Small area estimation under area-level generalized linear mixed models

Abstract

This paper introduces a general area-level model-based formulation to small area estimation based on generalized linear mixed models. By applying an optimization algorithm to the Laplace approximation of the likelihood, the maximum likelihood estimators of the model parameters are calculated. Empirical best predictors of small area quantities are derived and the corresponding mean squared errors are estimated by parametric bootstrap. Some simulation experiments are carried out to study the behavior of the fitting algorithm, the small area predictors and the estimators of the mean squared errors. By using data of the Spanish living condition survey of 2008, an application to the estimation of average annual net incomes in Spanish provinces by sex is given.

Keywords:

• Average income
• Bootstrap
• Empirical best predictor
• Gamma mixed models
• Mean squared error

MATHEMATICS SUBJECT CLASSIFICATION:

• 62J12 Generalized linear models
• 62P25 Applications to social sciences
• 62D05 Sampling theory
• sample surveys

Additional information

Funding

Supported by the Spanish grant PGC2018-096840-B-I00 provided by Ministerio de Ciencia, Innovación y Universidades, by the Czech grant SGS18/188/OHK4/3T/14 provided by Ministerstvo Školství, Mládeže a Tělovýchovy (MŠMT ČR) and from the European Regional Development Fund-Project “Center of Advanced Applied Sciences” (No. CZ.02.1.01/0.0/0.0/16_019/0000778).