Shonosuke Sugasawa

This study proposes a method for aggregating/synthesizing global and local sub‐models for fast and flexible spatial regression modeling. Eigenvector spatial filtering (ESF) was used to model spatially varying coefficients and spatial dependence in the residuals by sub‐model, while the generalized product‐of‐experts method was used to aggregate these sub‐models. The major advantages of the proposed method are as follows: (i) it is highly scalable for large samples in terms of accuracy and computational efficiency; (ii) it is easily implemented by estimating sub‐models independently first and aggregating/averaging them thereafter; and (iii) likelihood‐based inference is available because the marginal likelihood is available in closed‐form. The accuracy and computational efficiency of the proposed method are confirmed using Monte Carlo simulation experiments. This method was then applied to residential land price analysis in Japan. The results demonstrate the usefulness of this method for improving the interpretability of spatially varying coefficients. The proposed method is implemented in an R package spmoran.

Generalized estimating equation (GEE) is widely adopted for regression modeling for longitudinal data, taking account of potential correlations within the same subjects. Although the standard GEE assumes common regression coefficients among all the subjects, such an assumption may not be realistic when there is potential heterogeneity in regression coefficients among subjects. In this paper, we develop a flexible and interpretable approach, called grouped GEE analysis, to modeling longitudinal data with allowing heterogeneity in regression coefficients. The proposed method assumes that the subjects are divided into a finite number of groups and subjects within the same group share the same regression coefficient. We provide a simple algorithm for grouping subjects and estimating the regression coefficients simultaneously, and show the asymptotic properties of the proposed estimator. The number of groups can be determined by the cross validation with averaging method. We demonstrate the proposed method through simulation studies and an application to a real data set.