# Analyzing Multiscale Spatial Relationships between the House Price and Visual Environment Factors
## 1 Introduction
At present, many references at home and abroad generally confirm the spatial heterogeneity of some house price-influencing factors. Existing house price methods, such as the hedonic price model (HPM) proposed by [PERSON], typically only explore the relationships between influencing factors and the house price on a global scale, ignoring the spatial heterogeneity of influencing factors [16]. [PERSON] et al. [17] introduced the GWR to model the spatial relationships between influencing factors and house price appreciation. Although classic GWR can solve part of the spatial heterogeneity problem, which cannot be handled by traditional linear regression models, it ignores the scale problem of spatial heterogeneity of different influencing factors and causes large estimation errors [18; 19; 20]. [PERSON] [21] claimed, \"scale is perhaps the most important topic of geographical information science\". However, there is little research on the scale difference of spatial heterogeneity of different house price-influencing factors. When explaining a certain socioeconomic phenomenon, the understanding of the \"spatial scale effect\" is very important. MGWR was proposed by Fotheringham by allowing the bandwidths of each variable to be different, thereby obtaining more credible estimation results and giving the scale of influence of different variables. Recently, MGWR has been introduced to examine the spatial variation of researchers in China [22] and explore the spatially nonstationary relationships between variables and COVID-19 incidence rates [23]. However, there are few studies on MGWR modeling the house price-influencing factors. To sum up, quantifying the physical environment and exploring the influence of visual environment factors on house prices is of practical significance. Due to the spatial heterogeneity of influencing factors, using the geospatial model to understand the spatial relationship between influencing factors and house prices are necessary. In this work, we analyze the visual environment factors of house prices by considering multiscale effects. Compared with the traditional house price models, such as HPM and GWR, the MGWR can not only effectively deal with spatial heterogeneity of house price but can also identify the exclusive bandwidths for each influencing factor. The bandwidth can reflect the ranges of operational scales between influencing factors and house prices. First, ten visual elements of BSV images are extracted based on the deep learning methods, and six visual indexes affecting the house price are defined. Second, MGWR is introduced to explore the spatial heterogeneity relationships between six visual indexes and the house price. Last, the estimation accuracy of HPM, GWR, and MGWR are compared. Extensive experiments are conducted in Beijing and Chongqing, and results show that: (1) the influence intensity of six visual indexes on the house price in different regions of the city can be identified, while the same visual factors have different effects on different neighborhoods due to the combination differences of structure attributes and location attributes. The house prices in Beijing and Chongqing are very sensitive to visual factors, and there is a high degree of spatial heterogeneity. The scale of the GVI is the largest of all visual variables and is close to a global scale; (2) the R-squared and interpretation ability of MGWR are higher than HPM and GWR. The results of this study can provide a scientific basis and theoretical guidance for urban facilities planning and community street environment design in different cities.