Approximate MLE from Survey Data

Since under many situations from complex sample surveys, exact likelihoods are difficult to obtain and pseudo-likelihoods are used instead, we shall, in this chapter, consider some procedures and applications which are useful in obtaining approximate maximum likelihood estimates from survey data. After addressing the notion of ignorable sampling designs Sect. 8.2 considers exact MLE from survey data. The concept of weighted distributions due to Rao (Classical and contagious discrete distributions, pp 320–332, 1965b), Patil and Rao (Biometrics 34:179–189, 1978) and its application in maximum likelihood estimation of parameters from complex surveys have been dealt with in the next section. Subsequently, the notion of design-adjusted estimation due to Chambers (J R Stat Soc A 149:161–173, 1986) has been reviewed. We review in Sect. 8.5 the pseudo-likelihood approach to estimation of finite population parameters as developed by Binder (Stat Rev 51:279–292, 1983), Krieger and Pfeffermann (Proceedings of the symposium in honor of Prof. V.P. Godambe, 1991), among others. The following section addresses the mixed model framework which is a generalization of design-model framework considered by Sarndal et al. (Model assisted survey sampling, 1992) and others. Lastly, we consider the effect of sample selection on the standard principal component analysis and the use of alternative maximum likelihood and probability weighted estimators in this case.