Exploring the Influence of the Built Environment on the Demand for Online Car-Hailing Services Using a Multi-Scale Geographically and Temporally Weighted Regression Model

Abstract

Online car-hailing is gradually shifting towards a predominant use of electric vehicles, a change that is advantageous for developing a sustainable society. Understanding the patterns of changes in online car-hailing travel can assist transportation authorities in optimizing vehicle dispatching, reducing idle rates, and minimizing resource wastage. The built environment influences the demand for online car-hailing travel. Previous studies have commonly employed the geographically weighted regression (GWR) model and the geographically and temporally weighted regression (GTWR) model to examine the relationship between the demand for online car-hailing trips and the built environment. However, these studies have ignored that the impact range of the built environment also varies with time and space. To fully consider the variations in the impact range of the built environment, this study established multi-scale geographically and temporally weighted regression (MGTWR) to examine the spatiotemporal impacts of urban built environments on the demand for online car-hailing travel. An empirical study was conducted to assess the effectiveness of the MGTWR model using point of interest (POI) data and online car-hailing order data from Haikou. The evaluation indicators showed that the MGTWR model has higher fitting accuracy than the GTWR model. Moreover, the impact of each type of POI on the demand for online car-hailing travel was analyzed by examining the temporal and spatial distribution of the regression coefficients. Additionally, we observed that transport facility POIs and healthcare service POIs exerted the most pronounced influence on the demand for online car-hailing. In contrast, the impact of shopping service POIs and catering service POIs was relatively weaker.

1. Introduction

The development of digital technology has led to huge changes in the field of transport [1]. The development of internet technology has made it possible for users to conveniently use the web, enabling passengers and drivers to connect through online platforms. As a result, online car-hailing has emerged. The emergence of online car-hailing has rapidly spread to all major cities in China. As of the first half of 2022, the number of active users and drivers in the online car-hailing sector had reached 360 million and 4.53 million, respectively. Online car-hailing is progressively transitioning to electric vehicles, contributing to reduced resource consumption, lower carbon emissions, and achieving sustainable development. Online car-hailing is also essential in achieving China’s dual-carbon goals. Online car-hailing will be further developed to promote ease of travel and lower resource use. However, the rapid expansion of online car-hailing has resulted in various challenges, including long waiting times and high vehicle idling rates. It leads to wasted resources and decreased user satisfaction. To address these issues, gaining a deeper understanding of the root causes of changes in passenger flows is crucial.

Previous studies on online car-hailing have primarily focused on predicting trip demand and analyzing factors influencing passenger flow [2,3]. Such studies have highlighted the significance of online car-hailing as a mode of transportation. Nevertheless, there needs to be more investigation of the link between the built environment and passenger flow.

In mainstream academic journals, studies often use terms that start with a “D” to reflect features of the built environment. The urban built environment comprises “seven Ds”: density, diversity, design, destination accessibility, distance to transit, demographics, and demand management [4]. Existing studies have demonstrated a strong correlation between travel behaviors and the built environment [5]. Features of the built environment have varying impacts on different travel patterns. For bike-sharing, Ma et al. [6] used the GTWR model to compare differences in the built environment’s impact between docked and dockless bike-sharing systems. Chakour et al. [7] used a composite marginal likelihood (CML)-based ordered response probit (ORP) model to conclude that an effective way to increase bus ridership is by improving public transport service and accessibility. Gan et al. [8] applied a gradient boosting regression tree model to investigate the non-linear relationship between built environment characteristics and station-to-station ridership. For online car-hailing, Li et al. [2] employed the GWR model to examine the influence of the built environment on online car-hailing usage. They concluded that online car-hailing services play a significant role as a complementary mode of transportation to public transport services. For walking, Tao et al. [9] adopted the gradient boosting decision tree method to examine the relationships between walking distance and spatial attributes. The studies listed above demonstrate a strong link between different modes of travel and the urban built environment. While studies have been conducted to examine the relationship between the urban built environment and the demand for online car-hailing, further research is warranted on this aspect of the relationship.

Statistical modeling is commonly used in research to examine the relationship between travel behavior and the urban built environment. The ordinary least squares (OLS) model is the most representative and widely used among these models. However, the OLS model assumes that spatial variable relationships are fixed and do not change with spatial location, which is unrealistic [10]. However, the demand for online car-hailing exhibits spatial heterogeneity. Spatial heterogeneity refers to variations in the demand for online car-hailing trips at different spatial locations. Several models have been proposed to address spatial heterogeneity, including distance decay weighted regression, two-stage least squares regression, the passion model, and the GWR model [11]. The GWR model, introduced by Brunsdon in 1998, examines the impact of different factors on a localized scale by constructing regression equations for each sub-region within the study area [12]. The GWR model is used not only in the analysis of factors influencing passenger flow [13,14,15] but also in other fields [16,17]. It is also used in the context of the demand for online car-hailing travel. Bi et al. [3] clustered passenger flows into three patterns based on the time-varying characteristics of passenger flows and established a spatial passenger flow model based on the GWR model. The results verified that the built environment has different degrees of influence on the passenger flow of online car-hailing travels in the spatial and temporal dimensions. Grid size also affects model results. Zhao et al. [18] recognized this issue, partitioning the area into grids of different sizes and establishing a GWR model to investigate the variations in the influence of various factors on the demand for online car-hailing trips.

