A Fay–Herriot Model with Different Random Effect Variances

Abstract

A modification of the Fay–Herriot model is introduced to treat situations where small areas are divided in two groups and domain random effects have different variances across the groups. The model is applicable to data having a large subset of domains where direct estimates of the variable of interest cannot be described in the same way as in its complementary subset of domains. This is generally the case when domains are constructed by crossing geographical characteristics with sex. Algorithms and formulas to fit the model, to calculate EBLUPs and to estimate mean squared errors are given. Monte Carlo simulation experiments are presented to illustrate the gain of precision obtained by using the proposed model and to get some practical conclusions. A motivating application to Spanish Labour Force Survey data is also given.

Keywords:

• EBLUP
• Fay–Herriot model
• Labour Force Survey
• Linear mixed models
• Small area estimation

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62D06

Acknowledgments

The authors thank one of the referees for their valuable suggestions, including the proposal of introducing model (2.1). This work was supported by the grants MTM2009-09473 and MSMTV 1M0572.