Generalized Raking Procedures in Survey Sampling

Abstract We propose the name generalized raking for the class of procedures developed in this article, because the classical raking ratio of W. E. Deming is a special case. Generalized raking can be used for estimation in surveys with auxiliary information in the form of known marginal counts in a frequency table in two or more dimensions. An important property of the generalized raking weights is that they reproduce the known marginal counts when applied to the categorical variables that define the frequency table. Our starting point is a class of distance measures and a set of original weights in the form of the standard sampling weights 1/π k , where π k is the inclusion probability of element k. New weights are derived by minimizing the total distance between original weights and new weights. The article makes contributions in three areas: (1) statistical inference conditionally on estimated cell counts, (2) simple calculation of variance estimates for the generalized raking estimators, and (3) presentation of the new computer software CALMAR. Our conditional approach highlights the role played by interaction between the factors that define the frequency table. Absence of interaction implies that generalized raking is as efficient as complete post-stratification. The variance estimates we propose are calculated with the aid of the residuals from the fit of an additive analysis of variance (ANOVA) model. The CALMAR software, recently developed at I.N.S.E.E., is now used in various national surveys for calculating generalized raking weights. We illustrate its use with the aid of data from the 1990 survey of living conditions in France. In this application a table in seven dimensions with known marginal counts is used for generalized raking.