Abstract
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Highlights
INTRODUCTIONIn this article we describe generalized linear latent and mixed models (GLLAMMs) and illustrate their potential in epidemiology
In this article we describe generalized linear latent and mixed models (GLLAMMs) and illustrate their potential in epidemiology.We begin by briefly describing ‘generalized linear models’ [1] which encompass common epidemiological tools such as linear regression, dichotomous logistic regression and Poisson regression
GLLAMMs provide five extensions to generalized linear mixed models: 1. Multilevel factor structures
Summary
In this article we describe generalized linear latent and mixed models (GLLAMMs) and illustrate their potential in epidemiology. A crucial assumption of generalized linear models is that the responses of different units i are independent given the covariates xi This assumption is often unrealistic since data are frequently of a multilevel nature with units i nested in clusters j. The combined effect of all unobserved cluster-level covariates is modeled by including random effects eta(m2j) in the linear predictor which take on the same value for all units in the same cluster. Η0(2j) is a random intercept, allowing the overall level of the linear predictor to vary between clusters j over and above the variability explained by the covariates xij. GLLAMMs provide five extensions to generalized linear mixed models (where we refer to η as latent variables, including random effects, factors, etc.):
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