We are trying to fit a zero-weighted binomial model to our data set. The model is strongly supported by theory. In that context, we shall be grateful for any help on some of our problems:
(1) Like the way one can formally test for overdispersion in count data, can one test for underdispersion as well? If yes, what test and how to do that in STATA?
2) We would like to test whether zero-weighted binomial regression model is indeed a better model for our data set than the simple binomial regression model. Both AICs and BICs suggest that the zero-weighted model is the better one. However, can one test in STATA whether all the "inflation" parameters are zero jointly? If that test rejects the null hypothesis, can one then also comment that the zero-weighted model is a necessity here?