Comparison of nonspatial and spatial approaches with parametric and nonparametric methods in prediction of tree height

Nonparametric modelling has been popular in recent forestry applications. However, nonparametric modelling methods usually assume independent observations, that is, do not acknowledge the spatial relationships of most forest data sets. For these situations, mixed model and kriging approaches have been used. The aim of this paper was to compare accuracy of spatial parametric and nonparametric approaches, namely mixed models and a combination of k-nn method and mixed models, in prediction of tree height. The spatial approaches were compared to a nonspatial parametric model and k-nn method. Tree height was first modelled using either mixed model or k-nn. The residual error was divided into plot and tree effects. A nonspatial prediction was obtained using the fixed part of the models. The spatial prediction was obtained when this prediction was further adjusted using the estimates of within-plot correlation of errors and best linear predictor. The influence of the quality of modelling data was also considered. The adjustment of nonspatial estimates of both parametric and nonparametric approaches markedly improved the predictions in all study cases. For many applications, the combination of the nonparametric k-nn method for the fixed component of the model, along with random effects for spatial correlations to create a mixed model, could be used. This would allow for spatial prediction, which would likely provide improved predictions, as shown for predicting height in this paper. Also, there is the added benefit that the nonparametric k-nn does not require a particular model form. © 2012 Springer-Verlag.