In addition to spatial heterogeneity, the demand for online car-hailing travel also displays temporal heterogeneity, which is evident in the demand fluctuation over time. Temporal heterogeneity and spatial heterogeneity collectively constitute spatiotemporal heterogeneity. The GWR can only analyze space instability, which makes its spatiotemporal analysis incomplete. Therefore, the GTWR model was developed by improving the GWR model [19]. This model was first applied in the field of house price research and has since been used extensively in other fields as well. Shen et al. [20] analyzed the spatial and temporal distribution pattern of GTWR coefficients and compared the demand for different travel modes. Their results showed substantial spatial and temporal heterogeneity in the demand for different travel modes.

The GTWR and GWR models assume that all independent variables have the same bandwidth, meaning that the influence scope of the variables is the same. However, reality often deviates from this assumption. For instance, transportation facility POIs may attract online car-hailing services from a greater distance, indicating that the influence scale of such POIs is larger. This element was not addressed in any of the studies mentioned above, leading to significant model errors. The range of influence varies between variables, as reflected in the bandwidth of each variable. Therefore, the multi-scale geographically weighted regression (MGWR) model was proposed. Cao et al. [21] constructed MGWR models for different periods to derive significant spatial and temporal heterogeneity in the impact of various factors on the demand for online car-hailing trips.

In addition to GWR-derived models, other regression models are suitable for examining the relationship between travel demand and the built environment. For example, Liu et al. [22] used a generalized additive mixed model to study the relationship between the built environment and taxi demand. Sun et al. [23] clustered periods and then employed the spatial autoregressive moving average (SARMA) to investigate similar relationships. However, such regression models are far less effective in addressing spatial issues than GWR and its derivative models and are less commonly used.

Machine learning has gained popularity in research due to its higher fitting accuracy. Gan et al. [8] used gradient decision boosting trees to explore the relationship between the built environment and rail patronage in an urban setting. Hagenauer et al. [24] conducted a comparative analysis of modal choice modeling using multiple machine learning classifiers and found that random forests were the most accurate. Cheng et al. [25] also chose random forests to explore the effect of the built environment on travel behavior. Although they achieved a high level of model accuracy, they lacked consideration for spatiotemporal heterogeneity. Cheng et al. [26] addressed this limitation by employing an improved version of gradient decision boosting trees, taking spatial heterogeneity into complete account.

Compared to regression models, machine learning exhibits higher accuracy. However, machine learning models can only explore the impact of different built environments on the demand for online car-hailing within the study area, with less consideration of spatiotemporal heterogeneity. Considering spatiotemporal heterogeneity helps better explain the impact of a specific factor on online car-hailing travel in a particular spatiotemporal context.

Spatiotemporal positions influence the impact scales of different built environments. However, as shown in

Table 1. Review of the relationship between the built environment and travel modes in the literature.

Author	Mode of Transport	Methodologies	Spatial Heterogeneity	Temporal Heterogeneity	Influence Scope of Variables
Li et al. [2]	online car-hailing	GWR	√	-	-
Bi et al. [3]	online car-hailing	GWR	√	-	-
Ma et al. [6]	bike-sharing	GTWR	√	√	-
Chakour et al. [7]	bus	ordered response probit model	-	-	-
Gan et al. [8]	relationship	gradient lift regression tree	-	-	-
Tao et al. [9]	walking	gradient decision boosting trees	-	-	-
Zhao et al. [18]	online car-hailing	GWR	√	-	-
Shen et al. [20]	automobile	GTWR	√	√	-
Cao et al. [21]	online car-hailing	MGWR	√	-	√
Liu et al. [22]	taxi	GMM	√	-	-
Sun et al. [23]	online car-hailing	SMRMA	√	-	-
Gan et al. [8]	urban rail transit	gradient decision boosting trees	-	-	-
Hagenauer et al. [24]	travel mode choice	random forest	-	-	-
Cheng et al. [25]	travel mode choice	random forest	-	-	-
Cheng et al. [26]	intermodal transit trip	gradient decision boosting trees	√	-	-
Our study	online car-hailing	MGTWR	√	√	√

Note: A “√” indicates that the factor was considered and a “-” indicates that it was not.

