Small Area Estimation via Generalized Linear Models
Alasdair Noble, Stephen Haslett, and Greg Arnold
Marker (1999) proposed a general linear regression model framework for small area estimation. This framework included most methods that have been used for small area estimation except structure-preserving estimation (SPREE) which was not included because it was non-linear. Marker noted that SPREE can be expressed instead as a log-linear model. This article considers a generalized linear model in the sense of Nelder and Wedderburn (1972). All of the small area estimation methods discussed by Marker, as well as SPREE, are formulated in this more general setting, and a range of further extensions is considered.
Using an explicit log-linear model for SPREE allows an alternative approach to the estimation of the small area estimates. That is: model the census data with a log-linear model, fix the parameters for the main effects and interactions that are held constant and reestimate the other effects using the new margins from the survey data. This method is illustrated using New Zealand unemployment data for nine North Island regions by two sexes and three age groups.
The advantage of using generalized linear models is that the range of models can be extended beyond log-linear models fitted via SPREE. Models that contain any mix of discrete, interval, or continuous variables are possible, as is illustrated by an example.
SPREE; IGLS; log-linear models; multi level model.