## 2 Prior Research  
### Models for Estimating Transit Ridership  
Numerous studies have recently emerged that explore the influencing factors impacting transit ridership. We review the research focusing on direct demand models in transit ridership estimation (as summarized in Table 1). The most widely used direct demand model in this research field is OLS multiple regression. [PERSON] et al. (2004) [5], [PERSON] and [PERSON] (2010) [8], [PERSON] et al. (2010), [PERSON] and [PERSON] (2011) [10], [PERSON] et al. (2011) [1], [PERSON] et al. (2012) [11], [PERSON] et al. (2012) [12], [PERSON] et al. (2013) [13], [PERSON] and [PERSON] (2013) [14], [PERSON] et al. (2014) [15], [PERSON] et al. (2016) [16], [PERSON] et al. (2017) [17], and [PERSON] and [PERSON] (2018) [18] all used OLS regression models to fit the relationship between transit ridership and its influencing factors. However, OLS regression is limited by its assumption that the factors affecting transit ridership have nothing to do with the spatial location of stations, as OLS regression does not consider the spatial autocorrelation of variables. [PERSON] (1996) [19] proposed the geographically weighted regression (GWR) model, which is able to reveal the spatial correlations of variables under the condition of spatial heterogeneity, and thus is more suitable for dealing with spatial data analytics.  
GWR is widely used for spatial data analysis in many fields, such as economics, geography, and ecology. However, the model has rarely been applied to the field of transportation planning. The only analyses comparing the results of OLS and GWR modeling of the factors influencing transit ridership are those conducted by [PERSON] et al. (2012) [2] and [PERSON] et al. (2018) [20], who found a better fit for GWR. [PERSON] et al. (2015) [21] used mixed geographically weighted regression (MGWR) models incorporating both local and global factors to explore the association between metro ridership and land use features. Their work provides new research directions that justify further investigations using this type of model. However, their GWR models still have some limitations, such as ignoring the differences in travel demand between time periods and other network structure factors. Thus, there is room for improvement in the implementation of GWR in transit ridership modeling.  
Other methods have also been considered, such as multiplicative regression ([PERSON] et al., 2012; [PERSON] et al., 2014; [PERSON] et al., 2017) [3; 22; 23], two-stage least square regression (2 SLS) ([PERSON] et al., 2004; [PERSON] and [PERSON], 2008) [24; 25], Poisson regression ([PERSON], 2004; [PERSON] et al., 2012) [3; 6], negative binomial regression ([PERSON] et al., 2012) [11], and structural equation modelling (SEM) ([PERSON] and [PERSON], 2010) [8]; geographical methods such as distance-decay weighted regression ([PERSON] et al., 2011) [1] and the network Kriging method ([PERSON] and [PERSON], 2014) [26]; machine learning methods such as the decision tree (DT) and support vector regression (SVR); and item-based collaborative filtering methods based on cosine similarity (CF) ([PERSON] et al., 2016) [27], cluster analysis ([PERSON] and [PERSON], 2015) [28], and back propagation neural networks (BPNN) ([PERSON] et al., 2016) [29]. However, understanding the results is a major challenge in terms of the interpretability of the function modeled by the machine learning algorithm. In regression models, there is a very simple relationship between inputs and outputs, and thus we choose the GWR model for our study.  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{City} & Data & \multicolumn{6}{c}{Response Variable} & \multicolumn{6}{c}{Factors investigated} \\ \cline{2-13}  & Data & \multicolumn{2}{c}{Average Monthly} &