, limited research has considered both spatiotemporal heterogeneity and impact scales. The GWR, GTWR, and MGWR models cannot account for variable range and time scale. Machine learning can only explore the effect of a variable on travel behavior and cannot consider spatiotemporal heterogeneity. MGTWR, an extension of the GTWR model incorporating impact scales, is a beneficial tool for investigating spatiotemporal heterogeneity. This study will establish a MGTWR model to comprehensively explore the relationship between the built environment and the demand for online car-hailing trips.

Based on the issues mentioned above, our research study has the following contributions:

• To fully consider the range of influence of different factors and time scales, MGTWR and GTWR will be used to study the influencing factors of the demand for online car-hailing trips;
• There may be differences in travel demand between weekdays and holidays, which will be investigated separately;
• The impact of each built environment variable on the demand for online car-hailing trips will be analyzed from a spatiotemporal perspective.

The rest of this paper is organized as follows. Section 2 presents the data sources and data processing. Section 3 describes the methodology used for this study. Section 4 analyzes the results of the models. Section 5 concludes this paper with an outlook for the future.

2. Study Area and Data Collection

2.1. Study Area

Haikou, the capital and primary transportation hub of Hainan Province, boasts a household population of 2.89 million. In 2022, the city witnessed a substantial influx of visitors, with a staggering 22.58 million recorded. Additionally, Haikou’s gross domestic product (GDP) reached CNY 213.477 billion, reflecting its significant economic status.

Haikou has a well-established online car-hailing service, making it a suitable location for researching online car-hailing travel. The study area was selected based on the obtained data on online car-hailing orders and POI data, within the longitude range of 110.282° to 110.362° and latitude range of 19.972° to 20.050°, as shown in the red box in Figure 1. To facilitate the study, the area was divided into 20 × 20 grids, and the dates were categorized into holidays and working days, with each day divided into 12 time periods from a temporal perspective.

2.2. Data Description and Processing

The experimental dataset used in this study comprises a real-world open online car-hailing order dataset supplied by the Drip Travel Gaia Project. The dataset consists of online car-hailing orders in Haikou, Hainan Province, China, recorded between 1 May 2017, and 31 October 2017. To ensure data privacy, all personal information has been desensitized.

Table 2. Online car-hailing order data: sample table.

Order_id	Departure_ Time	Arrive_ Time	Starting_ lng	Starting_ lat	Dest_ lng	Dest_ lat
35,184	10 October 2017 22:06:11	10 October 2017 22:14:11	110.348	20.039	110.327	20.026

provides an overview of some relevant information for the dataset, while

Table 3. Dataset field description.

Field Name	Field Description
Order_id	Order identifier.
Departure_time	The time when the driver clicks ‘start billing’.
Arrive_time	The time when the driver clicks ‘arrive’.
Starting_lng	Longitude corresponding to the starting point filled in by the passenger.
Starting_lat	Latitude corresponding to the starting point filled in by the passenger.
Dest_lng	Longitude corresponding to the destination filled in by the passenger.
Dest_lat	Latitude corresponding to the destination filled in by the passenger.

presents a description of the fields.

The built environment data utilized in this study is the 2017 Haikou POI data, which was obtained by employing a Python-based web crawler to access the open platform APIs of Gaode Map and Baidu Map. This data was then imported into GIS for classification and sorting.

Table 4. POI dataset sample table.

Name	Type	Gpsx	Gpsy
Small Sun Music Training Center	Educational services	110.323693	20.028170

shows the specific form of the processed data, where the ‘Type’ column represents the type of POI. After deleting low-frequency POI and merging similar POI, there were 14 types of POI remaining, as shown in

Table 5. Categories of POIs.

No.	Type
1	Shopping services
2	Catering services
3	Domestic services
4	Address information
5	Corporate enterprises
6	Educational services
7	Business residences
8	Government agencies
9	Healthcare services
10	Accommodation services
11	Sports leisure services
12	Financial insurance services
13	Transport facilities
14	Car services

. The ‘Gpsx’ and ‘Gpsy’ columns indicate the latitude and longitude of each POI, respectively.

The distribution of POIs in the study area is presented in Figure 2. It is observed that the areas on the left have a significantly lower density of POIs compared to the areas on the right. Further analysis of available data suggests that the city center of Haikou lies in the upper right corner of the study area, where a higher land use and more POIs are present.

2.3. Multicollinearity Test

Multicollinearity refers to a situation in which the explanatory variables in a linear regression model exhibit an exact or high correlation. Multiple variables with strong multicollinearity are difficult to interpret. The presence of multicollinearity can lead to significant errors when explaining the effect of a particular independent variable, even though it does not affect the accuracy of model estimation. Therefore, it is crucial to test for multicollinearity among the alternative independent variables before performing regression analysis to ensure the explanatory accuracy of the independent variables. Pearson product–moment correlation coefficients (PCCs) and variance inflation factors (VIFs) were used to test for multicollinearity in this study.

