This note explores variance estimation of a combined ratio estimator from a purely model-based viewpoint. It shows that given a sample containing two distinct primary sampling units in every stratum, many of the standard randomizationbased variance estimators are equally good estimators of model variance. In fact, model-based comparisons of four variance estimators, a form of the linearization variance estimator, the standard form of the jackknife, and two common forms of balanced half sampling parallel well-known randomization-based results. By contrast, a “textbook” version of the linearization variance estimator does not estimate model variance as well as these four. Part of the analysis can be extended to estimated linear regression coefficients and to regression estimators for population means expressible in projection form.
