Statistical Modelling 7 (2007), 239–254
Ill-posed problems with counts, the composite link model and
penalized likelihood
Paul HC Eilers
Department of Methodology and Statistics,
Faculty of Social and Behavioural Sciences,
Utrecht University,
PO Box 80140,
NL–3508 TC Utrecht
The Netherlands
eMail:
P.H.C.Eilers@uu.nl
Abstract:
Certain data sets with distributions or counts can be
interpreted as indirect observations of latent distributions
or (time) series of counts. The structure of such data matches
elegantly with the composite link model (CLM). The parameters
can be estimated with iteratively re-weighted linear regression.
Unfortunately, the estimating equations generally are singular
or severely ill-conditioned. An effective solution is to impose
smoothness on the solution, by penalizing the likelihood with a
roughness measure. The optimal smoothing parameter is found
efficiently by minimizing Akaike's Information Criterion (AIC).
Several applications are presented.
Keywords:
back-calculation; mixtures; negative binomial distribution;
over-dispersion
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