A spatially based quantile regression forest model for mapping rural land values

Rural land valuation plays an important role in the development of land use policies for agricultural purposes. The advance of computational software and machine learning methods has enhanced mass appraisal methodologies for modeling and predicting economic values. New machine learning methods, like tree-based regression models, have been proposed as an alternative to linear regression to predict economic values from ancillary variables, since these algorithms are able to handle non-normality and non-linearity in the data. However, regression trees are commonly estimated assuming independent rather than spatially correlated data. This study aims to build a tree-based regression model that will help to tackle methodological problems related to the determination of prices of rural lands. The Quantile Regression Forest (QRF) algorithm was used to provide a regression model to predict and assess the uncertainty associated with model-derived predictions. However, the classical QRF ignores the autocorrelation underlying spatialized land values. The objective of this work was to develop, implement, and evaluate a spatial version of QRF, named sQRF, for computer-assisted mass appraisal of rural land values accounting for information from neighboring sites. We compared predictions of land values from sQRF with those obtained from spatial random forest, kriging regression, and linear regression models. sQRF performed well in predicting rural land values; indeed, it performed better than multiple linear regression. An important feature of sQRF is its ability to produce a direct uncertainty measure to assess the goodness of the predictions. Land values reflect a complex mix of agricultural returns, localization, and access to markets, which can be predicted from ancillary environmental variables. Good predictive models are essential to determine land values for multiple purposes including territorial taxation.