Table Of ContentLecture Notes in Statistics 104
Edited by P. Diggle, S. Fienberg, K. Krickeberg,
1. Olkin, N. Wermuth
G.U.H. Seeber
B.l. Prancis
R. Hatzinger
G. Steckel-Berger (Editors)
Statistical Modelling
Proceedings of the
10th International Workshop on
Statistical Modelling
Innsbruck, Austria, 10-14 1u ly, 1995
Springer Science+Business Media, LLC
Gilg U.H. Seeber Brian J. Francis
Institut fUr Statistik Centre for Applied Statistics
Universitllt lnnsbruck Lancaster University
Christoph-Probst-PlaI7. Fylde College
A-6020 lnnsbruck Lancaster, LAI 4YF
Austria England
Reinhold Hatzingcr Gabriele Steckel-Bergcr
Institut fur Statistik Institut fUr Statistik
Wirtschaftsuniversităt Universităt Innsbruck
Augasse 2-6 Christoph-Probst-Platz
A-1090 Wicn A-6020 lnnsbruck
Austria Austria
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© 1995 Springer Science+Business Media New York
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9 8 765 432 I
ISBN 978-0-387-94565-1 ISBN 978-1-4612-0789-4 (eBook)
DOI 10.1007/978-1-4612-0789-4
Preface
This volume presents the published proceedings of the lOth International
Workshop on Statistical Modelling, to be held in Innsbruck, Austria from
10 to 14 July, 1995.
This workshop marks an important anniversary. The inaugural workshop
in this series also took place in Innsbruck in 1986, and brought together
a small but enthusiastic group of thirty European statisticians interested
in statistical modelling. The workshop arose out of two G LIM conferences
in the U.K. in London (1982) and Lancaster (1985), and from a num
ber of short courses organised by Murray Aitkin and held at Lancaster in
the early 1980s, which attracted many European statisticians interested in
Generalised Linear Modelling. The inaugural workshop in Innsbruck con
centrated on GLMs and was characterised by a number of features - a
friendly and supportive academic atmosphere, tutorial sessions and invited
speakers presenting new developments in statistical modelling, and a very
well organised social programme. The academic programme allowed plenty
of time for presentation and for discussion, and made available copies of all
papers beforehand.
Over the intervening years, the workshop has grown substantially, and now
regularly attracts over 150 participants. The scope of the workshop is now
much broader, reflecting the growth in the subject of statistical modelling
over ten years. The elements ofthe first workshop, however, are still present,
and participants always find the meetings relevant and stimulating. The
number of submitted papers has grown with the number of participants, but
successful contributed papers still receive a relatively generous 30 minutes
of presentation time, and invited speakers one hour. Parallel sessions have
been avoided, allowing everyone both to learn and to contribute. Poster
sessions are now held, and software demonstrations and displays are organ
ised. One change is that the workshops have become more international in
nature. Participants now attend from all corners of the globe, and work
shops have travelled around Europe - to Perugia (1987), Vienna (1988),
Trento (1989), Toulouse (1990), Utrecht (1991), Munich (1992), Leuven
(1993) and Exeter (1994).
The current workshop, hopefully, will be no exception. The invited speakers
chosen for the meeting are all experts in their field, and all but one of their
contributions are included in this volume. It is particularly appropriate that
Murray Aitkin will deliver the opening paper of the workshop, as he was one
of the invited speakers at the initial workshop. He will be presenting work
VI Preface
on a general procedure for non-parametric maximum likelihood estimation
of mixing distributions. Anthony Atkinson will introduce participants to
optimal experimental design in generalised linear models, and Adelchi Az
zalini will be speaking on new software tools in S-Plus and related practical
problems in fitting models to repeated measurements. Last in the alpha
bet, but not least, James Booth will deliver work on bootstrap methods in
generalised linear mixed models, illustrated by practical datasets collected
in small spatial areas. This workshop, therefore, both continues with its
GLM heritage, and looks forward to new developments in the analysis of
repeated measures, mixed and random effect models.
There are also some forty contributed papers presented in this volume.
They, together with the invited papers, are presented in alphabetic order of
the name ofthe first author. These cover a wide variety of application areas,
from epidemiology to education, and from agriculture to sociology. Many
papers present analyses of real data sets, whereas others have a greater
emphasis on theoretical and technical issues. All have been subject to a
refereeing process by the Scientific Committee, who rejected approximately
half of the papers submitted.
The Editors of this volume would like to thank all members of the Scientific
Committee and other referees who again worked extremely hard in assessing
the large number of papers submitted. The local organisers of the workshop
listed below also deserve our thanks in advance, for what is always a busy
and onerous task. Finally, we thank the authors for simplifying considerably
the task of preparing this volume, both by submitting their papers in UTEX
in the correct format, by keeping strictly to the tight timescale, and for
restricting their interesting ideas to eight pages.
