I'm fitting a binomial GEE glm to predict presence or absence of sperm whales as a function of environmental variables. I am using latitude, longitude, depth, and distance to land, and year as a factor as my variables. I'm also including year interactions with each of the environmental variables such that: presence~ lat * year + long * year + depth * year+distance * year
Additionally, I'm trying different forms (linear or splined) for each of the continuous variables. For variable and variable form selection , I have been using Pan's (2001) QICu, which is what I've seen used in most papers.
However, this method is retaining all interactions that I put in the model. When I tried using the regular QIC to select the best model, some interactions and some main effects were dropped. Additionally, both final models have very similar performances abilities (measured by the % of correct presences and absences predicted). Also, when I plot the best model as indicated by QICu, the confidence intervals are huge! This is not the case when I plot results for the model selected through QIC. This made me think that the QICu was acting strange with my model.
When I was reading about this index, it states that "QICu approximates QIC when the GEE is correctly specified."
Specifically, I would like to know if it is valid to use the QIC (instead of the QICu) for variable selection? And is there a way of knowing whether my GEE is correctly specified?
please let me know if there is any way in which I can clarify the question