# Is there a simple rule for interpretation of Interactions (and their directions) in binary logistic regression? [duplicate]

I have a binary logistic regression with Y (a disease) and 5 independent variables (and some of their 2-sided interactions which did not cause multicollinearity). All of my single IVs significantly predict Y:

1. A: positive beta for males (males are more likely to get affected)
2. B: a positive beta (older people are more likely to be affected)
3. C (yes/no): a positive beta for smoking (smokers are more likely to be affected)
4. D (continuous): a positive beta (more traumatic patients are more likely to have disease)
5. E (yes/no): a Negative beta for treatment (treated cases were less likely to have diseases).

Now 4 interactions are significant and I want to interpret them. I know I should state that in a significant interaction, I should say that the effect of variable A on Y differed for B(1) and B(2). For example the effect of age on disease differed in males and females. But I don't know in which class (males or females), it was greater, and I don't know how to determine it.

The significant interactions and their direction of betas are as follows:

1. 4 by 3: positive beta
2. 4 by 5: positive beta
3. 1 by 2: Negative beta
4. 3 by 2: Negative beta

I would appreciate if you could kindly guide me. I searched for this issue but the discussions on the web are all sophisticated (e.g. this one) and beyond me. I just want to know is there a simple rule to determine the direction of interaction [i.e., "is A's effect on Y greater in B(1) or B(2)?"], given the directions of the coefficients of the involved variables (A and B) and the coefficient of the interaction itself (A*B)? (B(1) and B(2) are the levels of binary variables (man or woman) or extreme ends in continuous variables ([young and old], [easy or difficult])

Many thanks in advance.

• I believe this is a completely independent question compared to what is referred to, and marking it as a "duplicate" is misleading, IMHO. The reason is the style and concern of this question which totally differs from the other one. This one concerns in a general way with the direction of the interactions, while the other question is a technical question regarding a specific problem. The other one also uses R code to show the problem, while this one is of global generalizability, not only to R users but to anyone interested in stats or science or academia. So linking this to that is irrelevant – Vic Jun 7 '15 at 8:54

A positive interaction effect between A and B means that when A increases, the effect (in this case log odds ratio) of B increases. A negative interaction effect means that when A increases, the effect of B decreases.

When interpreting the results, I often find it easiest to work in the odds metric rather than the log(odds) metric. I tend to start with the baseline odds just to refresh my (and my audience's) memory on what odds are, then continue to interpret the odds ratios of the main effects (odds ratios are literary that: ratios of odds), and then go on to the interaction effects, which in logistic regression are ratios of odds ratios. A complete example is given in my answer to Interpreting interaction terms in logit regression with categorical variables

• Thanks a lot Maarten for your informative reply. I am a little bit familiar with OR and Beta as log(OR), but am curious how to use ORs, instead, to interpret interactions. This sentence was awesome "A positive interaction effect between A and B means ..." but i still have a question: Even if the effect of A itself is negative and B is positive, again that sentence applies to this situation? ("a negative interaction still shows that with decrease in A, the effect of B decreases? or since now the effect of A is negative, this sentence should be reversed?") – Vic Apr 24 '13 at 14:41
• no, the original sentence remains valid regardless of the sign of the main effect. The answer I linked to above gives an example of exactly that case. – Maarten Buis Apr 24 '13 at 15:07
• TRhanks a lot Maaten :) I would upvote your kind reply as soon as I gain enough points to qualify to vote (not that you care, of course!) :) – Vic Apr 24 '13 at 15:14

I'm not familiar with binary logistic regression, but in interaction effects in general, the way you understand them is by plotting (usually means, perhaps different in this case?). That will allow you to see the relationship between different levels and state the interaction effect specifically.

• Thanks Krysta. According to those sources I read on the net, interactions in logistic regression appear a little bit different, and also harder. But I will try to plot them, if I can. – Vic Apr 24 '13 at 13:57
• But I am still looking for some rules of thumb to tell effect of A is greater in B(1) or B(2). That could facilitate my interpretation. – Vic Apr 24 '13 at 13:59
• You probably already found this, but just in case not, there's good stuff here: ats.ucla.edu/stat/stata/seminars/interaction_sem/… – Krysta Apr 24 '13 at 14:00
• lol yes this is the one example I linked to in this page! :) but thanks anyhow. – Vic Apr 24 '13 at 14:03
• Darnit! Good luck finding simpler info--you're right, there doesn't seem to be much simple out there on the topic. The fact that there is a book all about (and called, in fact) Interaction Effects in Logistic Regression suggests that simple may not be in the cards! – Krysta Apr 24 '13 at 14:05