Statistical Modelling 3 (2003), 291–303
Longitudinal analysis of repeated binary data using autoregressive
and random effect modelling
Murray Aitkin
School of Mathematics and Statistics,
University of Newcastle upon Tyne,
and
Education Statistics Services Institute,
Washington, D.C.,
USA.
Marco Alfò
Dipartimento di Statistica, Probabilità e Statistiche Applicate,
Università 'La Sapienza' di Roma
P.le A. Moro, 5
I-00185 Rome,
Italy.
eMail: marco.alfo@uniroma1.it
Abstract:
In this paper we extend random coefficient models for binary repeated
responses to include serial dependence of Markovian form, with the aim
of defining a general association structure among responses recorded
on the same individual. We do not adopt a parametric specification for
the random coefficients distribution and this allows us to overcome
inconsistencies due to misspecification of this component. Model
parameters are estimated by means of an EM algorithm for nonparametric
maximum likelihood (NPML), which is extended to deal with serial
correlation among repeated measures, with an explicit focus on those
situations where short individual time series have been observed. The
approach is described by presenting a reanalysis of the well-known
Muscatine (Iowa) longitudinal study on childhood obesity.
Keywords:
Autoregressive models; nonparametric maximum likelihood (NPML) estimation;
random effects GLMs; repeated binary data.
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