A General Algorithm for Univariate Stratification

Abstract

This paper presents a general algorithm for constructing strata in a population using "X", a univariate stratification variable known for all the units in the population. Stratum "h" consists of all the units with an "X" value in the interval ["b" "h" - 1 , "b h") . The stratum boundaries {"b h"} are obtained by minimizing the anticipated sample size for estimating the population total of a survey variable "Y" with a given level of precision. The stratification criterion allows the presence of a take-none and of a take-all stratum. The sample is allocated to the strata using a general rule that features proportional allocation, Neyman allocation, and power allocation as special cases. The optimization can take into account a stratum-specific anticipated non-response and a model for the relationship between the stratification variable "X" and the survey variable "Y". A loglinear model with stratum-specific mortality for "Y" given "X" is presented in detail. Two numerical algorithms for determining the optimal stratum boundaries, attributable to Sethi and Kozak, are compared in a numerical study. Several examples illustrate the stratified designs that can be constructed with the proposed methodology. All the calculations presented in this paper were carried out with stratification , an R package that will be available on CRAN (Comprehensive R Archive Network). Copyright (c) 2009 The Authors. Journal compilation (c) 2009 International Statistical Institute.

Optimal Stratification and Allocation for the June Agricultural Survey

“…In the case of a priori allocation, only a subset of pairings of all possible stratifications and allocations are considered; this subset is unlikely to contain the optimal allocation for a given objective function due to ignoring administrative data. The importance and improvements provided by assuming neither a priori allocation nor using conditional allocation are discussed and displayed through empirical results in Benedetti et al (2008), Day (2009), Baillargeon and Rivest (2009), and Ballin and Barcaroli (2013). A comparison of a priori allocated designs for multivariate surveys can be found in Kozak (2006b); further discussion can be found in Gonzalez and Eltinge (2010).…”

“…In particular, an assumption that meeting quality constraints for the administrative variables may not imply meeting assumed quality constraints for the desired estimators. A discussion of this issue and proposed solution for univariate stratified designs using anticipated moments can be found in Baillargeon and Rivest (2009). Anticipated moments are moments of a random variable calculated under the sample design and the super population model (Isaki and Fuller 1982).…”

Accounting for differences in costs among sampling locations in optimal stratification

“…We used R package ‘stratification’ (Baillargeon & Rivest, , ) for computing strata with the cum method. The number of classes used in computing the stratum breaks was set to 2000 × L , which was substantially larger than the recommended value of 15 × L .…”

Comparison of Random Search Method and Genetic Algorithm for Stratification

“…Kozak's (2004) algorithm is a random search algorithm (RSM), whereas Keskintürk and Er's (2007) is a genetic algorithm (GA), so both are global optimization methods. The former has been found efficient by Baillargeon et al (2007) and Baillargeon and Rivest (2009) and proven to be more efficient than geometric stratification (Kozak and Verma, 2006). Yet there is no guarantee that it provides globally optimum stratification (Baillargeon et al, 2007, Baillargeon andRivest, 2009;Kozak, 2004).…”

“…The former has been found efficient by Baillargeon et al (2007) and Baillargeon and Rivest (2009) and proven to be more efficient than geometric stratification (Kozak and Verma, 2006). Yet there is no guarantee that it provides globally optimum stratification (Baillargeon et al, 2007, Baillargeon andRivest, 2009;Kozak, 2004). Keskintürk and Er (2007) also proved that their algorithm was more efficient than geometric stratification.…”