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In this article, I develop and implement the multiscale geographically weighted negative binomial (MGWNB) model, extending the spatially weighted interaction models by integrating a multiscale framework. This model effectively tackles the multiscale nonstationarity and overdispersion issues found in spatial interaction models. By comparing it with multiscale geographically weighted Poisson regression using simulated data, I demonstrate its superior performance in several aspects, including its capability to estimate the scale of processes, its effectiveness in capturing the spatial heterogeneity, and its ability to produce a better goodness of fit. The application of MGWNB in interprovincial population migration in China, using 2020 Chinese census data, also demonstrates its effectiveness and efficiency, revealing strong multiscale spatial heterogeneity in the migration patterns. [ABSTRACT FROM AUTHOR]

The multiscale geographically weighted regression (MGWR) model is an important extension of the classical geographically weighted regression (GWR) model that can be used to explore the spatial nonstationarity of the regression relationship in spatial analysis, but also allows for different scales on conditional relationships between response and different predictors. A Bayesian version of the MGWR model is proposed to obtain estimates of the spatially varying coefficients and the bandwidths simultaneously. The hierarchical form of the Bayesian MGWR model has attractive features, including obtaining posterior estimates of the bandwidths and local parameters simultaneously, and their uncertainty can be easily measured. For Bayesian posterior inference, an efficient algorithm based on integrated nested Laplace approximation is introduced to provide a great alternative of the classical Markov chain Monte Carlo algorithm under the Bayesian framework. The performance of the proposed method is evaluated through simulation study, and it is shown that the proposed approach can correctly identify the differences between scales of parameter surfaces and also obtain precise posterior estimates. Finally, for illustration, this approach is used to analyze monthly housing cost data in the state of Georgia. [ABSTRACT FROM AUTHOR]

This article attempts to identify and separate the role of spatial "context" in shaping voter preferences from the role of other socioeconomic determinants. It does this by calibrating a multiscale geographically weighted regression (MGWR) model of county-level data on percentages voting for the Democratic Party in the 2016 U.S. presidential election. This model yields information on both the spatially heterogeneous nature of the determinants of voter preferences and the geographical scale over which the effects of these determinants are relatively stable. The article, perhaps for the first time, is able to quantify the relative effects of context versus other effects on voter preferences and is able to demonstrate what would have happened in the 2016 election in two scenarios: (1) if context were irrelevant and (2) if every county had exactly the same population composition. In addition, the article sheds light on the nature of the determinants of voter choice in the 2016 U.S. presidential election and presents strong evidence that these determinants have spatially varying impacts on voter preferences. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]