Regression-based prediction for two-stage survey data with correlated normal errors

摘要

Regression-based prediction using the least squares estimates of the regression parameters is a popular practice. However, the application of such a method for a large scale survey data can be very misleading, especially if the population under study has a particular structure [1]. Recent studies by Hoque [2] and Bhatti [3] have revealed the special structure of the population in multistage survey data. In this paper, to accommodate the special population structure, we consider a heteroscedastic multiple regression model for the two-stage survey data from a population in which the observations within each “cluster” or “region” are equi-correlated, but uncorrelated with the units of different clusters. Assuming that the errors follow a multivariate normal distribution, the marginal likelihood estimate of the correlation parameter has been proposed, and the prediction distribution for a set of future responses is obtained by using the structural relation of the model. The prediction distribution is found to be Student-t whose number of degrees of freedom depends on the sample sizes and the dimension of the regression parameter.