A Bayesian approach for modelling non-linear longitudinal/hierarchical data with random effects in forestry

Abstract

Summary Longitudinal or hierarchical data are often observed in forestry, which can pose both challenges and opportunities when performing statistical analyses. The current standard approach for analysing these types of data is mixed-effects models under the frequentist paradigm. Bayesian techniques have several advantages when compared with traditional approaches, but their use in forestry has been relatively limited. In this paper, we propose a Bayesian solution to nonlinear mixed-effects models for longitudinal data in forestry. We demonstrate the Bayesian modelling process using individual tree height–age data for balsam fir ( Abies balsamea (L.)) collected from eastern Maine. Due to its frequent utilization in modelling dominant tree height growth over time, we choose to examine models based on the Chapman– Richards function. We established four different model formulations, each having varying subject-specific parameters, which we estimated using both frequentist and Bayesian approaches. We found the estimation results to be quite close between the two methods. In addition, an important feature of the Bayesian method is the unified manner in which estimation and prediction are handled. Specifically, local parameters can be predicted for a new dataset after setting the posterior distributions from the estimation stage as new priors in the prediction phase.