Generalized Linear Modeling of Sample Survey Data
The theme of this paper is regression analysis – extended to Generalized linear models (GLMs) – of sample survey data, with the data obtained by a more or less complex survey design and possibly affected by nonresponse.
The suggested approach is neither purely model based nor purely design based. In fact we consider, simultaneously, three sources of random variation, specified by a super-population model (a GLM), the sampling design and a response model.
Ordinary (ML-based) inference – being based on the assumption of independent observations – is not automatically valid in this situation. It is, however, shown that ordinary inference does apply under certain conditions. It is demonstrated – and illustrated by simulations – how these conditions can be checked and met by incorporating variables associated with the design and the response pattern into the model.
Furthermore, it is demonstrated by simulation results that ordinary, unweighted GLM inference – when valid – can be considerably more efficient than inference based on Horvitz-Thompson weighting.
Analysis of survey data; generalized linear models; superpopulation models; nonresponse.