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

We introduce the generalized threshold mixed model for piecewise-linearstochastic regression with possibly nonnormal time-series data.It is assumed that the conditional probability distributionof the response variable belongs to the exponential family,and the conditional mean response is linked to some piecewise-linearstochastic regression function. We study the particular casewhere the response variable equals zero in the lower regime.Some large-sample properties of a likelihood-based estimationscheme are derived. Our approach is motivated by the need formodelling nonlinearity in serially correlated epizootic events.Data coming from monitoring conducted in a natural plague focusin Kazakhstan are used to illustrate this model by obtainingbiologically meaningful conclusions regarding the thresholdrelationship between prevalence of plague and some covariatesincluding past abundance of great gerbils and other climaticvariables.