Adopting likelihood based methods of inference in the case of informative sampling often presents a number of difficulties, particularly, if the parametric form of the model that describes the sample selection mechanism is unknown, and thus requires application of some model selection approach. These difficulties generally arise either due to complexity of the model holding in the sample, or due to identifiability problems. As a remedy we propose alternative approach to model selection and estimation in the case of informative sampling. Our approach is based on weighted estimation equations, where the contribution to the estimation equation from each observation is weighted by the inverse probability of being selected. We show how weighted estimation equations can be incorporated in a Bayesian analysis, and how the full Bayesian significance test can be implemented as a model selection tool. We illustrate the efficiency of the proposed methodology by a simulation study.
Informative sampling Design variables Inclusion probability Bayesian significance measures Horvitz–Thompson estimator Population distribution Sample distribution
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The authors are grateful for the support of IME-USP, the Institute of Mathematics and Statistics of the University of São Paulo; FAPESP - the State of São Paulo Research Foundation (grant CEPID 2013/07375-0 and 2013/17746-5); and CNPq - the Brazilian National Counsel of Technological and Scientific Development (grant PQ 301206/2011-2). Finally, the authors are grateful for the advice of colleagues and anonymous referees used to improve this work.
Pfeffermann D (1996) The use of sampling weights for sampling data analysis. Stat Methods Med Res 5:239–261CrossRefGoogle Scholar
Pfeffermann D (2011) Modelling of complex survey data: why is it a problem? how should we approach it? Surv Methodol 37(2):115–136Google Scholar
Pfeffermann D, Sverchkov M (1999) Parametric and semi-parametric estimation of regression models fitted to survey data. Sankhya 61:166–186MathSciNetzbMATHGoogle Scholar
Pfeffermann D, Sverchkov M (2003) Fitting generalized linear models under informative sampling. In: Skinner C, Chambers R (eds) Analysis of survey data. Wiley, New York, pp 175–196CrossRefGoogle Scholar
Pfeffermann D, Krieger AM, Rinott Y (1998) Parametric distributions of complex survey data under informative probability sampling. Stat Sin 8:1087–1114MathSciNetzbMATHGoogle Scholar
Saärndal CE, Swensson B (1987) A general view of estimation for two phases of selection with applications to two-phase sampling and nonresponse. Int Stat Rev 55:279–294MathSciNetCrossRefzbMATHGoogle Scholar
Skinner CJ (1994) Sample models and weights. In Proceedings of the section on survey research methods, American Statistical Association, pp 133–142Google Scholar
Skinner CJ, Holt D, Smith TMF (1989) Analysis of Complex Surveys. Wiley, ChichesterzbMATHGoogle Scholar
Stern JM, Zacks S (2003) Testing the independence of poisson variates under the holgate bivariate distribution: the power of a new evidence test. Stat Probab Lett 66:313–320MathSciNetzbMATHGoogle Scholar