marginal Effect Plots for Linear Regression Models in R

Suppose we estimate the model $E(y) = \beta_0 + \beta_xx + \beta_zz + \beta_{xz}xz$ and want to calculate the the marginal effect of $x$ on $E(y)$ as $z$ varies $\left(\dfrac{\partial E(y)}{\partial x}\right)$ and its 90% confidence interval. Brambor, Clark, and Golder describe exactly how to do this and provide Stata code. Below is a bit of R code to do something similar. (Click here to continue reading.)

# compactr is now on CRAN

I've been working on a package called compactr  that helps create nice-looking plots in R and it is now up on CRAN.

You can get it by typing

directly into the command line in R. See how it works by typing  example(eplot)  or reading the details here. Below I describe the basic structure and functions. (Click here to continue reading.)

# Arguing for Negligible Effects

I just uploaded a newer version of my re-titled paper "Arguing for a Negligible Effect." You can find the latest version here. It has a "revise and resubmit" at AJPS and I'm sending it back on August 15 (when they re-open after the summer break), so I'd certainly appreciate any suggestions. The abstract is below:

Political scientists often theorize that explanatory variables should have "no effect" and support these claims by demonstrating that the estimated effects are not statistically significant. These empirical arguments are not particularly compelling, but I introduce applied researchers to simple, powerful tools that can strengthen their arguments for these hypotheses. With several supporting examples, I illustrate that researchers can use 90% confidence intervals to argue against meaningful effects and provide persuasive evidence for their hypotheses.

# Testing for Interaction in Logit Models

Andrew Gelman recently posted about testing for interaction in logistic regression models. This is something I've read and thought a little about, so I'm linking to several articles on the topic and offering my quick take. (Click here to continue reading.)