A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan

Noelle I. Samia*, Kung Sik Chan, Nils Chr Stenseth

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

17 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)101-118
Number of pages18
JournalBiometrika
Volume94
Issue number1
DOIs
StatePublished - Mar 2007

Keywords

  • Binomial distribution
  • Delay
  • Epizootic event
  • Exponential family
  • Plague outbreak
  • Stochastic regression

ASJC Scopus subject areas

  • Statistics and Probability
  • Mathematics(all)
  • Agricultural and Biological Sciences (miscellaneous)
  • Agricultural and Biological Sciences(all)
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan'. Together they form a unique fingerprint.

Cite this