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Biometrika Advance Access published online on May 14, 2007
Biometrika, doi:10.1093/biomet/asm030
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Copyright © 2007 Biometrika Trust

Article

Aster models for life history analysis

Charles J. Geyer

School of Statistics, University of Minnesota, 313 Ford Hall, 224 Church Street S. E., Minneapolis, Minnesota 55455, U. S. A.

Stuart Wagenius

Institute for Plant Conservation Biology, Chicago Botanic Garden, 1000 Lake Cook Road, Glencoe, Illinois 60022, U. S. A.

Ruth G. Shaw

Department of Ecology, Evolution and Behavior, University of Minnesota, 100 Ecology Building, 1987 Upper Buford Circle, St. Paul, Minnesota 55108, U. S. A.

charlie{at}stat.umn.edu

swagenius{at}chicagobotanic.org

rshaw{at}superb.ecology.umn.edu

Received for publication 1 September 2005. Revision received 1 September 2006.
  Abstract

We present a new class of statistical models, designed for life history analysis of plants and animals, that allow joint analysis of data on survival and reproduction over multiple years, allow for variables having different probability distributions, and correctly account for the dependence of variables on earlier variables. We illustrate their utility with an analysis of data taken from an experimental study of Echinacea angustifolia sampled from remnant prairie populations in western Minnesota. These models generalize both generalized linear models and survival analysis. The joint distribution is factorized as a product of conditional distributions, each an exponential family with the conditioning variable being the sample size of the conditional distribution. The model may be heterogeneous, each conditional distribution being from a different exponential family. We show that the joint distribution is from a flat exponential family and derive its canonical parameters, Fisher information and other properties. These models are implemented in an R package ‘aster’ available from the Comprehensive R Archive Network, CRAN.

Key Words: Conditional exponential family • Flat exponential family • Generalized linear model • Graphical model • Maximum likelihood


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