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

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  • Noelle I. Samia
  • Kung-Sik Chan
  • Nils Chr. Stenseth

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. Copyright 2007, Oxford University Press.

Suggested Citation

  • Noelle I. Samia & Kung-Sik Chan & Nils Chr. Stenseth, 2007. "A generalized threshold mixed model for analyzing nonnormal nonlinear time series, with application to plague in Kazakhstan," Biometrika, Biometrika Trust, vol. 94(1), pages 101-118.
    • Handle: RePEc:oup:biomet:v:94:y:2007:i:1:p:101-118
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    File URL: http://hdl.handle.net/10.1093/biomet/asm006
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    Cited by:

    1. Wu, K.Y.K. & Li, W.K., 2015. "Double Generalized Threshold Models with constraint on the dispersion by the mean," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 59-73.
    2. Tong, Howell, 2015. "Threshold models in time series analysis—Some reflections," Journal of Econometrics, Elsevier, vol. 189(2), pages 485-491.
    3. Andrew Hodge & Sriram Shankar, 2016. "Single-Variable Threshold Effects in Ordered Response Models With an Application to Estimating the Income-Happiness Gradient," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 34(1), pages 42-52, January.
    4. Tobias A. Möller & Maria Eduarda Silva & Christian H. Weiß & Manuel G. Scotto & Isabel Pereira, 2016. "Self-exciting threshold binomial autoregressive processes," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 100(4), pages 369-400, October.

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