Large-Sample Properties of Minimum Discriminant Information Adjustment Estimates Under Complex Sampling Designs

Abstract

Minimum discriminant information adjustment (MDIA), an approach to weighting samples to conform to known population information, provides a generalization of raking and poststratification. In the case of simple random sampling with replacement with uniform sampling weights, large-sample properties are available for MDIA estimates of population means and related functions of such means. This research report provides large-sample properties of MDIA estimates under complex sampling designs, such as stratified and two-stage sampling. Cases are considered for both sampling with replacement and sampling without replacement. MDIA is one case of calibration weighting, and this report includes results showing that sample calibration weights can exist only if MDIA weights exist, and MDIA weights can exist in situations where other calibration weights do not. Similarly, results in the report show that calibration weighting does properly generalize MDIA for populations. To illustrate results and explore the use of large-sample approximations in samples of moderate size, an application from Florida middle schools is examined for several sampling procedures to evaluate MDIA estimates for the prevalence of literacy coaches in those schools.