Prediction Inferences for Finite Population Totals Using Longitudinal Survey Data

In an infinite-/super-population (SP) setup, regression analysis of longitudinal data, which involves repeated responses and covariates collected from a sample of independent individuals or correlated individuals belonging to a cluster such as a household/family, has been intensively studied in the statistics literature over the last three decades. In general, a longitudinal, such as an auto-correlation structure for repeated responses for an individual or a two-way cluster–longitudinal correlation structure for repeated responses from the individuals belonging to a cluster/household, are exploited to obtain consistent and efficient regression estimates. However, as opposed to the SP setup, a similar regression analysis for a finite population (FP)-based longitudinal or clustered longitudinal data using a survey sample (SS) taken from the FP-based on a suitable sampling design becomes complex, which requires first defining the FP regression and correlation (both longitudinal and/or clustered) parameters and then estimating them using appropriate sampling weighted-design unbiased (SWDU) estimating equations. The finite sampling inferences, such as predictions of longitudinal changes in FP totals, would become much more complex, meaning that it would be necessary to predict the non-sampled totals after accommodating the longitudinal and/or clustered longitudinal correlation structures. Our objective in this paper is to deal with this complex FP prediction inference by developing a design cum model (DCM)-based estimation approach. Two competitive FP total predictors, namely design-assisted model-based (DAMB) and design cum model-based (DCMB) predictors are compared using an intensive simulation study. The regression and correlation parameters involved in these prediction functions are optimally estimated using the proposed DCM-based approach.