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,
Education Statistics Services Institute,
Washington, D.C.,

Marco Alf˛
Dipartimento di Statistica, ProbabilitÓ e Statistiche Applicate,
UniversitÓ 'La Sapienza' di Roma
P.le A. Moro, 5
I-00185 Rome,


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.


Autoregressive models; nonparametric maximum likelihood (NPML) estimation; random effects GLMs; repeated binary data.