Chambers, Raymond, Dorfman, Alan and Wang, Suojin
Maximum Likelihood Under Response Biased Sampling. Southampton, UK, Southampton Statistical Sciences Research Institute, 21pp.
(S3RI Methodology Working Papers, (M03/18) ).
Informative sampling occurs when the probability of inclusion in sample depends on
the value of the survey response variable. Response or size biased sampling is a
particular case of informative sampling where the inclusion probability is proportional
to the value of this variable. In this paper we describe a general model for response
biased sampling, which we call array sampling, and develop maximum likelihood and
estimating equation theory appropriate to this situation. The Missing Information
Principle (MIP) (Orchard and Woodbury, 1972) yields one (indirect) approach to
likelihood based survey inference (Breckling et al 1994). Some have questioned its
applicability in the case of informative sampling, because of the way it conditions on
the given sample. In this paper we describe a direct approach and show that it and the
MIP-based approach lead to identical results under array sampling. Comparison is
made to the weighted likelihood based approach described in Krieger and
Pfeffermann (1992). Extensions to the theory are also explored.
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