Statistical Modelling 9 (2009), 199–213
Latent trajectory modelling of multivariate binary data
Ken J Beath
Department of Statistics
Macquarie University
NSW 2109
Australia
eMail: ken.beath@mq.edu.au
Gillian Z. Heller
Department of Statistics
Macquarie University
Australia
London School of Hygiene and Tropical Medicine
Abstract:
Latent trajectory analysis is a form of latent class analysis, where
the manifest variables are longitudinal measurements of a single outcome.
The latent classes may correspond to either constant increasing or
decreasing levels of the outcome over time and describe different
severity or course of a disease. Extension to multiple outcomes at
each time point allows more accurate determination of classes, with
classes based on combination of the outcomes, however requiring models
which account for both correlation between outcomes and periods. Three
models are described for multiple binary outcomes, observed at each
time point: a latent class model where all outcomes are considered
independent at all time points, a model incorporating random effects
for subject only and one incorporating random effects for subject
and period. The methods are applied to data on asthma and allergy
symptoms in infants, with symptoms recorded at four time points,
and it is shown that the incorporation of subject and period
heterogeneity results in lower estimates of the number of latent classes.
Keywords:
latent class; latent trajectory; longitudinal; multilevel; random effects
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