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                <title xml:lang="en">Top-down scale approaches for multiscale GWR with locally adaptive bandwidths</title>
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                <term xml:lang="en">GWR</term>
                <term xml:lang="en">Multiscale geographically weighted regression</term>
                <term xml:lang="en">Adaptive bandwidth</term>
                <term xml:lang="en">Partially varying coefficients model</term>
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              <p>Spatially varying coefficient models are widely used in fields such as housing markets, land use, ecology, and seismology, where capturing spatial heterogeneity is essential. Compared to standard Geographically Weighted Regression (GWR), Multiscale Geographically Weighted Regression (MGWR) improves estimation by allowing each covariate to operate at its own spatial scale. Yet, MGWR relies on a backfitting algorithm that limits scalability to moderate datasets and leaves predictive performance largely unexplored. We propose the Top-Down Scale approach for MGWR, which introduces a structured sequence of decreasing bandwidths within the backfitting process. This avoids full re-optimization at each step, substantially reducing computational costs while improving reliability of the global optimum. The resulting algorithm, tds_mgwr, handles up to 50,000 observations and 20 covariates efficiently, combining speed with accurate estimation and enabling more flexible and accurate modeling of complex spatial patterns. We also introduce the Adaptive Top-Down Scale approach for MGWR (atds_mgwr), which incorporates a gradient boosting-like stage to refine covariate bandwidths sequentially. This captures multiple spatial scales simultaneously, moving beyond the notion of a single optimal bandwidth. Monte Carlo experiments show that tds_mgwr achieves fast convergence and high accuracy, while atds_mgwr excels in complex multiscale settings. However, applications to real datasets suggest that predictive gains from MGWR over single-scale GWR are often modest, underlining the need for careful cross-validation and AICc-based validation when adopting multiscale models.</p>
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