  In various applications with large spatial regions, the relationship between
the response variable and the covariates is expected to exhibit complex spatial
patterns. We propose a spatially clustered varying coefficient model, where the
regression coefficients are allowed to vary smoothly within each cluster but
change abruptly across the boundaries of adjacent clusters, and we develop a
unified approach for simultaneous coefficient estimation and cluster
identification. The varying coefficients are approximated by penalized splines,
and the clusters are identified through a fused concave penalty on differences
in neighboring locations, where the spatial neighbors are specified by the
minimum spanning tree (MST). The optimization is solved efficiently based on
the alternating direction method of multipliers, utilizing the sparsity
structure from MST. Furthermore, we establish the oracle property of the
proposed method considering the structure of MST. Numerical studies show that
the proposed method can efficiently incorporate spatial neighborhood
information and automatically detect possible spatially clustered patterns in
the regression coefficients. An empirical study in oceanography illustrates
that the proposed method is promising to provide informative results.
