Clark, Robert Graham, Incorporating household type in mixed logistic models for people in households, Centre for Statistical and Survey Methodology, University of Wollongong, Working Paper 3-13, 2013, 32.
Generalized linear mixed models (GLMMs), particularly the random intercept logistic regression model, are often used to model binary outcomes for people in households. A challenge in fitting these models is that the degree of dependency between co-householders often depends on the type of household, such as households of related people, households of unrelated people, and single person households. The use of a different variance component for each household type is investigated using two representative datasets, on voting behaviour and health risk factors and outcomes, and a simulation study. Variance components are found to be significantly different across household types in the examples. Models which ignore this understate covariate effects for household types with lower variance components, typically single person households.