Spatial quantile random forests for the analysis of upward mobility in Texas

This paper introduces a spatial quantile random forest extending classical random forests to spatially structured data through bivariate smooth functions of space. Tensor-product B-splines based on coordinate information are used to model the spatial effects with a regularization term that controls smoothness. Estimation of the model is performed using an iterative procedure: a quantile random forest is constructed first and then, the spline coefficients are obtained using penalized iterative reweighted least squares. By incorporating smoothing splines functions, this approach explicitly captures possible spatial dependence in the data, improving predictive performance and interpretability while preserving the flexibility of random forests. The effectiveness of the proposed method is illustrated through an empirical study on the relationship between intergenerational mobility and socioeconomic, demographic and meteorological factors across Texas census tracts.