Estimation of Small Area Proportions Under a Bivariate Logistic Mixed Model

Abstract

A variety of data is of geographic interest but is not available at a small area level from large-scale national sample surveys. Small area estimation can be used to estimate parameters of target variables to detailed geographical scales based on relationships between the target variables and relevant auxiliary information. Small area estimation of proportions is a topic of great interest in many fields of study, where binary variables are diffused, such as in labour force, business, and social exclusion surveys. The univariate generalised mixed model with logit link function is widely adopted in this context. The small area estimation literature has shown that multivariate small area estimators, where correlations among response variables are taken into account, provide more efficient estimates than the traditional univariate approaches. However, the estimation problem of multivariate proportions has not been studied yet. In this article, we propose a bivariate small area estimator of proportions based on a bivariate generalised mixed model with logit link function. A simulation study and an application are presented to evaluate the good properties of the bivariate estimator compared to its univariate setting. We found that the extent of the improved efficiency of the bivariate over the univariate approach is associated with the degree of correlation of the area-specific random effects and the intraclass correlation, whereas it is not strongly related to the area sample size.