Alternatives to the logit model in the situation of factor levels aggregation in binomial responses

The detailed study of the logit, probit and cloglog link functions is presented for the generalized linear model with binomial response in the presence of the problem of explanatory factors levels aggregation. Expressions are deduced for the estimators of the parameters and their variances, in general terms, which allows for finding the particular results for any link function chosen. The impact of the link function on the estimates is illustrated, concluding that the use of the appropriate variance in the levels aggregation is preferable, regardless of the link function to be used.