Simple Compromise Strategies in Multivariate Stratification Park, Inho;
Stratification (among other applications) is a popular technique used in survey practice to improve the accuracy of estimators. Its full potential benefit can be gained by the effective use of auxiliary variables in stratification related to survey variables. This paper focuses on the problem of stratum formation when multiple stratification variables are available. We first review a variance reduction strategy in the case of univariate stratification. We then discuss its use for multivariate situations in convenient and efficient ways using three methods: compromised measures of size, principal components analysis and a K-means clustering algorithm. We also consider three types of compromising factors to data when using these three methods. Finally, we compare their efficiency using data from MU281 Swedish municipality population.
Stratum boundaries;sample allocation;principal components analysis;measure of size;K-means clustering algorithm;
Ardilly, P. and Tille, Y. (2006). Sampling Methods: Exercise and Solutions, Springer-Verlag, New York.
Bethel, J. (1989). Sample allocation in multivariate surveys, Survey Methodology, 15, 47-57.
Golder, P. A. and Yeomans, K. A. (1973). The use of cluster analysis for stratification, Applied Statistics, 22, 213-219.
Hagood, M. J. and Bernert, E. H. (1945). Component indexes as a basis for stratification in sampling, Journal of the American Statistical Association, 40, 330-341.
Jain, A. K., Murty, M. N. and Flynn, P. L. (1999). Data clustering: A review, ACM Computing Surveys, 31, 264-323.
Jarque, C. M. (1981). A solution to the problem of optimum stratification in multivariate sampling, Applied Statistics, 30, 163-169.
Kish, L. and Anderson, D. W. (1978). Multivariate and multipurpose stratification, Journal of the American Statistical Association, 73, 24-34.
Kozak, M. and Verma, M. R. (2006). Geometric versus optimization approach to stratification: A comparison of efficiency, Survey Methodology, 32, 157-163.
Malec, D. (1995). Selecting multiple-objective fixed-cost sample designs using an admissibility criterion, Journal of Statistical Planning and Inference, 48, 229-240.
Mardia, K. V., Kent, J. T. and Bibby, J. M. (1980). Multivariate Analysis, Academic Press, London.
Samita, S. and Kumari, W. M. R. (2006). Multivariate based stratification as an alternative to multi-stage stratification in stratified random sampling, Sri Lankan Journal of Applied Statistics, 7, 55-69.
Sarndal, C. E., Swensson, B. and Wretman, J. (1992). Model Assisted Survey Sampling, Springer-Verlag, New-York.