Dynamic Spatio-Temporal Sequential Ordinal Models: Application to Invasive Weeds

Abstract

The multivariate sequential ordinal model is investigated for use in the Bayesian analysis of spatio-temporal ordinal data. The sequential ordinal model likelihood is equivalent to a binary model conditional on unknown regression coefficients and spatio-temporal random effects. Therefore, estimation and prediction in the space-time context can proceed using the well-established dynamic generalised linear model framework. Moreover, the sequential ordinal model avoids the ordering constraints on the threshold parameters that determine the category break points required by cumulative ordinal models, and so simplifies the estimation procedure for high-dimensional space-time applications using Bayesian inference. The dynamic spatio-temporal sequential ordinal model is applied to estimate foliage cover abundance of four actively managed invasive alien species. These invasive weed species are observed by means of a modified Braun-Blanquet score that is commonly used in vegetation studies and constitutes ordinal data. The multivariate ordinal data for the managed weeds species are sparsely distributed in space and time with few observations recorded in high foliage cover categories. A separable model for space-time dependence that maintains parameter interpretability in the presence of aggregated ordinal categories is therefore developed. Estimation and prediction is demonstrated using integrated nested Laplace approximation (INLA) methods developed for univariate spatio-temporal models. Bayesian estimation and prediction shows that the four invasive weed species differentially respond to habitat type, control effort and accessibility, and share similar magnitudes of dependence with short effective spatial ranges and strong temporal autocorrelations.