Evaluating marginal and conditional predictions of taper models in the absence of calibration data

Abstract

A systematic evaluation of nonlinear fixed- and mixed-effects taper models in volume prediction was conducted. Among 33 taper equations, the best 1- to 10-parameter fixed-effects models according to fitting statistics were further analysed by comparing their predictions against the modelling data and an independent data set. Three alternative prediction strategies were compared using the best equation (Kozak II) in the absence of calibration data (the usual situation in forestry practice). Strategy 1 used a fixed-parameter model (marginal model), strategy 2 utilized the fixed part of a mixed-effects model (conditional model), and strategy 3 calculated a marginal prediction based on the mixed-effects model by averaging the predictions over the estimated distribution of random effects. Strategies 1 and 3 performed better than strategy 2 in model evaluation (in modelling data) and model validation (independent data). Strategy 3 was less biased than strategy 1 in model validation, and both had the same mean squared deviation. Strategy 3 shares the most advantageous features of the other prediction methods and is therefore recommended for forestry practice and for further research in different modelling disciplines within forest science.