2.3.1. Pearson Product–Moment Correlation Coefficient Test

PCCs are employed to assess the degree of linear correlation between two variables with the following calculation formula [27]:

$$r=\frac{{\displaystyle \sum _{i=1}^n\left(X_{ i}-\overline{X}\right)\left(Y_{ i}-\overline{Y}\right)}}{\sqrt{{\displaystyle \sum _{i=1}^n{\left(X_{ i}-\overline{X}\right)}^2}}\sqrt{{\displaystyle \sum _{i=1}^n{\left(Y_{ i}-\overline{Y}\right)}^2}}}$$

(1)

where $r$ represents PCCs, $X_i$ and $Y_i$ are the i-th value of variable $X$ and the i-th value of variable $Y$, respectively, $\overline{X}$ and $\overline{Y}$ denote the mean of the variable.

When the $\left|r\right|$ value is greater than 0.7, these two variables are considered highly correlated and the choice is made to delete one of them.

Figure 3 illustrates a high correlation (correlation coefficient of 0.85) between catering service POIs and domestic service POIs. There are likely numerous catering POIs within the domestic service POI category. Therefore, domestic service POIs were removed. Similarly, educational service POIs, sports leisure service POIs, and financial insurance service POIs were removed, whereas business residence POIs were eliminated and replaced with transport facilities. Following the removal of these POI categories, Figure 4 depicts the correlation among the different types of POIs, with all correlations being less than 0.7, making them suitable for subsequent studies.

2.3.2. Variance Inflation Factor Test

The VIF measures the extent of multicollinearity among variables in a multiple linear regression model. VIF values range from 1 to positive infinity, with a value close to 1 indicating low multicollinearity. Higher values suggest severe multicollinearity. If the VIF exceeds 10, the variables in the regression model are considered to have severe multicollinearity [28]. The VIF for the k-th independent variable can be calculated using the following formula:

$${\mathrm{VIF}}_k=\frac{1}{1-R_k^2}$$

(2)

$R_k^2$ is the coefficient of determination of the independent variable $x_k$ to the remaining independent variables in a regression analysis.

$\Delta$ denotes the time interval and $t-n\Delta$ denotes t, which indicates the traffic flow and the statistics of each factor for the previous $n$ time periods.

Table 6. Results of the VIF calculation.

Variables	VIF
Shopping services	1.807
Catering services	3.202
Address information	1.201
Corporate enterprises	2.083
Transport facilities	2.976
Government agencies	1.491
Healthcare services	2.295
Accommodation services	1.841
Car services	1.086

presents the VIF calculations for the nine remaining variables. The results indicate that the maximum VIF for any of these variables is 3.202, suggesting no severe multicollinearity. Therefore, these variables do not exhibit a level of mutual influence that would compromise the accuracy of the regression analysis.

2.4. Spatial Autocorrelation Test

Spatial autocorrelation analysis is a statistical method used to examine the correlation between observations of a point in space and its neighboring points. This method proves helpful in identifying spatial heterogeneity and clustering patterns within a study area. Moran’s I test is the most used test for spatial variability and measures the degree of spatial autocorrelation of each explanatory variable. The formula for Moran’s I test is given below [29]:

$$I=\frac{n}{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}}}}\frac{{\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^n{w}_{ij}\left(y_i-\overline{y}\right)\left(y_j-\overline{y}\right)}}}{{\displaystyle \sum _{i=1}^n{\left(y_i-\overline{y}\right)}^2}}$$

(3)

where $n$ is the number of spatial units; $w_{ij}$ is the weight between positions $i$ and $j$; $y_i$ and $y_j$ are the observations at positions $i$ and $j$, respectively; and $\overline{y}$ is the average of all observations.

The Z-score is often applied as an indicator of the significance of Moran’s I statistic to test the null hypothesis [6]. It can be expressed as follows:

$$Z\left(I\right)=\frac{I-E\left(I\right)}{\sqrt{Var\left(I\right)}}$$

(4)

where $Var\left(I\right)$ and $E\left(I\right)$ are the variance and expectation of Moran’s I, respectively.

The range of Moran’s I is between −1 and 1. The higher Moran’s I, the more pronounced the spatial correlation; the smaller Moran’s I, the greater the spatial variation. A Moran’s I value of 0 indicates random distribution in space. A p-value is used to assess the significance of spatial autocorrelation and avoid unexpected results. A small p-value suggests that the observed spatial pattern is unlikely to have occurred by chance [6].

Spatial autocorrelation analysis was performed on each variable to calculate Moran’s I, Z-score, and p-values, presented in

Table 7. Calculation of Moran’s I.

