## 1 Introduction  
The dramatic increase in urbanization in the last few decades has made urban rail transit (URT) a central pillar of public transport, due to its efficiency and transport capacity. Identifying the dynamic mechanisms of urban transit is critical to both infrastructure planning and transportation operation, and thus urban indicators such as URT station ridership must be investigated systematically and comprehensively. URT ridership is a key factor used to determine a station's occupation in terms of space and the supporting facilities required. URT ridership is known to be affected by the interaction of specific urban elements (such as land use and socio-economics). Thus, understanding the impact of these elements is essential to accurately estimate travel demand and effectively plan and design urban systems, including planning infrastructure and deploying services and resources. URT ridership modeling can help estimate ridership and explore the influencing factors. The complex factors assumed to affect metro ridership include land use, socio-economics, intermodal transport accessibility, and network structures. Ridership modeling has long been applied in the field of transportation planning. Numerous models have been developed to explore the relationships between transit ridership and influencing factors. The four-step model (generation, distribution, mode choice, and assignment) was first developed in the 1950s and has since been dominant in traffic analysis. However, the four-step model has various practical shortcomings, such as its low level of accuracy, imprecise data, insensitivity to land use, institutional obstacles, and high cost [1]. The model is more applicable to transit ridership estimation in traffic zones (large regions) than in stations (small detailed regions) [2]. The direct demand model has recently attracted attention as an alternative to the four-step model. This estimates ridership via regression models and treats it as a function of its influencing factors in the pedestrian catchment area (PCA) and can thus identify influencing factors that can help to increase the volume of transit ridership [1; 3; 4; 5; 6]. In the model, the PCA is the geographical area from which the station draws its passengers. The shape and size of the PCA are determined by the accessibility of one station and the distance from other stations to it. Buffers can be used to generate circular catchment areas with a given distance, and Thiessen polygons are typically used to define an area around each station, where every location is nearer to this station than to all the others. The main advantages of the direct demand model in ridership modeling are simple usage, easy interpretation, quick response, and low expenses. Ordinary least squares (OLS) multivariate regression is a commonly used direct demand model, and assumes that the parameters are stable [1; 5; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16]. The advantages of spatial models are considered in direct demand models, and thus provide a better spatial interpretation by implementing geographically weighted regression (GWR), which can measure the nonstationarity and heterogeneity of spatial parameters. In addition, as real transportation systems are dynamic, the traffic demand of the transport network differs by the time of day and the day of week. The time-varying patterns of travel demand are accompanied by time-varying ridership, which is influenced by several factors. If the time dependence of travel demands is not considered, inaccurate estimations of ridership and incorrect analyses of the influencing factors may result. Thus, the specific factors influencing transit ridership at station level at different time periods should be identified so follow-up dynamic ridership forecasting can be accurately conducted, thus providing a theoretical foundation for real-time traffic management. In summary, the current direct demand models have various shortcomings while the GWR model has various advantages in the modeling of latent spatially varying relations.