scholarly journals Measuring Bandwidth Uncertainty in Multiscale Geographically Weighted Regression Using Akaike Weights

2019 ◽  
Author(s):  
Ziqi Li ◽  
Alexander Stewart Fotheringham ◽  
Taylor M. Oshan ◽  
Levi John Wolf
Keyword(s):  
Geographically Weighted Regression ◽  
Regression Models ◽  
Bandwidth Selection ◽  
Information Criterion ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Multi Scale ◽  
Single Scale ◽  
Heterogeneous Processes ◽  
Key Parameter

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 paper, we find that bandwidth selection is subject to uncertainty in both single-scale and multi-scale 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.

scholarly journals On the Measurement of Bias in Geographically Weighted Regression Models

2019 ◽  
Author(s):  
Hanchen Yu ◽  
Alexander Stewart Fotheringham ◽  
Ziqi Li ◽  
Taylor M. Oshan ◽  
Levi John Wolf
Keyword(s):  
Geographically Weighted Regression ◽  
Regression Models ◽  
Simulated Data ◽  
Information Criterion ◽  
Weighted Regression ◽  
Parameter Estimates ◽  
Local Parameter ◽  
Data Set ◽  
Trade Off ◽  
Parameter Values

Under the realization that Geographically Weighted Regression (GWR) is a data-borrowing technique, this paper derives expressions for the amount of bias introduced to local parameter estimates by borrowing data from locations where the processes might be different from those at the regression location. This is done for both GWR and Multiscale GWR (MGWR). We demonstrate the accuracy of our expressions for bias through a comparison with empirically derived estimates based on a simulated data set with known local parameter values. By being able to compute the bias in both models we are able to demonstrate the superiority of MGWR. We then demonstrate the utility of a corrected Akaike Information Criterion statistic in finding optimal bandwidths in both GWR and MGWR as a trade-off between minimizing both bias and uncertainty. We further show how bias in one set of local parameter estimates can affect the bias in another set of local estimates. The bias derived from borrowing data from other locations appears to be very small.

scholarly journals Computational improvements to multiscale geographically weighted regression

2019 ◽  
Author(s):  
Ziqi Li ◽  
Alexander Stewart Fotheringham
Keyword(s):  
Geographically Weighted Regression ◽  
Parallel Implementation ◽  
Additive Model ◽  
Large Datasets ◽  
Computational Method ◽  
Weighted Regression ◽  
Multi Scale ◽  
Single Scale ◽  
Gwr Model ◽  
Python Package

Geographically Weighted Regression (GWR) has been broadly used in various fields to model spatially non-stationary relationships. Multi-scale Geographically Weighted Regression (MGWR) is a recent advancement to the classic GWR model. MGWR is superior in capturing multi-scale processes over the traditional single-scale GWR model by using different bandwidths for each covariate. However, the multiscale property of MGWR brings additional computation costs. The calibration process of MGWR involves iterative back-fitting under the additive model (AM) framework. Currently, MGWR can only be applied on small datasets within a tolerable time and is prohibitive on moderately large datasets (greater than 5,000 observations). In this paper, we propose a parallel implementation that has crucial computational improvements to MGWR calibration. This improved computational method reduces both memory footprint and runtime to allow MGWR modelling to be applied to moderate-to-large datasets (up to 100,000 observations). These improvements are integrated into the mgwr python package and MGWR 2.0 software, both of which are freely available to download.

Second-hand housing batch evaluation model of zhengzhou city based on big data and MGWR model

2021 ◽  
pp. 1-20
Author(s):  
Chaojie Liu ◽  
Jie Lu ◽  
Wenjing Fu ◽  
Zhuoyi Zhou
Keyword(s):  
Real Estate ◽  
Geographically Weighted Regression ◽  
Euclidean Distance ◽  
Evaluation Model ◽  
Housing Prices ◽  
Information Criterion ◽  
Access Point ◽  
Least Square ◽  
Weighted Regression ◽  
Spatial Error

How to better evaluate the value of urban real estate is a major issue in the reform of real estate tax system. So the establishment of an accurate and efficient housing batch evaluation model is crucial in evaluating the value of housing. In this paper the second-hand housing transaction data of Zhengzhou City from 2010 to 2019 was used to model housing prices and explanatory variables by using models of Ordinary Least Square (OLS), Spatial Error Model (SEM), Geographically Weighted Regression (GWR), Geographically and Temporally Weighted Regression (GTWR), and Multiscale Geographically Weighted Regression (MGWR). And a correction method of Barrier Line and Access Point (BLAAP) was constructed, and compared with three correction methods previously studied: Buffer Area (BA), Euclidean Distance (ED), and Non-Euclidean Distance, Travel Distance (ND, TT). The results showed: The fitting degree of GWR, MGWR and GTWR by BLAAP was 0.03–0.07 higher than by ND. The fitting degree of MGWR was the highest (0.883) by BLAAP but the smallest by Akaike Information Criterion (AIC), and 88.3% of second-hand housing data could be well interpreted by the model.

Modeling the Spatial Variation in U.S. Airfares Utilizing Geographically Weighted Regression

2014 ◽  
Vol 5 (4) ◽  
pp. 54-71
Author(s):  
Hilton A. Cordoba ◽  
Russell L. Ivy
Keyword(s):  
Spatial Variation ◽  
Influencing Factors ◽  
Geographically Weighted Regression ◽  
Regression Models ◽  
Yield Management ◽  
Weighted Regression ◽  
Local Models ◽  
Multivariate Approach ◽  
Global Models ◽  
Economic Changes

Modeling airline fares is quite challenging due to the constantly changing fare structure of the airlines in response to competitors, yield management principles, and a variety of political and economic changes, and has become more complex since deregulation. This paper attempts to add to the literature by providing a more in-depth look at fare structure using a multivariate approach. A total 6,200 routes between 80 primary U.S. airports are analyzed using linear and geographically weighted regression models. The results from the global models reinforce some of the expectations mentioned in the literature, while the local models provide an opportunity to analyze the spatial variation of influencing factors and predictability.

Fast Geographically Weighted Regression (FastGWR): a scalable algorithm to investigate spatial process heterogeneity in millions of observations

2019 ◽  
Vol 33 (1) ◽  
pp. 155-175 ◽  
Author(s):  
Li ◽  
Fotheringham ◽  
Li ◽  
Oshan
Keyword(s):  
Los Angeles ◽  
Open Source ◽  
Geographically Weighted Regression ◽  
Message Passing Interface ◽  
House Price ◽  
Weighted Regression ◽  
Spatial Process ◽  
Parameter Estimates ◽  
Single Family ◽  
Scalable Algorithm

Geographically Weighted Regression (GWR) is a widely used tool for exploring spatial heterogeneity of processes over geographic space. GWR computes location-specific parameter estimates, which makes its calibration process computationally intensive. The maximum number of data points that can be handled by current open-source GWR software is approximately 15,000 observations on a standard desktop. In the era of big data, this places a severe limitation on the use of GWR. To overcome this limitation, we propose a highly scalable, open-source FastGWR implementation based on Python and the Message Passing Interface (MPI) that scales to the order of millions of observations. FastGWR optimizes memory usage along with parallelization to boost performance significantly. To illustrate the performance of FastGWR, a hedonic house price model is calibrated on approximately 1.3 million single-family residential properties from a Zillow dataset for the city of Los Angeles, which is the first effort to apply GWR to a dataset of this size. The results show that FastGWR scales linearly as the number of cores within the High-Performance Computing (HPC) environment increases. It also outperforms currently available open-sourced GWR software packages with drastic speed reductions – up to thousands of times faster – on a standard desktop.

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