Comparison of height-diameter models based on geographically weighted regressions and linear mixed modelling applied to large scale forest inventory data

Abstract

Aim of the study: The main objective of this study was to test Geographically Weighted Regression (GWR) for developing heightdiameter curves for forests on a large scale and to compare it with Linear Mixed Models (LMM).Area of study: Monospecific stands of Pinus halepensis Mill. located in the region of Murcia (Southeast Spain). Materials and Methods:The dataset consisted of 230 sample plots (2582 trees) from the Third Spanish National Forest Inventory (SNFI) randomly split into training data (152 plots) and validation data (78 plots). Two different methodologies were used for modelling local (Petterson) and generalized height-diameter relationships (Cañadas I): GWR, with different bandwidths, and linear mixed models. Finally, the quality of the estimated models was compared throughout statistical analysis.Main results: In general, both LMM and GWR provide better prediction capability when applied to a generalized height-diameter function than when applied to a local one, with R 2 values increasing from around 0.6 to 0.7 in the model validation. Bias and RMSE were also lower for the generalized function. However, error analysis showed that there were no large differences between these two methodologies, evidencing that GWR provides results which are as good as the more frequently used LMM methodology, at least when no additional measurements are available for calibrating.Research highlights: GWR is a type of spatial analysis for exploring spatially heterogeneous processes. GWR can model spatial variation in tree height-diameter relationship and its regression quality is comparable to LMM. The advantage of GWR over LMM is the possibility to determine the spatial location of every parameter without additional measurements.Keywords: Spatial analysis; Pinus halepensis Mill; forest modelling. Abbreviations used: GWR (Geographically Weighted Regression); LMM (Linear Mixed Model); SNFI (Spanish National Forest Inventory).Citation: Quirós-Segovia, M., Condés-Ruiz, S., Drápela, K. (2016). Comparison of height-diameter models based on geographically weighted regressions and linear mixed modelling applied to large scale forest inventory data. Forest Systems, Volume 25, Issue 3, e076. http://dx

A geographically weighted deep neural network model for research on the spatial distribution of the down dead wood volume in Liangshui National Nature Reserve (China)

“…However, there are many differences between the LMM and GWR model. For example, Quirós-Segovia et al (2016) discovered that the quality of the height-diameter models of GWR and LMM regressions were comparable. Wei et al (2019) studied the spatial distribution of PM2.5 and found that the LMM was better than the GWR model; however, the GWR model has been shown to perform better than the LMM in many other studies (Liu et al 2014, Zhang & Gove 2005.…”

“…However, spatial effects in data often appear in the form of patches or geographic gradients, which can violate the independence and homogeneity assumptions of OLS and other traditional statistical methods (Green et al 2005, Subedi et al 2018. To this end, to include spatial effects in the regression framework, scholars have used spatial regression models, which estimate the covariance matrix to model the spatial autocorrelation of variables in adjacent locations; examples include the spatial lag model (SLM), the spatial error model (SEM) and the linear mixed model (LMM - Anselin 2001, Lu & Zhang 2011, Quirós-Segovia et al 2016, Qi et al 2020). The GWR model fits the spatial relationship of each location within a given bandwidth, explores the nonstationarity of a space and enhances the description and prediction of the spatial distribution, which makes it a very attractive tool for forestry modeling (Brunsdon et al 1996, Mennis 2006.…”