Chambers, R. and Wang, S., Maximum Likelihood Logistic Regression With Auxiliary Information, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 12-08, 2008, 22p.
In this paper we use the general approach to maximum likelihood estimation for complex survey data described in Breckling et. al. (1994) to develop methods for efficiently incorporating external population information into linear logistic regression models fitted via sample survey data. In particular, we use innovative saddlepoint and smearing methods to derive highly accurate approximations to the score and information functions defined by the model parameters under random sampling and under case-control sampling when auxiliary data on population moments are available. Simulation-based results illustrating the resulting gains in efficiency are provided.