We are interested in fitting a multiple logistic regression model using data obtained from a national survey of children with special health care needs. The data has an accompanying weight variable intended to standardize children to the national population in which we intend to make inference. This weight variable does not sum to 1 nor are the weights integral (they may take values such as 23.2). This model is being fit using SAS v9.2. In consulting the documentation for the logistic procedure, I notice in the syntax description the following statement:
Caution: PROC LOGISTIC does not compute the proper variance estimators if you are analyzing survey data and specifying the sampling weights through the WEIGHT statement. The SURVEYLOGISTIC procedure is designed to perform the necessary, and correct, computations.
I don't understand why this should be an issue. If model based standard errors are being computed, then the weighted maximum likelihood estimator should give standard errors which are correct for the population of interest. Is this correct? What likelihood function is SAS's logistic regression solver optimizing if the above statement is correct?