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

Abstract

SUMMARY 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.