Geometric versus optimization approach to stratification: A comparison of efficiency - ARCHIVED

In this paper, the geometric, optimization-based, and Lavallée and Hidiroglou (LH) approaches to stratification are compared. The geometric stratification method is an approximation, whereas the other two approaches, which employ numerical methods to perform stratification, may be seen as optimal stratification methods. The algorithm of the geometric stratification is very simple compared to the two other approaches, but it does not take into account the construction of a take-all stratum, which is usually constructed when a positively skewed population is stratified. In the optimization-based stratification, one may consider any form of optimization function and its constraints. In a comparative numerical study based on five positively skewed artificial populations, the optimization approach was more efficient in each of the cases studied compared to the geometric stratification. In addition, the geometric and optimization approaches are compared with the LH algorithm. In this comparison, the geometric stratification approach was found to be less efficient than the LH algorithm, whereas efficiency of the optimization approach was similar to the efficiency of the LH algorithm. Nevertheless, strata boundaries evaluated via the geometric stratification may be seen as efficient starting points for the optimization approach.