I am analyzing a dataset looking at procedural skill development. The data itself is binomial, whether or not a procedure was successful. When averaged over multiple participants by attempt, it forms what appears to be a growth curve (or Gompertz as I have read).

I would like to run a GLM to identify which other factors play a significant role e.g. location of the procedure, perceived difficulty, patient factors, etc. I have run a GLM in SPSS with the procedure attempt number as a cofactor (i.e. first attempt, second, third....). The output looks like what I would have predicted, but I feel like I should not be using the attempt as a co-factor since it's relationship is non-linear.

Is this fine, or is there another test I should be looking into? Or is there a way to linearize the dependent variable? I've read a few things about taylor series, but am getting way in over my head.