Variable	Moran’s I	Z-Score	p-Values
Shopping services	0.257	9.953	0.000
Catering services	0.415	16.02	0.000
Address information	0.249	9.619	0.000
Corporate enterprises	0.382	14.76	0.000
Transport facilities	0.515	19.83	0.000
Government agencies	0.410	15.809	0.000
Healthcare services	0.433	16.691	0.000
Accommodation services	0.332	12.825	0.000
Car services	0.319	12.322	0.000

. The results demonstrate that each variable has a Moran’s I more significant than 0 and a p-value less than 0.000, indicating significant positive spatial correlation among the variables. Hence, all variables passed the spatial autocorrelation test at this significance level.

3. Method

Multi-Scale Geographically and Temporally Weighted Regression

In spatial analysis, the relationship between variables can vary as the geographic location changes. To explore this variation, the GWR model creates a local regression equation for each region of space. The GWR model can be represented as follows [12]:

$$y_i={\beta }_{i0}\left({\mu }_i,v_i\right)+{\displaystyle {\sum }_{k=1}^m{\beta }_{ik}\left({\mu }_i,v_i\right)x_{ik}}+{\epsilon }_i,\hspace{1em}i=1,2,\cdots ,n$$

(5)

where $y_i$ denotes the dependent variable for the $i$-th sample point, ${\beta }_{i0}$ is the intercept distance, $\left({\mu }_i,v_i\right)$ are the geographical coordinates of the sample points, $m$ is the number of dependent variables, ${\beta }_{ik}$ indicates the regression coefficient of the $k$-th independent variable, $x_{ik}$ is the $k$-th independent variable, and ${\epsilon }_i$ indicates random error.

When time is incorporated into the model, the GWR model is extended to the GTWR model. It is represented by the following equation [6]:

$$y_i={\beta }_{i0}\left({\mu }_i,v_i,t_i\right)+{\displaystyle {\sum }_{k=1}^m{\beta }_{ik}\left({\mu }_i,v_i,t_i\right)x_{ik}}+{\epsilon }_i,\hspace{1em}i=1,2,\cdots ,n$$

(6)

where $\left({\mu }_i,v_i,t_i\right)$ are the coordinates in the spatiotemporal dimension.

The MGTWR model builds on the foundation of the classical GWR model and improves on the limitations of the GTWR model by enabling variable-specific bandwidth selection. It allows for a better representation of spatial heterogeneity among variables. The independent variable in this study is the number of POIs in each area, and different bandwidths are used to determine the POIs’ impact ranges. The MGTWR model can be expressed as follows [30]:

$$y_i={\beta }_{i0,b0}\left({\mu }_i,v_i,t_i\right)+{\displaystyle {\sum }_{k=1}^m{\beta }_{ik,bik}\left({\mu }_i,v_i,t_i\right)x_{ik}}+{\epsilon }_i,\hspace{1em}i=1,2,\cdots ,n$$

(7)

The regression coefficients ${\widehat{\beta }}_i\left({\mu }_i,v_i,t_i\right)$ are calculated using the least squares method, corresponding to the following matrix expressions:

$${\widehat{\beta }}_i\left({\mu }_i,v_i,t_i\right)={\left[X^{T}W\left({\mu }_i,v_i,t_i\right)X\right]}^{-1}{X}^{T}W\left({\mu }_i,v_i,t_i\right)Y$$

(8)

where $X$ is the independent variable observation matrix; $Y$ denotes the observation vector of the dependent variable. $W\left({\mu }_i,v_i,t_i\right)$ is composed of weight $w_{ij}$ space weight diagonal matrix. The expression is as follows:

$$W\left({\mu }_i,v_i,t_i\right)=\left[\begin{array}{cccc}{w}_{i1}& 0& \cdots & 0\\ 0& w_{i2}& \cdots & 0\\ ⋮& ⋮& \ddots & ⋮\\ 0& 0& \cdots & w_{im}\end{array}\right]$$

(9)

where $w_{ij}$ represents the weight between sample point $i$ and sample point $j$, which can be calculated by the following equation:

$$w_{ij}=\exp \left[-{\left(\frac{d_{ij}^{ST}}{b^{’}}\right)}^2\right]$$

(10)

where $d_{ij}^{ST}$ is the spatiotemporal distance between sample points $i$ and $j$; $b^{\prime }$ indicates spatiotemporal bandwidth.

$$d_{ij}^{ST}=\sqrt{\lambda \left[{\left(u_i-u_j\right)}^2+{\left(v_i-v_j\right)}^2\right]+\mu {\left(t_i-t_j\right)}^2}$$

(11)

where $\lambda$ and $\mu$ are parameters that balance spatiotemporal differences because of the different units of space and time.

The bandwidths are calculated as shown in Figure 5. The steps are as follows [30,31]:

Step 1: Use the GTWR model to initialize the parameters;

Step 2: Let $f_k$ be the regression value of the $k$-th variable and calculate the initialized residual $\epsilon =y-{\displaystyle \sum _{k=1}^m{f}_k}$;

Step 3: Sum this residual with the regression value of the 1st variable, and use the summation result $\epsilon +f_1$ as the response variable to perform GTWR calculation with the independent variable to obtain the optimal bandwidth of the 1st independent variable. Calculate the new residual;

Step 4: Repeat the above steps until the optimal bandwidth is calculated for all variables;

Step 5: Determine whether it converges or not; if it converges, the calculation is finished, otherwise go back to step 3.

