Multilevel models for censored and latent responses

Multilevel models were originally developed to allow linear regression or A NOVA models to be applied to observations that are not mutually independent . This lack of independence commonly arises due to clustering of the units of observations into 'higher level units' such as patients in hospitals. In linear mixed models, the within-cluster correlations are modelled by inclu ding random effects in a linear model. In this paper, we discuss generalizations of linear mixed models suitable f or responses subject to systematic and random measurement error and interva l censoring. The first example uses data from two cross-sectional surveys of schoolchild ren to investigate risk factors for early first experimentation with cigare ttes. Here the recalled times of the children's first cigarette are likely to be subject to both systematic and random measurement errors as well as b eing interval censored. We describe multilevel models for interval censored survival times as special cases of generalized linear mixed models and dis cuss methods of estimating systematic recall bias. The second example is a longitudinal study of mental health problems of pat ients nested in clinics. Here the outcome is measured by multiple questionn aires allowing the measurement errors to be modelled within a linear latent growth curve model. The resulting model is a multilevel structural equatio n model. We briefly discuss such models both as extensions of linear mixed models and as extensions of structural equation models. Several different m odel structures are examined. An important goal of the paper is to place a number of methods that readers may have considered as being distinct within a single overall modelling fr amework.