Geographically Weighted Regression Using a Non-Euclidean Distance Metric with a Study on London House Price Data

This paper explores the impact of different distance metrics on collinearity in local regression models such as geographically weighted regression. Using a case study of house price data collected in Hà Nội, Vietnam, and by fully varying both power and rotation parameters to create different Minkowski distances, the analysis shows that local collinearity can be both negatively and positively affected by distance metric choice. The Minkowski distance that maximised collinearity in a geographically weighted regression was approximate to a Manhattan distance with (power = 0.70) with a rotation of 30°, and that which minimised collinearity was parameterised with power = 0.05 and a rotation of 70°. The results indicate that distance metric choice can provide a useful extra tuning component to address local collinearity issues in spatially varying coefficient modelling and that understanding the interaction of distance metric and collinearity can provide insight into the nature and structure of the data relationships. The discussion considers first, the exploration and selection of different distance metrics to minimise collinearity as an alternative to localised ridge regression, lasso and elastic net approaches. Second, it discusses the how distance metric choice could extend the methods that additionally optimise local model fit (lasso and elastic net) by selecting a distance metric that further helped minimise local collinearity. Third, it identifies the need to investigate the relationship between kernel bandwidth, distance metrics and collinearity as an area of further work.

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

Journal of Intelligent & Fuzzy Systems ◽

10.3233/jifs-210917 ◽

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.

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

International Journal of Geographical Information Science ◽

10.1080/13658816.2018.1521523 ◽

2019 ◽

Vol 33 (1) ◽

pp. 155-175 ◽

Cited By ~ 17

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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Augmenting Geostatistics with Matrix Factorization: A Case Study for House Price Estimation

ISPRS International Journal of Geo-Information ◽

10.3390/ijgi9050288 ◽

2020 ◽

Vol 9 (5) ◽

pp. 288

Author(s):

Aisha Sikder ◽

Andreas Züfle

Keyword(s):

Matrix Factorization ◽

Geographically Weighted Regression ◽

House Prices ◽

Housing Prices ◽

House Price ◽

Weighted Regression ◽

Regression Kriging ◽

Truncated Svd ◽

Latent Features ◽

Kriging Approach

Singular value decomposition (SVD) is ubiquitously used in recommendation systems to estimate and predict values based on latent features obtained through matrix factorization. But, oblivious of location information, SVD has limitations in predicting variables that have strong spatial autocorrelation, such as housing prices which strongly depend on spatial properties such as the neighborhood and school districts. In this work, we build an algorithm that integrates the latent feature learning capabilities of truncated SVD with kriging, which is called SVD-Regression Kriging (SVD-RK). In doing so, we address the problem of modeling and predicting spatially autocorrelated data for recommender engines using real estate housing prices by integrating spatial statistics. We also show that SVD-RK outperforms purely latent features based solutions as well as purely spatial approaches like Geographically Weighted Regression (GWR). Our proposed algorithm, SVD-RK, integrates the results of truncated SVD as an independent variable into a regression kriging approach. We show experimentally, that latent house price patterns learned using SVD are able to improve house price predictions of ordinary kriging in areas where house prices fluctuate locally. For areas where house prices are strongly spatially autocorrelated, evident by a house pricing variogram showing that the data can be mostly explained by spatial information only, we propose to feed the results of SVD into a geographically weighted regression model to outperform the orginary kriging approach.

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