A commonly used convergence criterion is the score of change (SOC) of the residual sum of squares (RSS), expressed as follows:

$${\mathrm{SOC}}_{\mathrm{RSS}}=\frac{\left|{\mathrm{RSS}}_{new}-{\mathrm{RSS}}_{old}\right|}{{\mathrm{RSS}}_{new}}$$

(12)

where ${\mathrm{RSS}}_{old}$ denotes the RSS from the previous cycle and ${\mathrm{RSS}}_{new}$ denotes the RSS of the current cycle. When it is less than a given parameter, the algorithm determines that the iterative process satisfies the convergence condition; otherwise, it is considered that is did not satisfy the convergence condition. The threshold value chosen for this study is ${10}^{-5}$.

The formula for calculating the RSS is as follows:

$$\mathrm{RSS}={\displaystyle \sum _{i=1}^n{\left(y_{ i}-{\widehat{y}}_{ i}\right)}^2}$$

(13)

where ${\widehat{y}}_i$ and $y_i$ denote the fitted values and actual values, respectively. The RSS takes values from 0 to positive infinity. The larger the value of the RSS, the worse the fit.

4. Experiment

In this section, we will compare the model results and analyze the impacts of different POIs on the demand for online car-hailing trips in both the temporal and spatial dimensions.

4.1. Evaluation metrics

The corrected Akaike information criterion (AICc) and the coefficient of determination (R²) were used to evaluate the fit of our model. AICc and R² are calculated as follows [32,33]:

$$\mathrm{AICc}=n\cdot \ln \left(\mathrm{RSS}\right)+2\left(p+1\right)-n\ln \left(n\right)+\left[2p\left(p+1\right)/n-p-1\right]$$

(14)

$${\mathrm{R}}^2=1-\frac{{\displaystyle \sum _{i=1}^n{\left({\widehat{y}}_i-y_i\right)}^2}}{{\displaystyle \sum _{i=1}^n{\left(\frac{1}{n}{\displaystyle \sum _{i=1}^n{y}_i}-{\widehat{y}}_i\right)}^2}}$$

(15)

where $n$ represents the number of samples, $p$ represents number of variables, and ${\widehat{y}}_i$ and $y_i$ denote the fitted values and actual values, respectively.

The AICc takes values from 0 to positive infinity. The larger the value of the AICc, the worse the fit.

The value R² ranges from 0 to 1. An R² value closer to 1 means that the prediction is better. If the R² value is 0, each predicted sample value equals the mean, the same as the mean model. If the R² value is less than 0, the constructed model is not as good as the mean model.

4.2. Performance of the MGTWR Model

Table 8. Comparison of GTWR and MGTWR models.

Evaluation Metrics	Workday		Holiday
	MGTWR	GTWR	MGTWR	GTWR
R2	0.68	0.618	0.702	0.645
AICc	72737	74277	71058	73605

presents the fitting accuracy of the GTWR and MGTWR models for weekdays and holidays. For both weekdays and holidays, the AICc of the MGTWR model is smaller than that of the GTWR model, with a reduction of 1540 and 2547, respectively. Additionally, the R2 of the MGTWR model is higher than that of the GTWR model for both workdays and holidays, with an increase of 0.062 and 0.057, respectively. These indicators indicate that the MGTWR model outperforms the GTWR model’s fitting accuracy for workdays and holidays. Therefore, the subsequent analysis will use the MGTWR results to explore the impact of different types of POIs on the demand for online car-hailing trips.

The impact of different types of POIs on the demand for online car-hailing is different.

Table 9. MGTWR model coefficients on workdays.

Variable	Mean	Standard Deviation	Minimum	Maximum
Shopping services	−0.017	0.238	−0.72	−0.559
Catering services	2.336	2.295	−0.794	8.322
Address information	−1.11	1.062	−3.728	1.541
Corporate enterprises	1.767	2.203	−4	12.153
Government agencies	2.131	1.439	−0.429	5.617
Healthcare services	−3.201	10.196	−27.079	27.375
Accommodation services	5.603	5.152	−12.05	21.631
Traffic facilities	21.376	11.87	1.011	40.752
Car services	0.99	1.958	−10.42	7.465

and

Table 10. MGTWR model coefficients on holidays.