GUHS, RH, BJF, GS-B (April 1995)
Scientific Committee: J. Engel (Eindhoven), L. Fahrmeir (Munich), A. de
Falguerolles (Toulouse), A. Forcina (Perugia), B.J. Francis (Lancaster), P.
Gherardini (Rome), R. Gilchrist (London), R. Hatzinger (Vienna), P. van
der Heijden (Utrecht), J. Hinde (Exeter), E. Lesaffre (Leuven), B. Marx
(Stanford), Ch.E. Minder (Berne), G.U.H. Seeber (Innsbruck), G. Tutz
(Berlin).
Local Organising Committee: G. Marinell, G.U.H. Seeber, G. Steckel
Berger, Ch.M. Traweger, H. Ulmer, M. Volp (Innsbruck); R. Dittrich, R.
Hatzinger (Vienna).
Table of Contents
Preface v
NPML estimation of the mixing distribution in general statistical mod
els with unobserved random effects
MURRAY AITKIN 1
Some topics in optimum experimental design for generalized linear mod
els
ANTHONY C. ATKINSON 11
Autoregressive modelling of Markov chains
ANDRE BERCHTOLD 19
A case-study on accuracy of cytological diagnosis
A. BIGGERI, M. BINI 27
Dynamics and correlated responses in longitudinal data models
R. BLUNDELL, R. GRIFFITH, F. WINDMEIJER 35
Bootstrap methods for generalized linear mixed models with applica
tions to small area estimation
JAMES BOOTH 43
Confidence intervals for threshold parameters
R.C.H. CHENG, W.B. LIU 53
Optimal design for models incorporating the Richards function
G.P.Y. CLARKE, L.M. HAINES 61
Mixed Markov renewal models of social processes
R.B. DAVIES, G.R. OSKROCHI 67
Statistical inference based on a general model of unobserved hetero
geneity
EKKEHART DIETZ, DANKMAR BOHNING 75
An extended model for paired comparisons
R. DITTRICH, R. HATZINGER, W. KATZENBEISSER 83
Vlll Table of Contents
Indirect observations, composite link models and penalized likelihood
PAUL H.C. EILERS 91
Model estimation in nonlinear regression
JOACHIM ENGEL, ALOlS KNEIP 99
Pearson statistics, goodness of fit, and overdispersion III generalised
linear models
C.P. FARRINGTON 109
M-estimation: Some remedies
ROBERT GILCHRIST, GEORGE PORTIDES 117
Subject-specific and population-averaged questions for log-linear regres
sion data
ULRIKE GROMPING 125
Radon and lung cancer mortality: An example of a Bayesian ecological
analysis
ULRICH HELFENSTEIN, CHRISTOPH E. MINDER 133
IRREML, a tool for fitting a versatile class of mixed models for ordinal
data
A. KEEN, B. ENGEL 141
Towards a general robust estimation approach for generalised regression
models
JAYALAKSHIMI KRISHNAKUMAR 151
Comparing local fitting to other automatic smoothers
MICHAEL MADERBACHER, WERNER G. MULLER 161
Iterative reweighted partial least squares estimation for G LMs
BRIAN D. MARX 169
Protective estimation of longitudinal categorical data with nonrandom
dropout
BART MICHIELS, GEERT MOLENBERGHS 177
Analysis of counts generated by an age-dependent branching process
SALOMON MINKIN 185
Quantitative risk assessment for clustered binary data
GEERT MOLENBERGHS, LIEVEN DECLERCK, MARC AERTS 193
Optimal design and lack of fit in nonlinear regression models
TIMOTHY E. O'BRIEN 201
Table of Contents i x
N onparametric regression, kriging and process optimization
M. O'CONNELL, P. HAALAND, S. HARDY, D. NYCHKA 207
Frailty in multiplicative intensity models
GH.R. OSKROCHI 215
Methods for assessing the adequacy of probability prediction models
JOSEPH G. PIGEON, JOSEPH F. HEYSE 225
Forecast methods in regression models for categorical time series
HELMUT PRUSCHA 233
Standard errors, correlations and model analysis
K.L.Q. READ 241
Mean and dispersion additive models: Applications and diagnostics
ROBERT A. RIGBY, MIKIS D. STASINOPOULOS 249
Computational aspects in maximum penalized likelihood estimation
ORI ROSEN, AYALA COHEN 257
Risk estimation using a surrogate marker measured with error
AMRIK SHAH, DAVID SCHOENFELD, VICTOR DE GIWTTOLA 267
Estimating attributable risks under an arithmetic mixture model
KAREN STEINDORF, JAY LUBIN 277
A non parametric method for detecting neural connectivity
KLAUS J. UTIKAL 287
On the design of accelerated life testing experiments
A.J. WATKINS 297
Splitting criteria in survival trees
HEPING ZHANG 305
The different parameterizations of the GEEI and GEE2
ANDREAS ZIEGLER 315
List of authors 325
NPML estimation of the mixing
distribution in general statistical
models with unobserved random
effects
Murray Aitkin
ABSTRACT: General maximum likelihood computational methods have
recently been described for longitudinal analysis and related problems using
generalized linear models. These developments extend the standard meth
ods of generalized linear modelling to deal with overdispersion and variance
component stnlctures caused by the presence of unobserved random eHects
in the models. The value of these methods is that they are not restricted
by particular statistical model assumptions about the distribution of the
random effects, which if incorrect might invalidate the conclusions. De
spite this generality these methods are fully efficient, in the sense that the
model is fitted by (nonparametric) maximum likelihood, rather than by
approximate or inefficient methods. The computational implementation of
the methods is straightforward in GLM packages like GLIM4 and S+.
