# Interpreting the direction of an interaction effect in Binary Logistic Regression

I have reviewed prior posts in the forum and can't seem to find an answer to a problem I am having with interpreting an interaction:

The goal: interpret the direction of the interaction term.

Variables: I have two continuous predictors (heart rate [HR] and pupil dilatation [PD]), predicting a dichotomous outcome (diagnosis of conduct disorder - no=0, yes=1) I am controlling for age and gender.

Results: The interaction between HR and PD is significant, the beta is positive (suggesting a positive interaction - as HR increases so does PD). And my odds ratio is above 1 (3.1) so I interpret the odds ratio as meaning an increase in both HR and PD elevates the likelihood of being diagnosed with conduct disorder.

Here's the catch; I am not sure if I am looking at this correctly. I have been told that the positive interaction could indicate HR and PD are both negative resulting in a positive interaction also. Therefore, how do I find out if the positive interaction means it is high HR and high PD or if it is low HR and low PD?

My closing thoughts are that the odds ratio may help explain this but I am not entirely sure if this is accurate.

I am open to suggestions, and would love to have some feedback on how to interpret this interaction term in regards to the direction of effect. It looks like you're confused as to what an interaction is in general. In particular, from the bit "suggesting a positive interaction - as HR increases so does PD", it sounds like you believe that the interaction term for a pair of independent variables (IVs) tells you how the IVs are associated with each other. It doesn't. Rather, it tells you how the dependent variable (DV) is associated with the product of the two IVs.

To interpret an interaction, it's often less helpful to look at the coefficients themselves than to look at the effect of interaction in combination with the associated main effects. For example, we can plot the effects of HP, BD, and HP × BD like this (change HP and BP values as appropriate for your actual data):

d = expand.grid(hp = c(-1, 0, 1), bd = c(-1, 1))
d = transform(d, effect = -.0324*hp + 1.4095*bd + 1.1849*hp*bd)
library(ggplot2)
qplot(bd, color = ordered(hp), effect, data = d) We see that as HP increases, the effect of BD on the DV also increases.

• This is great, thank you. I also really appreciate the simplicity of your explanations. So as I understand it, to explain the results with the plot would be: "the regression showed children who had high levels of HP and BD were 3 times more likely to have a diagnosis of conduct disorder. Figure X displays the effect size of HP on BD increasing the odds of being diagnosed with conduct disorder. Specifically, high levels of HP and BD had a larger effect when predicting children with conduct disorder". Does this accurately reflect the plot you have provided? – user121248 Jun 25 '16 at 18:22
• I am assuming you created hp into three groups (low, medium, and high levels), while BD remained continuous - is that correct? – user121248 Jun 25 '16 at 18:23
• "Does this accurately reflect the plot you have provided?" — No, I don't agree with any of those three sentences. I don't know where you got "3 times more likely", there is nothing here about an effect of HP on BD (see the first paragraph of my answer), and your last sentence suggest a comparison to some other DV, when seems to be only one DV at play here. – Kodiologist Jun 25 '16 at 18:50
• "I am assuming you created hp into three groups (low, medium, and high levels), while BD remained continuous - is that correct?" — That's how the plot presents them, yes. – Kodiologist Jun 25 '16 at 18:50
• Thanks for your responses. 3 times more likely is from the regression output, and not to do with the plot. I am just trying to understand how to communicate (effectively) what the plot means in people terms to support the regression model. – user121248 Jun 25 '16 at 20:12

I have just come across Jeremy Dawson's plot templates to help interpret interaction effects in a binary logistic regression (and other methods). I figured I'd post it here for those who do not use r.