Sample Size Selection in Regression Analysis When there is Nonresponse

Assuming nonresponse, inference concerning the regression coefficients of a multiple linear regression is considered from a Bayesian viewpoint. We exploit a two-phase sampling scheme. At each phase the sample design is of the following type: Select a random sample of size n with n 1 responses obtained. Then, a subsample of size n 2(0 ≤ n 2 ≤ n — n 1) is selected from the n — n 1 nonrespondents. Assuming 100 percent response from the units in the subsample, the principal objectives are: (1) to ascertain at the second phase of sampling the optimal number of nonrespondents to be subsampled; and (2) to determine the optimal overall sample size at the second phase.