Optimum stratification using decision tree

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Moradi Mohammad; Kasani Elnaz

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Journal Paper

Paper Information

Journal: Mathematical Researches Year:2024 | Volume:10 | Issue:2 Page(s): 51-65

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Information Journal Paper

Title

Optimum stratification using decision tree

Author(s)

Moradi Mohammad | Kasani Elnaz | Issue Writer Certificate

Keywords

Strata boundries

homogeneity of units within strata

stratified sampling efficiency

penalty.

Abstract

Stratified sampling is one of the most widely used sampling designs. In some cases, it is up to the researcher to determine the boundaries of the strata, and in some cases, the population is already stratified. The optimal classification is obtained for a situation of Strata boundries, where the variance of the population mean (or total) estimator reaches its lowest value. In traditional methods, the variance of the estimator is considered as a function of the strata boiundries for the response variable, in order to reach the minimum of the variance, equations are obtained which are often solved by numerical methods. The first deficiency of this method is not considering all auxiliary variables. For example, in estimating the average income, classifying the society based on factors such as gender and job history can not only increase the efficiency of the estimator, but also make the interpretability and generalizability of the results easier. The second one is complex equations that do not have a closed and understandable solutions
n this paper, we have tried to construct the optimal classification based on a new criterion that is a combination of variance and a penalty.for increasing the number of strata, so that important auxiliary variables in the formation of the decision tree determine the boundries of the strata. The classification process starts from the saturated tree and with successive pruning until reaching the root node, the number of strata decreases, the optimal stratification is achieved based on the introduced combined criterion.

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