# Help interpreting an interaction in Binary Logistic Regression

#### 2+2=5

##### New Member
Firstly, thank you for taking the time to read my problem that I am having.

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). I interpret the odds ratio meaning the 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. 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. Another method I know may be plotting a simple slopes model but this is tricky because I have covariates.

I am open to suggestions, and would love to have some feedback on how to interpret this interaction term.

....................Estimate Std.
(Intercept):....-2.3594
age:..............0.2037
gender1:.......-1.8419*
HP:................-0.0324
BD:................1.4095*
HP:BD:...........1.1849*

..........................OR
(Intercept)..........0.0944774
age:...................1.2259709
gender:...............0.1585216
hp:.....................0.9681189
BD:....................4.0936999
HP:BD................3.032873

Many thanks in advance

#### mmercker

##### Member
You know that the probability of conduct disorder increases with increasing BD, that is what you see from your regression. The positive interaction with HP now means that for relative low values of HP, this dependency is not as strong as for large values of HP. This holds also the other way round: You see that the probablity of conduct disorder decreases with HP. However, for stronger values of BD this relationship is strong, for lower values of BD this depdendency is less strong.

But take in mind that it is not valid to interpret the main effects of HP and BD in the presence of an interaction term in the usual way. In this case, the interpretation of the main effect of HP for example hold only for the case that BD = 0 (which probably does not make sense), and the other way round. Thus, it is better to center the variables before the analysis around a reasonable value, e.g. the mean value.

#### 2+2=5

##### New Member
Thanks so much for your feedback. Yes, I agree I won't be interpreting main effects in the final model with the interaction term. These variables have been centered.

So my question still remains, and I'll try to state it more eloquently -

How do I know if the interaction between HP and PD represents either (1) high HP and high PD OR (2) low HP and low PD?

#### rogojel

##### TS Contributor
hi,
I would look at the log odds to interpret the interaction : in the binary logistic regression the log odds is a linear model as in: log odds = a0 + a1*x1+a2*x2 +a12*x1*x2

So, the interpretation would be that the effect of an increase by one unit in x1 on the log odds depends on the value of x2 and is Delta(log odds)=a1+a12*x2. Similarly the effect of an increase of one unit of x2 on the log odds depends on the value of x1 and is Delta(log odds)=a2+a12*x1

the change in log odds can then easily be recalculated to get the odds ratios , the point being that the odds ratios depend on the concrete value of the other variable.

regards