## 3 Methodology
### Model Implementation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & **Variables** & **Definitions** & **Unit** & **Mean** & **Sd.** \\ \hline Target & & & & \\ variable & Transfer passenger flow & & & & \\  & & & & \\  & & Weather variables & & & \\  & Wind Speed & & & & \\  & Temperature & The maximum temperature per hour & \({}^{\circ}\)C & 26.74 & 3.47 \\  & Visibility & Minimum visibility per hour & m & 33.75 & 10.13 \\  & Precipitation & The cumulative precipitation per hour & mm & 0.15 & 0.93 \\  & & Socio-economic and demographic variables (near metro station) & & & \\  & Housing Price & & Average housing prices & USD/m\({}^{2}\) & 8932.7 & 2585.9 \\  & Housing Rent & & & USD/m\({}^{2}\) & 12.57 & 3.26 \\  & Geographical GDP & GDP level & USD billion & 40.84 & 6.71 \\  & Population Density & Hourly crowd density & - & 5.62 & 1.19 \\ External & & Built environment variables (near metro station) & & & \\ factors & Transfer Distance & & Average transfer distance between metro & m & 328.20 & 91.65 \\  & Bus Lines & & The number of bus lines & 19 & 8 \\  & Bus Stops & & The number of bus stops & - & 26 & 11 \\  & Distance from CBD & Distance of metro station from CBD & m & 9600 & 6604 \\  & & POI information (near metro station) & & & \\  & Scenic Spots & Number of scenic spots & - & 13 & 9 \\  & Shopping Malls & The number of shopping malls & - & 27 & 20 \\  & Technology and Culture & The number of technology and culture & - & 195 & 119 \\  & Finance and Insurance & The number of finance and insurance & - & 124 & 123 \\  & Business Housing & The number of business housing & - & 214 & 143 \\  & Hotel Services & The number of hotel services & - & 94 & 88 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Definition and statistical characteristics of the target and external variables. 1. MLR [42]: The multiple linear regression (MLR) model considers the linear effect of multiple factors on the target variable. When these factors are linearly related to the target variable, the MLR model has excellent explanatory and predictive power. 2. GPR [43]: Generalized Poisson regression (GPR) is a typical linear regression model. If the target variable is counting data and complies with Poisson distribution, the GPR model has good explanatory performance and predictive results. 3. GWR [44]: Geographically weighted regression (GWR) is a spatial analysis algorithm. GWR explores the spatial variations of target variables at a given scale and the associated drivers by building the local regression equations at each point in the spatial ranges. Because it considers local spatial effects, GWR is capable of making predictions for target variables with higher accuracy. 4. RF [45]: The RF algorithm is a classifier that integrates multiple decision trees, with its output determined by the multiple output types of each tree. Several features and training data are randomly picked and the forecasting label with the most occurrences serves as the final result. The RF algorithm can tackle a large number of input variables and has good accuracy on the incomplete datasets. 5. LSTM [37]: LSTM is a temporal RNN which can control the transmission state using several gating structures. Compared to RNNs, LSTM enables better modeling performance in various complex long sequences. ### Experimental Setups

In this study, we investigated the prediction performance of Joint-IF based on the transfer passenger flow of public transportation systems in two general missing data scenarios: random missing (RM) and non-random missing (NM). To conduct these experiments, we used the first 70% of the transfer flow dataset as the training set and the remaining 30% as the test set. Meanwhile, to verify the imputation performance of Joint-IF under various missing modes, we set the missing rates to the most likely 10%, 30%, 50% and 70% (by 20% steps), respectively, and multiple combinations of missing rates and missing scenarios were produced for testing the Joint-IF model. Based on the incomplete dataset, our Joint-IF model was proposed to predict the transfer passenger flow.