ABSTRACT
In inference for finite populations, an important task is the estimation of population parameters, such as totals, means and more complex parameters written as a function of these quantities from sample survey data. The model- assisted approach improves over the classical Horvitz-Thompson estimation by incorporating additional population information and modelling into the design-based approach through the use of auxiliary information and a working model. The overall aim is to improve the efficiency of the final difference-type estimators while maintaining the desirable design-based properties of approximate unbiasedness and consistency irrespective of possible model misspecifications.
This chapter discusses the model-assisted approach when complex survey data are available and auxiliary population level information regards the spatial structure of the relationship among units, such as their geo-referenced location. Different and increasingly more complex working models are discussed and analysed in order to account for spatial information in estimating population means and totals of both continuous and binary variables of interest. In particular, linear multiple regression models, generalized linear models and geo-additive models are considered. An analytic measure of precision of the final estimates is also provided and discussed. For each of the analysed models, R code is provided and numerical examples based on data from the U.S. Northeastern Lakes survey are illustrated.
