Modelling non-hierarchical structures

Abstract

In the models discussed in this book so far we have assumed the populations from which data has been drawn are hierarchical. This assumption is not always justified. Two main types of nonhierarchical model are considered in this chapter. Cross classified models and multiple membership models. This chapter draws on the work of Rasbash and Goldstein(1996) and Hill and Goldstein(1998) 1 Cross-classified models This section is divided into four parts. In this first part we look at situations in health research that can give rise to a two way cross-classification and suggest some notation to describe this model. In the second part we look at more complicated cross-classified structures and extend the notation. In the third part we describe general rules for the notation construction. In the final part we describe the analysis of an example data set. 1.1 Two way cross-classifications – a basic model. Suppose, we have data on a large number of patients, attending many hospitals and we also know the neighbourhood in which the patient lives and that we regard patient, neighbourhood and hospital all as important sources of variation for the patient level outcome measure we wish to study. Now, typically hospitals will draw patients from many different neighbourhoods and the inhabitants of a neighbourhood will go to many hospitals. No pure hierarchy can be found and patients are said to be contained within a cross-classification of hospitals by neighbourhoods. This can be represented diagrammatically, for the case of twenty patients contained within a cross-classification of three neighbourhoods by five hospitals: Table 1: patients cross classified by hospital and neighbourhood neighbourhood 1 Neighbourhood 2 neighbourhood 3