A Comparison of Clustering Criteria for Evaluating Multivariate Stratifications of Primary Sampling Units

• Activity Number: 29 - SPEED: Survey Methods, Transportation Studies, SocioEconomics, and General Statistical Methods Part 1
• Type: Contributed
• Date/Time: Sunday, July 28, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Survey Research Methods Section
• Author(s): Padraic Murphy*
• Companies: U.S. Census Bureau
• Keywords: clustering criteria; multi-stage sampling; stratification; first stage sampling variance

Abstract

A previous paper compared two methods, A and B, for stratifying Primary Sampling Units (PSUs.) (Murphy and Chesnut, 2018) Both methods evaluate large numbers of possible PSU stratifications that satisfy specified size constraints. From these they select ones with minimum values of clustering criterion functions F_A and F_B, respectively. The methods differ both in their criterion definition and their stratification algorithms, resulting in potentially different sets of stratifications. A method A stratification could have a lower value of F_B than the stratification selected by method B, and vice versa; but method A usually finds the better stratification if we choose to use F_A as our evaluation criterion, and similarly for method B. Consequently, our choice of method depends on our choice of evaluation criterion function. In the previous paper we tentatively decided on method A. In this paper, we show that with reasonable assumptions F_A is objectively better than F_B. Using simulated PSUs, we calculate F_A, F_B, and the sampling variance V of an estimator for large sets of stratifications. We find that F_A is usually more highly correlated with V than F_B.