An important feature of these computational methods is that they are
applicable to a much broader class of models than the GLMs described
above, and provide new general computational solutions to fitting a very
wide range of models using latent variables.
KEYWORDS: Mixture; Overdispersion; Variance Components; Nonpara
metric Maximum Likelihood; EM Algorithm; Gauss-Newton Algorithm
1 Background
The analysis of longitudinal studies with normally distributed response
variables is well-established, and maximum likelihood methods are widely
available for modelling intra-class (equal) correlation structures of the re
peated measures over time. (Maximum likelihood methods for autoregres
sive or other patterned correlation structures are also available, though
much less widely.) The same methods apply to the analysis of hierarchi
calor nested studies, for example in school effectiveness studies which test
pupils nested in schools. However for binary, categorical or count data mea-
2 Murray Aitkin
sured repeatedly, the available statistical methods are much less satisfac
tory. The difficulty is that the generalizations of the standard exponential
family (binomial, Poisson or gamma) models which allow for repeated mea
sures by common random effects (equal correlation) do not have a closed
analytic form for the likelihood function, and standard methods for nor
mally distributed variables cannot be applied.
To avoid this difficulty, two different approximate procedures have been
used. The first is to assume that the common random effects are normally
distributed as in the normal variance component model, and to approxi
mate the exponential family likelihood in one of several ways by a normal
likelihood; this allows methods for normal variance component models to
be applied approximately to non-normal distributions. This conditional ap
proach has been applied in slightly different ways by McGilchrist (1994),
Longford (1994 Chapter 8) and Goldstein (1991). The second is to assume
that the marginal distribution of the response is from the exponential fam
ily and to model the covariance structure induced by the repeated measures
in one of several reasonable ways (Liang and Zeger 1986, Diggle, Liang and
Zeger 1994); the model is fitted by a generalized quasi-likelihood method
(generalized estimating equations, GEE). This second marginal approach
is inconsistent with the random effect model structure, since the marginal
distribution ofthe response must be a mixed, not a pure, exponential family
distribution. Thus the GEE approach actually fits a different model; there
is considerable disagreement over whether the conditional or the marginal
approach is preferable.
A disadvantage of any approach using a specified parametric form (e.g.
normal) for the mixing distribution of the random effects is the possible
sensitivity of the conclusions to this specification. The influential paper by
Heckman and Singer (1984) showed substantial changes in parameter es
timates in variance component models with quite small changes in mixing
distribution specification; Davies (1987) showed similar effects. This diffi
culty can be avoided by nonparametric maximum likelihood (NPML) esti
mation of the mixing distribution, concurrently with the structural model
parameters. In this approach the random effect distribution is unspecified,
but remarkably can itself be estimated by ML (Kiefer and Wolfowitz 1956).
The NPML estimate is well-known to be a discrete distribution on a fi
nite number of mass-points (Kiefer and Wolfowitz 1956, Laird 1978, Lind
say 1983), but actually finding the NPML estimate is widely regarded as
computationally intensive, the particular difficulty being the location of
the mass-points. Current approaches use Gateaux or directional deriva
tives (Ezzet and Davies 1988, Follmann and Lambert 1989, Lesperance and
Kalbfleisch, 1992, Bohning, Schlattman and Lindsay 1992). Barry, Francis
and Davies (1989) remark: "[NPMLj is not a simplification of the paramet
ric approach as the identification of the number, location and masses of
these points of support present formidable computational problems."
An important paper by Hinde and Wood (1987) addressed the computa-
