Isolating Location Value Using SHAP and Interaction Constraints

This paper describes how machine learning techniques and explainable artificial intelligence can be leveraged to estimate combined location value. We analyze listed apartment rents using gradient boosted trees, which allow for flexible modelling of non-linear effects and high order interactions among covariates. We then separate location value from structure value by imposing interaction constraints. Finally, we use the additivity property of SHapley Additive exPlanations (SHAP) to extract the combined effects of location-related covariates. These effects are then compared across different geographical levels (regional and national). The empirical analysis uses a rich dataset consisting of listed rents and property characteristics for approximately 300,000 apartments in Switzerland. We start with an unconstrained model that allows for flexible interactions between location variables and structural characteristics. We then impose interaction constraints such that structural characteristics no longer interact with location variables or each other. This step is required to extract the pure value of location independent of any interactions with structural characteristics. The constrained model improves interpretability while retaining a high degree of accuracy. What would otherwise be a cumbersome calibration of locational values is replaced by a simple extraction of the corresponding feature effects using SHAP. The results should prove useful in improving hedonic models used by property tax assessors, mortgage underwriters, valuation firms, and regulatory authorities.