Variable	Mean	Standard Deviation	Minimum	Maximum
Shopping services	0.227	0.425	−0.455	1.285
Catering services	3.323	2.710	−0.226	9.171
Address information	−1.056	1.018	−3.638	1.642
Corporate enterprises	1.543	2.078	−3.952	10.74
Government agencies	−1.142	0.892	−1.833	−3.741
Healthcare services	−8.368	11	−34.065	12.06
Accommodation services	7.01	6.270	−12.272	25.041
Traffic facilities	20.61	11.807	1.149	38.732
Car services	0.602	1.871	−7.101	10.482

present the regression coefficients’ mean, standard deviation, and minimum and maximum values for different types of POIs in the MGTWR model. A positive regression coefficient indicates that the POIs facilitate demand for online car-hailing trips. A more significant value corresponds to a greater facilitating role. Conversely, a negative coefficient suggests a disincentive effect on demand. The mean value provides an overall estimate of the impact of POIs on online car-hailing trips in the study area. At the same time, standard deviation indicates the stability of the effect. For both weekdays and holidays, the mean regression coefficients for shopping service POIs, address information POIs, and car service POIs are close to zero, indicating a weak impact on the demand for online car-hailing trips. On the other hand, corporate enterprise POIs and government agency POIs have a more significant impact on weekdays.

4.3. Temporal Features of Variable Coefficients

Figure 6, Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12 and Figure 13 illustrate the fluctuations in the average coefficient of each explanatory variable over a day, with the blue line representing holidays and the red line representing workdays.

Figure 6 indicates that shopping service POIs have a more pronounced effect on promoting online car-hailing during holidays. This can be attributed to increased demand for online car-hailing due to more people shopping during holidays. Furthermore, holidays have an even more noticeable effect on demand for online car-hailing, with the boosting effect starting to increase sharply from around 10:00. This change is because passengers tend to leave later during holidays. During part of the weekday period, the regression coefficient is less than 0, which means that shopping service POIs create less demand for online car-hailing trips during this time. The regression coefficient is close to 0 for most of the weekday period. This suggests that shopping service POIs have little to no effect on the demand for online car-hailing trips.

Compared to shopping service POIs, catering service POIs have a more significant impact on demand for online car-hailing trips during holidays, and the boost on weekdays is lesser than during holidays. Catering service POIs contribute to demand for consistent online car-hailing trips. The highest demand occurs between 20:00 and 22:00. Demand experiences a rapid growth between 12:00 and 14:00 due to the need for transportation after meals.

There is minimal variation in the promotion of online car-hailing by POIs of corporate enterprises during weekdays and holidays. This illustrates the existence of holiday work in some businesses. As people do not work during the evening hours, these POIs tend to create much less demand for online car-hailing services during this time. The peak of the off-duty period is at 16:00–18:00, which is when corporate enterprise POIs have the greatest impact on boosting demand for online car-hailing trips.

Due to their high traffic volume, transport facility POIs, such as ports, airports, and train stations, are the main contributors to the demand for online car-hailing trips. Their effect is more pronounced during working days than during holidays. However, between 2:00 and 6:00, the number of passengers is low, and the positive effect is the lowest. As the number of passengers increases, the boost in demand becomes more evident.

Figure 10 shows that government agency POIs consistently contribute to the demand for online car-hailing trips. However, on holidays, some government institutions are closed or operate with limited staff, resulting in less promotion of online car-hailing travel than on weekdays. The demand for online car-hailing trips is greatest between 16:00 and 20:00, when employees are likely to take a taxi to reach their destination. Increased demand is also more pronounced between 10:00 and 14:00 due to the need to travel or go home for a lunch break. Additionally, some government agencies are in regular business on holidays and thus generate some demand.

Figure 11 demonstrates that the impact of healthcare service POIs on the demand for online car-hailing trips is highly variable. However, the changes are relatively consistent. The most significant increase is observed between 8:00 and 12:00, but this effect decreases rapidly in the afternoon and becomes negative. It indicates that healthcare service POIs switch from facilitating to suppressing demand for online car-hailing trips. There is a partial rebound during the evening peak on weekdays, after which the effect declines again.

The impact of accommodation service POIs on the demand for online car trips peaks mainly between 8:00 and 14:00, as shown in Figure 11. During holidays, hotel occupants increase, resulting in an even greater boost. Accommodation service POIs mainly refer to hotels, and check-out times are between 8:00 and 14:00, leading to a higher demand for online car-hailing trips. However, after this period, the demand for travel decreases, and the promotion effect rapidly drops. The demand is lowest between 20:00 and 24:00, and during this time, accommodation service POIs even suppress the demand for online car-hailing trips.

Car service POIs mainly include places for car repair, car sales, car cleaning, and other car-related services. The impact of car service POIs on the demand for online car-hailing trips is complex. For instance, car cleaning services are likely to have a negative effect on the demand for online car-hailing trips, whereas the impact of car repair and car sales on online car-hailing trips is uncertain. It is puzzling that most car service POIs are closed at night. However, they contribute the most to the demand for online car-hailing trips during this time.

