LIMITED INFORMATION LIKELIHOOD ANALYSIS OF SURVEY DATA

Analysts of survey data are often interested in modelling the populati on process, or superpopulation, that gave rise to a 'target' set of su rvey variables. An important tool for this is maximum likelihood estim ation. A survey is said to provide limited information for such infere nce if data used in the design of the survey are unavailable to the an alyst. In this circumstance, sample inclusion probabilities, which are typically available, provide information which needs to be incorporat ed into the analysis. We consider the case where these inclusion proba bilities can be modelled in terms of a linear combination of the desig n and target variables, and only sample values of these are available. Strict maximum likelihood estimation of the underlying superpopulatio n means of these variables appears to be analytically impossible in th is case, but an analysis based on approximations to the inclusion prob abilities leads to a simple estimator which is a close approximation t o the maximum likelihood estimator. In a simulation study, this estima tor outperformed several other estimators that are based on approaches suggested in the sampling literature.