An Extension of Generalized Regression Estimator to Dual Frame Surveys

Estimation from multiframe survey data is essentially a problem of combining domain estimates such that the new auxiliary information (for key study variables, z) obtained from several estimates for overlapping domains is used in addition to the usual auxiliary information for sociodemographic and geographic variables (x) used in poststratification. A natural approach is to use optimal regression, but as in the case of single frame surveys, it may be unstable due to insufficient degrees of freedom available for estimating regression coefficients when the number of zvariables is large while estimating for all z in a multivariate sense. As an alternative, an extension of the generalized regression (GREG or GR) estimator can be used which is suboptimal but has stable regression coefficient estimates in the case of multivariate z, and has a convenient calibration form involving final weights. The main problem in GR formulation is how to take account of possibly different designs from multiple frames. An earlier attempt (MRdualframe of Singh and Wu, 1996), based on the modified regression (MR) methodology of Singh (1994,1996), was made using the relative effective sample size (based on design effect) as the scaling factor in the GREG covariance matrix, but only with partial success. In this paper, we present an enhancement of MR-dualframe which takes account of different designs, allows for range-restricted weights as in single frame surveys, provides calibration weights, has built-in bias-correction due to difference in survey mode effects and can be applied to dependent samples. Monte Carlo simulation results on relative performance of a few dual frame estimators are also presented.