Ali, Mehboob; Kauermann, Göran
:
Second Phase Sample Selection For Repeated Survey.

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Abstract
The paper describes the scenario of a survey where a relatively large
random sample is drawn at a first phase and a response variable Y and
a set of (cheap) covariates x are observed, while (usually expensive)
covariates z are missing. In a second phase, a smaller random sample
is drawn from the first phase sample where the additional covariates z
are also recorded. The overall intention is to fit a regression model of
y on both, x and z. The question tackled in this paper is how to select
the second phase random sample. We assume further that the survey is
drawn repeatedly over time, that is data on Y , x and z are available from
previous studies. As example for such setting we consider rental guide
surveys, regularly run in German cities. We propose to draw the second
phase sample such that it minimizes the estimation variability in the
underlying regression model. This step is carried out with imputation
using the previous survey data. The norm of matrix can be used to find
simulation based second phase sample which maximize design matrix
of imputed data. The proposed sampling scheme is numerically rather
simple and performs convincingly well in simulation studies as well as
in the real data example.