How can I compare performance of two logistic regression models after splitting into two the combined datasets relating to hospital mortality? I have data on patients with candidaemia and have analysed a range of predictor variables  associated with 30-day in hospital mortality using binary logistic regression in STATA version 14. I can also use SPSS Version 24.
One of the predictor variables  is location of this set of patients, i.e. hospital (Hospital A, Hospital B), referring to the hospitals where these patients were first seen and managed up to 30 days. These two hospitals function separately in terms of patients' management but are managed admistratively by one organisation (UK NHS Trust).
The analysis I have done is for all patients combined.
What I want to see is if the final models would remain the same(in terms of the vector of coefficients/predictabilty)  when I split the data into hospital A and Hospital B, according to the difference in  likelihood ratio tests performed on the two split samples. Would the patients in Hospital A versus Hospital B  behave the same in terms of mortality as defined?
I read around nested models and full models, less restrictive and more restrictive models, etc. But I am not sure how they can help me answer my question: As an example, what is the estimated probability of dying at 30-day for a patient aged 70 in Hospital A, and Hospital B? Are the probabilities the same or different according to the final models of the respective Hospitals?
Thank you for your help.

The most direct way to evaluate this is to include an interaction term for the hospital predictor with each of the other predictors, in a model of all the data. (I assume that hospital is already included as a predictor on its own in the model.)
Each interaction term will tell you how much the hospitals differ with respect to that predictor's association with outcome. For an overall test, you can do a likelihood-ratio test on two nested models, one with all the interaction terms and one without.
Doing separate models on the two split data sets isn't an efficient use of the data. You end up with less precision in the models because each only uses half the data. The two models aren't nested, as nested models mean that one model contains a proper subset of the predictors in the other model and both models are fit to the same data. Split models have identical predictors and different data.
If you do need separate results for the two hospitals, use the predictions from the combined model including the interaction terms. With binary coding of hospital, the single-predictor coefficients will be those for the reference hospital; you add each hospital interaction coefficient to the corresponding single-predictor coefficient to get the coefficients for the other. Be careful, as SPSS doesn't choose the same default reference levels for categorical predictors as other software (like R) does.
