Generalised Linear Models Incorporating Population Level Information: An Empirical Likelihood Based Approach

Abstract

In many situations information from a sample of individuals can be supplemented by population level information on the relationship between a dependent and explanatory variables. Inclusion of the population level information can reduce bias and increase the efficiency of the parameter estimates.

Population level information can be incorporated via constraints on the model parameters. In general the constraints are nonlinear making the task of maximum likelihood estimation harder. In this paper we develop an alternative approach exploiting the notion of an empirical likelihood. It is shown that within the framework of generalised linear models, the population level information corresponds to linear constraints, which are comparatively easy to handle. We provide a two-step algorithm that produces parameter estimates using only unconstrained estimation. We also provide computable expressions for the standard errors. We give an application to demographic hazard modeling by combining panel survey data from the British Household Panel Survey (BHPS) with birth registration data.