Fitting statistical models for longitudinal survey data under informative sampling
Jul 27, 09:00
Data collected by longitudinal surveys, are used extensively to make inferences on assumed population models. Often, survey design features (clustering, stratification, unequal probability selection, etc.) are ignored and the longitudinal sample data are then analyzed using classical methods based on simple random sampling. To take into account sampling design features in the analysis of longitudinal data, we propose to use the sample distribution, which is the distribution of the observed outcomes given the selected sample. When the sample selection probabilities depend on the values of the model response variable, even after conditioning on auxiliary variables, the sampling mechanism becomes informative and the selection effects need to be accounted for in the inference process. In this paper, under informative sampling design, we discussed three statistical models that widely used in longitudinal data, namely; time series models, general linear model using different covariance structures: the exponential correlation model and the uniform correlation model, and subject-specific effects models. The idea behind the proposed approach is to extract the model holding for the sample data as a function of the model in the population and the first order inclusion probabilities, and then fit the sample model using maximum likelihood, and pseudo maximum likelihood methods. Also we consider test of informative sampling design. In order to evaluate the performance of the new estimators obtained using sample likelihood method, we conduct a simulation study. The main feature of the proposed estimators is their behaviors in terms of the informativeness parameters. We also show that the use of the classical estimators, that ignores the informative sampling design, yields biased estimators.