We introduce a model class that includes many types of correlation structures for
non-Gaussian models. We then show how to check the underlying model assumptions to
discriminate between different correlation patterns and demonstrate how to select
suitable models. Strawberry data are used to discuss the choice between fixed- and
random-effect models for the fertility effect in agricultural experiments.
Prostate-cancer data are used to demonstrate the method applied to the analysis of
longitudinal studies and Scottish lip-cancer data to illustrate an application to
spatial statistics.
Baltagi BH
(1995) Economic analysis of panel data.
New York: Wiley
.
2.
Besag J
,
Green P
,
Higdon D
,
Mengersen K
(1995)
Bayesian computation and stochastic systems (with discussion)
. Statistical Science10,
3-66
.
3.
Besag J
,
Higdon P
(1999)
Bayesian analysis of agriculture field experiments (with discussion)
. Journal of the Royal Statistical Society B61,
691-746
.
4.
Breslow NE
(1984)
Extra-Poisson variation in log-linear models
. Applied Statistics33,
38-44
.
5.
Breslow NE
,
Clayton DG
(1993)
Approximate inference in generalized linear mixed models
. Journal of American Statistical Association88,
9-25
.
6.
Clayton D
,
Kaldor J
(1987)
Empirical Bayes estimates of age-standardized relative risks for use in
disease mapping
. Biometrics43,
671-681
.
7.
Cressie N(1993) Statistics for spatial data.
New York: Wiley
.
8.
Diggle PJ
,
Liang K
,
Zeger SL
(1994) Analysis of longitudinal data.
Oxford: Clarendon Press
.
9.
Diggle PJ
,
Tawn JA
,
Moyeed RA
(1998)
Model-based geostatistics
. Applied Statistics47,
299-350
.
10.
Durbin J
,
Koopman SJ
(2000)
Time series analysis of non-Gaussian observations based on state space
models from both classical and Bayesian perspectives (with discussion)
. Journal of the Royal Statistical Society B62,
3-56
.
11.
Gabriel KR
(1962)
Ante-dependence analysis of an ordered set of variables
. Annals of Mathematical Statistics33,
201-212
.
12.
Harvey AC
(1989) Forcasting, structural time series models and the
Kalman filter.
Cambridge: Cambridge University Press
.
13.
Haussman JA
(1978)
Specification tests in econometrics
. Econometrica49,
1377-1398
.
14.
Holford TR
(1983)
The estimation of age, period and cohort effects for vital rates
. Biometrics39,
311-324
.
15.
Hsiao C
(1995) Analysis of panel data. Econometric Society
Monograph,
Cambridge: Cambridge University Press
.
16.
Kenward MG
,
Smith DM
(1995)
Computing the generalized estimating equations with quadratic covariance
estimation for repeated measurements
. Genstat Newsletter32,
50-62
.
17.
Laird N
,
Ware JH
(1982)
Random-effects models for longitudinal data
. Biometrics38,
963-974
.
18.
Lee Y
(2000a)
Fixed-effect versus random-effect models for evaluating therapeutic preferences
. Statistics in Medicine (to appear).
19.
Lee Y
(2000b)
Discussion in Durbin and Koopman’s paper
. Journal of the Royal Statistical Society B62,
47-47
.
20.
Lee Y
,
Nelder JA
(1996)
Hierarchical generalized linear models (with discussion)
. Journal of the Royal Statistical Society58,
619-678
.
21.
Lee Y
,
Nelder JA
(1998)
Generalized linear models for the analysis of quality-improvement experiments
. The Canadian Journal of Statistics26,
95-105
.
22.
Lee Y
,
Nelder JA
(2000a) HGLMs: a synthesis of GLMs, random effect models and
structured dispersions. Technical Report,
Imperial College
.
23.
Lee Y
,
Nelder JA
(2000b)
Two ways of modelling overdispersion for non-normal data
. Applied Statistics49,
591-598
.
24.
Lindsey JK
,
Lambert P
(1998)
On the appropriateness of marginal models for repeated measurements in
clinical trials
. Statistics in Medicine17,
447-469
.
25.
McCullagh P
,
Nelder JA
(1989) Generalized linear models, 2nd edn.London: Chapman and Hall
.
26.
Nelder JA
,
Lee Y
(1998)
Joint modelling of the mean and dispersion
. Technometrics40,
168-175
.
27.
Zeger SL
,
Liang KY
,
Albert PS
(1988)
Models for longitudinal data: a generalized estimating equation approach
. Biometrics44,
1049-1060
.
