Abstract
AbstractSpatial soil applications frequently involve binomial variables. If relevant environmental covariates are available, using a Bayesian generalized linear model (BGLM) might be a solution for mapping such discrete soil properties. The geostatistical extension, a Bayesian generalized linear geostatistical model (BGLGM), adds spatial dependence and is thus potentially better equipped. The objective of this work was to evaluate whether it pays off to extend from a BGLM to a BGLGM for mapping binary soil properties, evaluated in terms of prediction accuracy and modelling complexity. As motivating example, we mapped the presence/absence of the Pleistocene sand layer within 120 cm from the land surface in the Dutch province of Flevoland, using the BGLGM implementation in the R‐package geoRglm. We found that BGLGM yields considerably better statistical validation metrics compared to a BGLM, especially with – as in our case – a large (n = 1,000) observation sample and few relevant covariates available. Also, the inferred posterior BGLGM parameters enable the quantification of spatial relationships. However, calibrating and applying a BGLGM is quite demanding with respect to the minimal required sample size, tuning the algorithm, and computational costs. We replaced manual tuning by an automated tuning algorithm (which eases implementing applications) and found a sample composition that delivers meaningful results within 50 h calculation time. With the gained insights and shared scripts spatial soil practitioners and researchers can – for their specific cases – evaluate if using BGLGM is feasible and if the extra gain is worth the extra effort.Highlights Does adding spatial correlation to a Bayesian GLM for mapping a binary soil variable pay off? We aim to make spatial Bayesian hierarchical modelling accessible for pedometricians. Most hierarchical models work well when enough observations are provided, even without covariates. Including spatial correlation might sometimes be worth the extra effort and computational costs.
Highlights
In many soil mapping applications, spatial variables are continuous and can, perhaps after a transformation (Müller, 2007), conveniently be modelled using Gaussian spatial models
The objective of this work was (a) to make spatial Bayesian hierarchical modelling accessible and understandable for pedometricians, and (b) to evaluate whether it pays off to extend from a Bayesian generalized linear model (BGLM) to a Bayesian generalized linear geostatistical model (BGLGM) for mapping binary soil properties, when evaluated in terms of prediction accuracy, modelling effort and computational costs
We extend this GLM to a Bayesian generalized linear model (BGLM) and a Bayesian generalized linear geostatistical model (BGLGM), the two models to be compared in this research
Summary
In many soil mapping applications, spatial variables are continuous and can, perhaps after a transformation (Müller, 2007), conveniently be modelled using Gaussian spatial models. One could calculate both the prediction probability density as provided above and the corresponding weight factor f ðθ, yjzÞ in Equation (17) for every possible combination of parameters and signal at the observation locations, and numerically integrate the outcomes to infer the posterior predictive distribution f ðyÃjzÞ. Computational costs can be substantially reduced by integrating out the regression coefficients β and variance of the spatial signal σ2 (see Appendix S1), rather than being part of numerically approximating the posterior This “integrating out” means that these parameters, as such, disappear from the equation, while their influence remains, expressed in the relations between the remaining variables.
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