MULTIVARIATE SMALL AREA ESTIMATION FOR MULTIDIMENSIONAL WELL-BEING INDICATORS

UoM administered thesis: Phd

Abstract

Using multivariate statistical models in small area estimation (SAE) may improve the efficiency of the small area estimates over the univariate SAE. In this thesis, we study the multivariate SAE problem of multidimensional well-being indicators. We first investigate the univariate EBLUP for a single latent variable estimated through confirmatory factor analysis. We use factor scores as composite estimates and calculate the EBLUP of factor score means and compare the use of these with the traditional approach of weighted and simple averages of standardized univariate EBLUPs of a dashboard of single observed indicators. Our simulation studies show that the use of factor scores provides more accurate and efficient estimates than weighted and simple averages in SAE. We also propose a bootstrap algorithm that accounts for the factor analysis model variability in the mean squared error (MSE) estimation of an EBLUP of factor score means. Next, we examine the use of multivariate EBLUP to estimate factor score means (for two latent factors) and compare to the use of weighted and simple averages of standardized EBLUPs of a dashboard of single observed indicators that are estimated in a univariate approach and in a multivariate SAE. We show that in general the multivariate EBLUP is more efficient than the univariate EBLUP, however, when the data correlation is taken into account before SAE estimates are computed (the case of factor scores) multivariate EBLUP does not provide large improvements in efficiency over the univariate case. Finally, we propose an MSE bootstrap estimator of a multivariate EBLUP. The results are in line with the SAE literature in terms of MSE comparisons of the multivariate EBLUP over the univariate EBLUP.

Details

Original languageEnglish
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Award date1 Aug 2018