I have a longitudinal, three-wave, panel (repeated measures within subjects) data set with a binary outcome Y. In a proc glimmix model (SAS 9.4) with one level-1 predictor (time = 0, 1, 2) and a random intercept, the predicted probability of Y at time = 0, based on the intercept (exp (b0) / (1 + exp (b0))), using a likelihood method of estimation (quad or laplace), is very different than the probability of Y, from the raw data (predicted probability at time = 0 from model = .18, probability from raw data = .25). What’s surprising is that when I use simple logistic regression (ignoring the clustering within subjects) or the same multilevel model in proc glimmix with a pseudo-likelihood method of estimation (like MSPL), the predicted probability of Y at time = 0 based on the intercept is much closer to the probability of Y, from the raw data. Estimates of the fixed effect of time (the odds ratio) are similar across all modeling methods and consistent with the change in probability of Y in the raw data across waves. Any thoughts on why? Any suggested tweaks in the glimmix setup with likelihood estimation that might make the predicted probability of Y at time = 0 closer to the raw probability? Thanks in advance for your thoughts!
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