Ridge regression approach to sample balancing with maximum effective base

Abstract

Sample balancing, or raking, or post-stratification, is widely utilized in survey research for weighting sample data for a better correspondence to Census or other known population quotas. Cross-tables of counts are mostly used in the Deming-Stephan iterative proportional fitting to find the weights for adjusting data to known margins. The paper suggests an objective for finding weights with the minimum variance, so with the maximum effective sample size. The model can be expressed as a ridge regression, which is applied to the original data, without its collapsing to cross-tables. The explicit regression solution allows to study the weighting analytically, which helps interpret and improve the sample balance results.