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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.
|
Bachetti P
,
Segal MR
and
Jewell NP
(1993)
Backcalculation of HIV infection rates
. Statistical Science, 2,
82–119
. Google Scholar | Crossref | ISI | |
|
Baddeley A
and
Vedel Jensen EB
(2005) Stereology for statisticians.
Chapman and Hall/CRC
. Google Scholar | |
|
Böhning D
,
Schlattmann P
and
Lindsay B
(1993)
Computer-assisted analysis of mixtures
. Biometrics, 48,
283–304
. Google Scholar | Crossref | ISI | |
|
Eilers PHC
(1994)
Nonparametric estimation of mixed discrete distributions with penalized likelihood
. Paper presented at the XVIIth International Biometric Conference, Hamilton. Google Scholar | |
|
Eilers PHC
(1995)
Indirect observations, composite link models and penalized likelihood
. In
Seeber GUH
,
Francis BJ
,
Hatzinger R
and
Steckel-Berger G
eds Proceedings of the 10th International Workshop on Statistical Modelling. New York: Springer-Verlag,
91–98
. Google Scholar | |
|
Eilers PHC
and
Borgdorff MW
(2004)
Modeling and correction of digit preference in tuberculin surveys
. International Journal of Tuberculosis and Lung Diseases, 8,
232–39
. Google Scholar | Medline | ISI | |
|
Eilers PHC
and
Marx BD
(1996)
Flexible smoothing using B-splines and penalized likelihood (with comments and rejoinder)
. Statistical Science, 11,
89–121
. Google Scholar | Crossref | ISI | |
|
Fahrmeir L
and
Tutz G
(2001) Multivariate statistical modelling based on generalized linear models, 2nd edition.
New York
:
Springer-Verlag
. Google Scholar | Crossref | |
|
Gersch W
and
Kitagawa G
(1996) Smoothness priors analysis of time series.
New York
:
Springer-Verlag
. Google Scholar | |
|
Hasselblad V
,
Stead AG
and
Galke W
(1980)
Analysis of coarsely grouped data from the lognormal distribution
. Journal of the American Statistical Association, 75,
771–78
. Google Scholar | Crossref | ISI | |
|
Hastie TJ
and
Tibshirani RJ
(1990). Generalized additive models.
London
:
Chapman and Hall
. Google Scholar | |
|
Heisterkamp S
(1995) Quantitative analysis of AIDS/HIV: development of methods to support policy making for infectious disease control. PhD Dissertation,
Leiden
. Google Scholar | |
|
McCullagh P
and
Nelder JA
(1989) Generalized additive models (2nd edition).
London
:
Chapman and Hall
. Google Scholar | Crossref | |
|
Nelder JA
and
Wedderburn RWM
(1972)
Generalized linear models
. Journal of the Royal Statistical Society A, 135,
370–84
. Google Scholar | Crossref | ISI | |
|
Pole A
,
West M
and
Harrison J
(1994) Applied Bayesian forecasting and time series analysis.
London
:
Chapman and Hall
. Google Scholar | Crossref | |
|
Raabe-Hesketh S
and
Skrondal A
(2007)
Multilevel and latent variable modeling with composite links and exploded likelihoods
. Psychometrika, 72,
123–40
. Google Scholar | Crossref | ISI | |
|
Rindskopf D
(1992)
A general approach to categorical data analysis with missing data, using generalized linear models with composite link
. Psychometrika, 57,
29–42
. Google Scholar | Crossref | ISI | |
|
Simonoff JS
(1996) Smoothing methods in statistics.
New York: Springer-Verlag
. Google Scholar | Crossref | |
|
Skrondal A
and
Raabe-Hesketh S
(2004a) Generalized latent variable modeling.
Chapman and Hall/CRC
. Google Scholar | Crossref | |
|
Skrondal A
and
Raabe-Hesketh S
(2004b)
Generalised linear latent and mixed models with composite links and exploded likelihoods
. In
Biggeri A
,
Dreassi E
,
Lagazio C
and
Marchi M
eds 19th International Workshop on Statistical Modeling. Florence: Firenze University Press. Google Scholar | |
|
Stoyan D
,
Kendall WS
and
Mecke J
(1995) Stochastic geometry and its Applications, 2nd edition.
New York: Wiley
. Google Scholar | |
|
Sun JG
and
Kalbfleisch JD
(1993)
The analysis of current status data on point-processes
. Journal of the American Statistical Association, 88,
1449–54
. Google Scholar | Crossref | ISI | |
|
Thompson R
and
Baker RJ
(1981)
Composite link functions in generalized linear models
. Applied Statistics, 30,
125–31
. Google Scholar | Crossref | |
|
Uh HW
and
Eilers PHC
(2005)
Haplotype estimation with the penalized composite link model (abstract)
. Proceedings of the 25th European Meeting of Statisticians, Oslo. Google Scholar | |
|
Wand MP
and
Jones MC
(1995) Kernel smoothing.
London: Chapman and Hall
. Google Scholar | Crossref |
