Joint Treatment of Nonignorable Dropout and Informative Sampling for Longitudinal Survey Data

In this paper, we study, within a modeling framework, the joint treatment of nonignorable dropout and informative sampling for longitudinal survey data, by specifying the probability distribution of the observed measurements when the sampling design is informative. The sample distribution of the observed measurements model is extracted from the population distribution model, assumed to be multivariate normal. The sample distribution is derived first by identifying and estimating the conditional expectations of first order sample inclusion probabilities, (assuming complete response at the first time period), given the study variable, based on a variety of models, such as linear, exponential, logit and probit. Next, we consider a logistic model for the informative dropout process. The proposed method combines two methodologies used in the analysis of sample surveys: for the treatment of informative sampling and informative dropout. One incorporates the dependence of the first order inclusion probabilities at the initial time period on the study variable, see Eideh and Nathan (2006), while the other incorporates the dependence of the probability of nonresponse on unobserved or missing observations, see Diggle and Kenward (1994). An empirical example based on British Labour Force Survey data illustrates the methods proposed. 1