In a logistic regression model after including interaction effect R2 increases significantly, but the p value of interaction term is not significant. Should the interaction term be included in the final model ??
What do you mean by increasing _significantly_ the R² ? Is it from a formal test, like in « the p-value is significant for the interaction term »? If not, you have your answer…
Keeping in mind that just selecting terms based on p-values to construct a model is not very scientific and that computation of p-values in logistic regression may hide some surprises sometimes…
If yes… You'll have to consider even more carefully the previous paragraph, « keeping in mind [...] »
Bear in mind too that the R2 values you see in logistic regression output are pseudo-R2 values, and cannot be interpreted in the same way as R2 for an OLS model. See this nice UCLA page for more info.
https://stats.idre.ucla.edu/other/mult-pkg/faq/general/faq-what-are-pseudo-r-squareds/
HTH.
Generally, it depends on the dataset and on the task. It's natural to expect that R2 will be reduced by adding new variables. But this may be over-fitting. Information criteria penalizing for the number of variables (e.g., AICc) should give a better indication of which model is better.
It isn't possible for a correctly specified interaction to significantly increase R^2 and have a non-significant interaction term in a general linear model. In a generalised linear model (as Bruce Weaver noted) R^2 isn't uniquely defined so I don't think you can have a significance test of the change in R^2. It is just about possible for the change in deviance for the model to be significant and the Wald test to be non-significant (but unlikely with large n). In these case the change in deviance using the likelihood ratio chi-square (the likelihood ratio test) is more accurate than the Wald test.
A simple answer, don’t add the interaction term. Adding any term can increase R square. If the contribution of the term is not large enough, you may drop it. P value is not a good index, since it depends on sample size. You’d better check deviance the interaction term explained, or use AIC.
Xinhai Li : simple, yes, but over simple.. .If interaction is suspected, you'd better include it, even if non significant because lack of power... Risks of overfit and difficulty of interpretation are better arguments to avoid interaction terms, but absolutely not the fact that they are harder to detect with a significant term...
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