Statistical Modelling 8 (2008), 385–401
Modelling general patterns of digit preference
Carlo G. Camarda
Max Planck Institute for Demographic Research
Konrad-Zuse-Straße 1
D–18057 Rostock
Germany
eMail:
camarda@demogr.mpg.de
Paul H.C. Eilers
Methodology and Statistics, Faculty of Social and Behavioural Sciences
Utrecht University
The Netherlands
and
Data Theory Group, Leiden University
The Netherlands
Jutta Gampe
Max Planck Institute for Demographic Research
Rostock
Germany
Abstract:
In many applications data can be interpreted as indirect observations of a
latent distribution. A typical example is the phenomenon known as digit
preference, i.e. the tendency to round outcomes to pleasing digits. The
composite link model (CLM) is a useful framework to uncover such latent
distributions. Moreover, when applied to data showing digit preferences,
this approach allows estimation of the proportions of counts that were
transferred to neighbouring digits. As the estimating equations generally
are singular or severely ill-conditioned, we impose smoothness assumptions
on the latent distribution and penalize the likelihood function. To estimate
the misreported proportions, we use a weighted least-squares regression with
an added L1 penalty. The optimal smoothing parameters are found by minimizing
the Akaike’s information Criterion (AIC). The approach is verified by a
simulation study and several applications are presented.
Keywords:
composite link model digit preference; L penalty; penalized likelihood;
smoothing
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