Simultaneous prediction of plot-level and tree-level harvest occurrences with correlated random effects

Abstract

In forestry, harvest models have become popular for forecasting thinning under business-as-usual scenarios. There are two binary processes involved in thinning operations: (i) whether a plot is to be thinned and (ii) whether a particular tree within that plot is to be harvested. These processes can be modeled using logistic regressions. The data used to fit such models come from forest inventories, where the observations are not usually independent. Random effects can be used to deal with these correlations. However, fitting the plot-level and tree-level models independently hinders the estimation of the covariance between the random effects of both models. The objective of this paper was to develop a statistical method for the simultaneous prediction of harvest probabilities at the plot and tree levels in a single mixed-effects model. We developed a maximum likelihood estimator based on the joint distribution of the probability that a given plot is thinned and the probability that a given tree within that plot is harvested. The estimator was derived from a zero-altered binomial form, but it assumed distinct harvest probabilities for each single tree. The estimator was tested in the case study of mixed stands of oak (Quercus spp.) and beech (Fagus sylvatica L.) in Northern France.