Hi all, I have a large dataset (19k) and I am using logistic regression to estimate probabilities of experiencing an event at the patient level. I am interested in looking at the effect of a facility characteristic on the odds of said event. This facility characteristic is naturally continuous and I have constructed quartiles. I calculated the crude rate of event within each quartile. When I call for the predicted probabilities from a logistic regression model with patient and disease characteristics, the mean predicted probabilities of event across the facility-characteristic quartiles are very similar to each other as well as the overall crude rate (within a thousandth). I am struggling to understand the following: when I add facility-characteristic quartile to the above model and call for the predicted probabilities, the means of the probabilities of event across the factility-characteristic quartiles are equivalent to the crude rates. I understand that the mean of the predicted probabilities will be equivalent to the crude rates across facility-characteristic quartiles when it is the only predictor in the model, but it is not here. Can anyone help me understand why this is? Happy to provide coefficients and output. With much appreciation!
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