The analysis of data from sample surveys under informative sampling
Sampling designs for surveys are often complex and informative, in the sense that the selection probabilities are correlated with the variables of interest, even when conditioned on explanatory variables. In this case, conventional analysis that disregards the informativeness can be seriously biased, since the sample distribution differs from that of the population. We consider the relationships between the distribution of the sampled values and that of the population. Using different models for the conditional expectations of the inclusion probabilities, given the values of the variable of interest, we obtain the sample distributions and propose methods for estimation of their parameters. The results are applied to the analysis of longitudinal surveys, using an autoregressive model, and to surveys with two-stage cluster designs, with informative selection at each of the two stages.