Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights

• Published in: Annals of the American Association of Geographers Vol. 110; no. 5; pp. 1500 - 1520
• Main Authors: Li, Ziqi, Fotheringham, A. Stewart, Oshan, Taylor M., Wolf, Levi John
• Format: Journal Article
• Language: English
• Published: Washington Routledge 02.09.2020; Taylor & Francis Ltd
• Subjects: Akaike weight; amplitud de banda; bandwidth; Bandwidths; Computer simulation; Confidence intervals; Criteria; escala de procesos espaciales; incertidumbre en la selección del modelo; model selection uncertainty; multiscale geographically weighted regression; Obesity; Parameter estimation; peso Akaike; regresión geográficamente ponderada a multiescala; Regression analysis; Regression models; Simulation; spatial processes scale; Statistical analysis; Uncertainty; 多尺度地理加权回归; 带宽; 模型选择不确定性; 空间过程规模; 赤池权重
• ISSN: 2469-4452; 2469-4460
• DOI: 10.1080/24694452.2019.1704680

Bandwidth, a key parameter in geographically weighted regression models, is closely related to the spatial scale at which the underlying spatially heterogeneous processes being examined take place. Generally, a single optimal bandwidth (geographically weighted regression) or a set of covariate-specific optimal bandwidths (multiscale geographically weighted regression) is chosen based on some criterion, such as the Akaike information criterion (AIC), and then parameter estimation and inference are conditional on the choice of this bandwidth. In this article, we find that bandwidth selection is subject to uncertainty in both single-scale and multiscale geographically weighted regression models and demonstrate that this uncertainty can be measured and accounted for. Based on simulation studies and an empirical example of obesity rates in Phoenix, we show that bandwidth uncertainties can be quantitatively measured by Akaike weights and confidence intervals for bandwidths can be obtained. Understanding bandwidth uncertainty offers important insights about the scales over which different processes operate, especially when comparing covariate-specific bandwidths. Additionally, unconditional parameter estimates can be computed based on Akaike weights accounts for bandwidth selection uncertainty.