What is the best way to test a group of interaction effects in a GLM? I have a binary outcome Y and predictors a, b, c, and d. I have a logistic regression model which includes all the predictors, plus all the interactions between all the predictors. What is the right approach to determining whether all the interactions can be removed from the model? My thought was that a partial F-test would be suitable:
partial_f_test <- anova(reduced,full)

However, calling "partial_f_test" returns Resid. Df, Resid. Dev, Df, Deviance. I'm not sure how to interpret the results I got, namely Df = 9 and deviance = 2. Is a partial F-test even the right approach here, and if so, how do I interpret the results?

Conceptually, you are on the right path, but the details are wrong because you have a logistic regression model.  With linear (ordinary least squares) models, you can conduct a nested model test using the multiple partial $F$ test.  With logistic regression, you can do the analogous thing by using a likelihood ratio test of the nested model.  A logistic regression model is typically fit by using a version of the Newton-Raphson search algorithm to find the model that minimizes the deviance, whereas an OLS model uses a formula that minimizes the sum of squared errors.  The anova() output lists deviances because you have logistic regression models.  But the basic ideas are all the same.  You needn't worry too much about the underlying math—you use the function in largely the same way and interpret the output the same way.  You'll just need to use anova(, test="LRT") in the function call.  Lastly, when discussing it, you wouldn't call it a partial F test, you call it a likelihood ratio test.
