Statistical Modelling 7 (2007), 217–238
Using cross-classified multivariate mixed response models with
application to life history traits in great tits (Parus major)
William J Browne
Department of Clinical Veterinary Science,
University of Bristol,
Langford House,
Langford, Bristol BS40 5DU
UK
eMail:
william.browne@bristol.ac.uk
Robin H McCleery
Edward Grey Institute,
University of Oxford
UK
Ben C Sheldon
Edward Grey Institute,
University of Oxford
UK
Richard A Pettifor
Institute of Zoology
UK
Abstract:
Longitudinal observations on known individuals are an important
source of data with which to test evolutionary theory within
natural populations, in particular, the evolution and maintenance
of life-history traits. In this paper, we concentrate on the
reproductive behaviour and survival of a small passerine bird,
the great tit (Parus major). The dataset we consider is taken
from the long-term study of great tits in Wytham Woods in
Oxfordshire. The models we consider are designed to relate
variation in several phenotypic response variables that are
linked to evolutionary fitness, alongside the correlations
between them, to both general environmental and individual-specific
factors. We fit multivariate cross-classified random effects
models using a Markov chain Monte Carlo (MCMC) estimation
algorithm described in the paper. Our results show for which
traits variability is influenced by environmental factors and
for which traits individual bird factors are more important.
The partitioning of correlations is particularly illuminating,
producing some pairs of ‘antagonistic’ correlations which are
biologically meaningful.
Keywords:
complex data structures; cross-classified models;
Markov chain Monte Carlo (MCMC); mixed responses;
multilevel modelling
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