Weighted Multiple Regression Estimation for Survey Model Sampling

by James R. Knaub, Jr.

Abstract: Model-based inference has performed well for electric power establishment survey data at the Energy Information Administration (EIA), using weighted, simple linear regression, as pioneered by K.R.W. Brewer, R.M. Royall, and others. Cutoff sampling is used because it is not practical to collect frequently from among the smallest members of these highly skewed distributions, where nonsampling error and respondent burden can be particularly serious problems. Further, certain generation and sales for resale data have proved to be relatively difficult candidates for sampling. A weighted, multiple linear regression model, using a cutoff sample, where one regressor is the data element of interest as captured in a previous census, and another regressor is the nameplate capacity of the generating entity, has proved to be extremely valuable. This has been applied to monthly sampling, where regressor data have come from previous annual census information. Estimates of totals, with their corresponding estimates of variance, have been greatly improved by this methodology. Heteroscedasticity with respect to each regressor is addressed.

Key Words: variance of totals, heteroscedasticity with respect to each regressor, establishment surveys, cutoff sampling, stability

James R. Knaub, Jr., jknaub@eia.doe.gov

Editor: Aurelio Tobias, atobias@imim.es

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