Multiple Stratification Variables in Multipurpose Surveys: Simulation Evaluations using Predicted Values. - Ballar, Kier Jesse (Quezon City University of the Philippines, 2023)
ABSTRACT

In stratified random sampling, strata are often created through strata boundary construction methods, such as the cum √f method or the LH method for skewed populations. These construction methods require a univariate stratification variable in creating optimal strata. However, in practice, rarely do surveys focus on a single variable of interest. Most surveys are multipurpose surveys where there are multiple variables of interest. A problem now arises in constructing strata for multipurpose surveys---how do we chose the stratification variable when there are many variables of interest and multiple potential stratification variables?

Previous studies have addressed this by creating a univariate composite stratification variable out of the multiple potential stratification variables through principal components analysis (PCA). As such this study explores advances in the PCA, specifically the Sparse PCA (SPCA), Hastie and Stuelze's Principal Curves (HS PC), and Einbeck, Tutz, and Evers' (2005) Local Principal Curves (LPC), to create a univariate composition stratification variable which yields more precise and more accurate estimates compared to the univariate composite stratification variable created through the PCA. In addition, this study also introduces a novel evaluation approach in assessing the precision and accuracy of the sample estimates. Specifically, we use two evaluation methods--1) the usual evaluation method where auxilliary data was used to create predicted target variable values of the unknown target variables.

Through sampling simulations, we find several interesting results. First, we discovered that the composite stratification variable created through SPCA does not result in more precise and more accurate estimates compared to the PCA Stratification. This can be attributed to the sparsity feature of the SPCA --where sample estimates for variables with zero SPCA loadings are less precise and less accurate compared to the PCA. Second, we observed that the composite stratification variable constructed using the HS PC and the LPC resulted in more precise and more accurate sample estimates compared to the PCA Stratification in certain cases. Specifically, in cases--when there are several variables in the data that influence the classification of observations as multivariate outliers--then the HS PC and LPC result in more precise and more accurate sample estimates for variables influencing the multivariate outlier classification the most. Third, the magnitude of the precision and accuracy increase of the HS PC and LPC sample estimates over the PCA was often greater compared to the magnitude of the precision and advances in the PCA, specifically the HS PC and LPC, could further improve the construction and accuracy of the stratified sample estimates.
Keywords: Surveys; Multiple Surveys; Stratified sampling; Principal Components Analysis; Principal Curves; Local Principal Curves