I have a question about interaction terms in logistic regression: I find an interaction effect between two binary variables. One of the four categories (0*0) consists however of only 15 respondents (5% of the sample). Is this a problem?
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Without context it is difficult to answer the question. If the sample size is 100,000, 0.05 of the sample will represent an adequate number of subjects on which to estimate the interaction effect. Otherwise you may be right to be concerned. Interaction tests (double differences) have much lower power and precision than main effect tests (single differences). The precision of an interaction effect estimate for two binary $X$s is limited by the lowest sample size in the four cells.
How did you pre-specify the potential interactions? Or did you search many interactions? If the one interaction was not fully pre-specified you have other problems to deal with.
answered Apr 27, 2014 at 12:52
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$\begingroup$ Thanks! The sample size of the smallest category is 15 (out of about 900). I did search many interactions. This does however make "theoretical sense"... But you mean that even if the product term becomes significant, I can´t make inferences based on it or..? $\endgroup$– MarthaCommented Apr 27, 2014 at 14:22
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$\begingroup$ It is doubtful that your sample size is sufficient for assessing interactions. And if you were not able to pre-specify two or fewer interactions this is particular problematic. Searching for interactions in my experience results in findings that are unlikely to replicate. Problems include low precision, low power, interaction terms co-linear with omitted main effects, interaction terms co-linear with each other. Since your interaction search is not hyothesis-driven, if you do want to assess several interactions you need penalization (shrinkage). $\endgroup$ Commented Apr 27, 2014 at 15:28