Small area estimation of proportions in business surveys

Abstract

Binary data are often of interest in business surveys, particularly when the aim is to characterize grouping in the businesses making up the survey population. When small area estimates are required for such binary data, use of standard estimation methods based on linear mixed models (LMMs) becomes problematic. We explore two model-based techniques of small area estimation for small area proportions, the empirical best predictor (EBP) under a generalized linear mixed model and the model-based direct estimator (MBDE) under a population-level LMM. Our empirical results show that both the MBDE and the EBP perform well. The EBP is a computationally intensive method, whereas the MBDE is easy to implement. In case of model misspecification, the MBDE also appears to be more robust. The mean-squared error (MSE) estimation of MBDE is simple and straightforward, which is in contrast to the complicated MSE estimation for the EBP.

Keywords:

• small area proportions
• model-based direct estimation
• generalized linear mixed model
• empirical best predictor

AMS Subject Classification :

• 62D05
• 62J99