Joint Spatial Modeling of Recurrent Infection and Growth with Processes under Intermittent Observation

In this article, we present a new statistical methodology for longitudinal studies in forestry, where trees are subject to recurrent infection, and the hazard of infection depends on tree growth over time. Understanding the nature of this dependence has important implications for reforestation and breeding programs. Challenges arise for statistical analysis in this setting with sampling schemes leading to panel data, exhibiting dynamic spatial variability, and incomplete covariate histories for hazard regression. In addition, data are collected at a large number of locations, which poses computational difficulties for spatiotemporal modeling. A joint model for infection and growth is developed wherein a mixed nonhomogeneous Poisson process, governing recurring infection, is linked with a spatially dynamic nonlinear model representing the underlying height growth trajectories. These trajectories are based on the von Bertalanffy growth model and a spatially varying parameterization is employed. Spatial variability in growth parameters is modeled through a multivariate spatial process derived through kernel convolution. Inference is conducted in a Bayesian framework with implementation based on hybrid Monte Carlo. Our methodology is applied for analysis in an 11-year study of recurrent weevil infestation of white spruce in British Columbia.