Understanding specifics of glm() model in R I have been provided a sample logistic regression as follows:
glm(formula = output ~ X1 + X2 + X3 + X4 + X5 + X1:term + term:X5 - 1, family="binomial", data=mydata)
There are a few things I'm confused by here:
1) What is going on with the X1:term + term:X5 terms? What do they mean in the context of glm()?
2) There does not seem to be an intercept term in the output under Coefficients. Could this be for any other reason than there simply not being an intercept term?
3) The AIC for the model is 50000. How should I interpret this? Can I interpret this without more models to compare to? If it is not useful, what else should I be looking for instead?
 A: 1) In standard R regression formulas, x1:x2 means to include a new covariate that is the product of x1 and x2. It is more common, and generally better practice, to use x1*x2, which fits main effects for x1 and x2 and interaction term between x1 and x2, i.e. x1 * x2 == x1 + x2 + x1:x2. So in this regression formula, there is no main effect of term, i.e. it is only used to alter the effect of X1 and X5. There may be some very special reason for this in this model, but it is unusual. 
EDIT: As pointed out by Scortchi, if the formula contains a categorical variable (which term may well be one), then when R expands the formula, it does not chose a baseline category to drop, as the model will still be identifiable with all categories included. This may be helpful in regards to simplifying interpretation. For example, suppose I have ~ gender * treatment. Then if I want to interpret the effect of treatment on females (assuming males as baseline), I need to look at treatment + treatment:genderFemale. On the other hand, if I fit ~ gender * treatment - 1, I can look directly at genderFemale:treatment for the estimated effect of treatment on females. 
2) By writing - 1, the R formula implies that no intercept should be fit. This is generally a bad idea if the covariates are all continuous, but may lead to an easier interpretation in certain cases with categorical variables. 
3) AIC, for an individual model, is not particularly useful. 
