Is the binomial response "captured versus not-captured" "tagged versus not-tagged" "infected versus healthy" "dead versus alive" or something else? What are your variables? What was your sample size? What are the goals? The more you tell us the more we can help. Or is this a simulation model that you are running and you are trying to predict the outcome? Why not run both models and see which one fits better? That is probably the best approach. Then figure out why you got this answer, and in this effort you will gain a much better understanding of how the models work with your data. Try other models, try other programs. The different analysis programs are not all equally good for all possible data sets.
Thanks for your recommendations Timothy. My M. Sc. Thesis consist on a data analysis of risk factors for clinical hypocalcemia in cows using a database of 235971 reported calving and we (my professor and I) estimated heritability and repeatability using pedigree from this database, the response variable is binomial (positive or negative to clinical hypocalcemia), so threshold model should be a better approach, but it seems that the linear model (using normal distribution) fits better (more consistent results). I probably will describe both models results, but I am hesitating about the appropriate model to recommend in similar situations. We used a logit model using GLIMMIX procedure (METHOD=RSPL, DIST-BIN, LINK-LOGIT) of SAS 9.3 software and GLMM using ASReml software both for binomial and normal distributions and using a sire and an animal model.
I am not sure I know what a threshold model is. I may know it under a different name. Could you post the SAS code for the threshold model and for the linear model?