Horizontal and Vertical Spatial Equity Analysis Based on Accessibility to Living Service Amenities: A Case Study of Xi’an, China

Accessibility is closely related to residents’ well-being and quality of life and is a potential indicator of social equity. This study aims to present a methodology for assessing the combined equity of living service amenities (LSAs) based on accessibility. This study focuses on fourteen types of LSAs in six dimensions and improves the three-step floating catchment area (3SFCA) model by considering the behavioral demand characteristics of different age groups. Taking the main built-up area of Xi’an as an example, the modified 3SFCA model is applied to assess the accessibility of LSAs, and the supply–demand index is used to measure the supply and demand level of the horizontal dimension. Furthermore, random forest regression was used to screen the key socioeconomic indicators affecting the accessibility of LSAs, and then the binary spatial correlation local index was used to reveal the spatial distribution characteristics between LSA accessibility and key socioeconomic indicators in the vertical dimension. Finally, the comprehensive equity of LSAs is evaluated by space superposition. The results showed that there was a serious imbalance between the supply and demand of LSAs in Xi’an’s main built-up area, with polarized oversupply and weak supply areas, especially for accessibility to low-grade LSAs. Accessibility is relatively low for children and young and middle-aged groups, and intergenerational inequalities were particularly pronounced among them. The lower-income group was generally at a disadvantage in accessing the high-demand amenities, and those who resided in affordable housing in the periphery of the city were more likely to face social exclusion. This study emphasizes the importance of distributing urban resources equitably among different social groups, which can help decision makers achieve a balance between horizontal equity and vertical equity in the allocation of urban LSAs and promote spatial equity and sustainable social development.