4.4. Spatial Feature of Variable Coefficients

Figure 14, Figure 15, Figure 16, Figure 17, Figure 18, Figure 19, Figure 20 and Figure 21 illustrate the spatial variation in the regression coefficients of each explanatory variable across the study area.

Figure 14 indicates that as the research area shifts from west to east, the impact of shopping service POIs on the demand for online car-hailing trips changes from negative to positive. The figure also highlights that the positive effect of shopping service POIs is more pronounced during holidays, especially in the upper right-hand corner of the study area. Furthermore, the distribution chart of POIs illustrates a positive correlation between the number of shopping service POIs and the demand for online car-hailing trips, with the number of shopping service POIs increasing from left to right. In other words, a higher quantity of shopping service POIs corresponds to a greater demand for online car-hailing travel.

Catering service POIs consistently positively impact the demand for online car-hailing trips within the study area, which is further pronounced during holidays. The impact of catering services POI on online car-hailing trips gradually increases from the lower left corner to the upper right corner of the study area. Similar to the effects of shopping service POIs, there is a positive correlation between the density of catering service POIs and the demand for online car-hailing trips, where a higher density leads to a more prominent positive impact.

The demand for online car-hailing trips from corporate enterprise POIs remains constant across different types of dates. The distribution map of corporate enterprise POIs reveals a gradual increase in their number from the lower left corner to the upper right corner of the study area. However, the positive impact of these POIs on the demand for online car-hailing progressively decreases in the same direction. A negative correlation exists between the number of corporate enterprise POIs and their resulting impact, which may be due to differences in travel convenience. As transportation facilities in the lower left corner are fewer and more inconvenient to use, employees in this area may have a higher demand for online car-hailing services.

Overall, transport facility POIs contribute to the demand for online car-hailing trips. Transport facility POIs have the greatest impact on the demand for online car-hailing trips in the lower left corner of the study area. This may be due to the low number of transport facility POIs in the area, making travel more inconvenient and increasing the demand for online car-hailing.

The impact of government agency POIs on the demand for online car-hailing is highly dependent on the type of day. The positive effect of government agency POIs on the demand for online car-hailing trips during workdays is greater than during holidays, indicating that some POI staff may not work during holidays or some agencies may close. Like corporate enterprise POIs, the bottom left region, where the demand for online car-hailing trips is most influenced by government agency POIs, has the most significant positive impact. In the other areas, government agency POIs are evenly distributed, which leads to a slight variation in the spatial distribution of the coefficients.

The influence of healthcare service POIs on the demand for online car-hailing trips is consistently negative during holidays, while only the top left corner has a boosting influence on weekdays. The regression coefficient in the study area presents a bottom–up increase, with sharper changes on the left and gradual increases on the right. In general, there is a positive correlation between the density of healthcare service POIs and the demand for online car-hailing trips.

Accommodation service POIs are primarily utilized by tourists, who often require online car-hailing services. Consequently, during the holiday season, accommodation service POIs positively impact online car-hailing, and the promotion is more noticeable. The facilitating effect of accommodation service POIs on the demand for online car-hailing travel increases from the lower right to the upper left corner of the study area. This effect is more prominent in areas with low POI density and less noticeable in areas with high POI density, as indicated by the POI distribution map.

The regression coefficient for car service POIs is positive in most regions, indicating that car service POIs contribute to the demand for online car-hailing travel. However, there is a negative impact of car service POIs on the demand for online car-hailing in the bottom right part of the region. The effect of car service POIs on demand for online car-hailing trips changes from negative to positive as one moves from the lower left to the upper right corner, eventually decreasing to approximately zero. This change is consistent with the change in the density of automotive service POIs, indicating a positive correlation between the resulting impact and density.

5. Conclusions

This paper explored the correlation between travel demand and different categories of POIs by constructing a GTWR model and an MGTWR model employing POI data and online car-hailing data. The results showed that the MGTWR model has a better regression effect than the classical GTWR model. Then, the result of the MGTWR model was used to analyze the spatiotemporal heterogeneity of the influence of different POIs on travel demand. Finally, we also obtained some findings with the regression coefficients for each type of POI. Transport facility POIs had the greatest boosting effect on the demand for online car-hailing trips, while healthcare services had the opposite and the most significant inhibiting effect. Recreational POIs were had the most significant promoting effects on holidays, while corporate enterprise POIs, government agency POIs, and healthcare service POIs were more prominent on weekdays.

In the future, the following research questions will be explored:

First, the generalizability of the model has yet to be substantiated. Due to the current limitations of the available data, it has not been possible to validate its generalization capability in other regions. In subsequent research, data from different areas will be utilized to demonstrate its generalization ability.

Second, the current study performed zoning with relatively simple meshing, which is too idealistic and may increase errors.

Finally, the data limitations resulted in unmatched online orders not being captured, leading to a potential discrepancy between the actual demand and orders. Subsequent efforts will be made to obtain these missing data.