Biometrika Advance Access first published online on February 6, 2007
This version published online on February 19, 2007
Biometrika, doi:10.1093/biomet/asm006
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A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan
Department of Statistics & Actuarial Science, University of Iowa, Iowa City, Iowa 52242, U.S.A.
Centre for Ecological and Evolutionary Synthesis, Department of Biology, University of Oslo, P.O. Box 1066 Blindern, N-0316 Oslo, Norway
n-samia{at}northwestern.edu
kung-sik-chan{at}uiowa.edu
n.c.stenseth{at}bio.uio.no
Received for publication 1 July 2005.
Revision received 1 May 2006.
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Abstract |
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We introduce the generalized threshold mixed model for piecewise-linear stochastic regression with possibly nonnormal time-series data. It is assumed that the conditional probability distribution of the response variable belongs to the exponential family, and the conditional mean response is linked to some piecewise-linear stochastic regression function. We study the particular case where the response variable equals zero in the lower regime. Some large-sample properties of a likelihood-based estimation scheme are derived. Our approach is motivated by the need for modelling nonlinearity in serially correlated epizootic events. Data coming from monitoring conducted in a natural plague focus in Kazakhstan are used to illustrate this model by obtaining biologically meaningful conclusions regarding the threshold relationship between prevalence of plague and some covariates including past abundance of great gerbils and other climatic variables.
Key Words: binomial distribution • delay • epizootic event • exponential family • plague outbreak • stochastic regression
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