5.1. Results of Ordinary Linear Regression
To assess the relationships between the influencing factors and vibrancy in each of the TAZs, a series of linear regressions was conducted. The population per hour on weekdays, weekends and holidays in each TAZ constituted the dependent variable
, which was tested to conform to a normal distribution. All independent variables and dependent variables were standardized. However, it was necessary to perform collinearity diagnostics before constructing multiple linear regression models. Multicollinearity refers to the distortion of a model estimation due to the existence of an exact correlation or a high correlation between explanatory variables within the linear regression model; these correlations can be caused by lag variables and incorrect model settings in addition to a limited number of samples. The collinearity of the indicators was determined through the tolerance and the variance inflation factor (VIF). When the tolerance is less than 0.1 or the VIF is greater than 10, the indicator can be considered to possess severe collinearity. The spatial distributions of integration and choice are consistent; therefore, a high level of collinearity exists between integration and choice. Based on the
values and VIF values of these two variables, we deleted the variable of choice. The results of the diagnostic information are listed in
Table 2. Ultimately, eight factors were used to construct the regression models. Then, we separated weekdays from weekends and used the number of people per hour over 24 h as the dependent variable. To observe the overall temporal effects of various influencing factors, ordinary linear regression (OLR) models were established for each hour. The OLR results are shown in
Table 3 and
Table 4.
Table 3 shows that, on weekdays, the commerce density and road integration are significantly positively correlated with vibrancy throughout the day. The residence density, leisure density, distance to airport and mixing degree are not statistically significant for urban vibrancy during the day but have significant effects at night. In contrast, the relationship between the distance to the city centre and urban vibrancy is negative during the daytime, that is, the greater the distance is to the city centre, the lower the vibrancy is; however, this relationship at night is not significant. These phenomena occur because the motivation for the daily activities of urban residents is relatively singular, i.e., work is the main driving force of a diversity of activities. Therefore, during the daytime, the majority of people are gathered in the city centre, while the influences of leisure, residence and mixing are relatively small. At night, when people return to their residential areas after work, the influences of the two locational factors are weakened, while the influences of the four density functions, especially the functions of residence and leisure, on urban vibrancy increase [
7,
58].
Table 4 shows that, on weekends, the largest difference from weekdays lies in that the residence and leisure density have a significant positive linear correlation to vibrancy on all days. The distance to the city centre only has significant negative effects from 15:00 to 19:00. The causes of these phenomena are that many people have no work requirements in the city centre, locational factors are reduced, and the diversity of urban function enables people to meet the needs of leisure, entertainment, and social aspects, significantly increasing city vigour on days off. In addition, on rest days, the degree of road integration, as an indicator of the potential of regional travel destinations, is still significantly positively correlated with urban vibrancy.
5.3. Visual Analysis of the GTWR Results
To better show the effects of the explanatory variables on vibrancy in the spatial and temporal dimensions, the results for each index on the weekdays and weekends were statistically analysed and plotted separately. In this way, the temporal differences and spatial differences are visualized.
1. Temporal differences
Using the hour as the statistical unit, we calculated and visualized the average coefficients in each TAZ at each time unit for both the weekdays and the weekends. The yellow and green curves in
Figure 3 show the variations in the regression coefficients on the weekdays and weekends, respectively. The coefficients of integration, which is positively correlated with urban vibrancy, are positive on weekdays and weekends. The degree of integration reflects the centrality of road traffic and the potential of a given segment as a destination. Therefore, improving the degree of road integration is conducive to enhancing the vibrancy of a city in general. According to the changes in the curve, the effects of integration reach a peak during the working hours on the weekdays and are relatively low at night. The reason for this is potentially because the degree of network integration is higher in work areas, and residents need to agglomerate in areas with good network development. In contrast, the changes in the estimated coefficients are relatively stable on the weekends without work.
The degree of functional mixing is used to express the functional diversity of a TAZ. Many theoretical studies have mentioned that the degree of functional mixing is an important element for improving local vibrancy [
7,
8]. In this study, the estimated coefficients of the functional mixing degree are negative during the working hours of a day, which may have an inhibitory effect on urban vibrancy; this finding is different from the results of many previous theoretical studies in addition to common sense. These results are explained as follows. During the daytime on weekdays, the demand of residents for urban function is relatively singular because they place work as their first priority; thus, a high degree of functional mixing does not attract people, while the work function occupies a relatively small portion and inhibits the vibrancy of the city. Meanwhile, on the weekends, the estimated coefficients are positive; people are affected by factors such as entertainment, leisure and social contact, and the demand for diversified functions increases. Therefore, a high degree of functional mixing is conducive to enhancing urban vibrancy.
Residence, traffic, commerce and leisure all positively affect urban vibrancy on the weekdays and weekends. The general trend of the influence of the residential density on vibrancy is greater during the night than during the day, and the influence on the weekends is greater than that on the weekdays, thereby reflecting the living habits of Shenzhen residents to some extent. The traffic density during the workday has larger effects on the vibrancy of the city than that during the weekends. There are two peaks at approximately 10:00 and approximately 19:00; these peaks are apparently associated with commuting peaks. With the formation of Shenzhen’s polycentric structure, urban residential areas and urban working areas are spatially separated; accordingly, the demand to travel to work increases the effect of traffic on vibrancy. During the weekends, especially in the evening, residents tend to rest and participate in recreational activities either at home or in their neighbourhood, while they avoid places with heavy traffic. Therefore, the influence of traffic is reduced. The effects of commerce are larger during the weekends than during the weekdays in general, while the changes in the trend are larger during the weekdays. Two low values exist at 9:00 and 18:00, which are also affected by the working hours. These two time periods are more dependent on the traffic density, and the business spending ability is weakened at these times. The influence of the leisure function on the vibrancy of Shenzhen is relatively stable during both the daytime and the night-time; to some extent, this finding indicates that Shenzhen, a bustling city, provides an abundant nightlife for its residents.
The coefficients of the distance to the city centre on working days are negative; hence, the farther the distance is, the weaker the vibrancy of the city. In addition, the effects of the city centre reach a peak during the daytime on weekdays; this is possibly because the central region of Shenzhen is a comprehensive area that encompasses enterprise, business and political functions. These places close to the central region are relatively prosperous; here, the vibrancy of the city increases. In contrast, the coefficients of the distance to the airport on weekdays and weekends are all negative, indicating that the city vibrancy improves with the attenuation of the distance from the airport. More importantly, the magnitude of the improvement in the vibrancy on weekends is greater than that during the daytime on weekdays, suggesting that peoples’ demands for travel to locations outside the city and the demands of people arriving from outside the city are higher during non-working hours.
2. Spatial differences
Taking the TAZ as the statistical unit, we calculated the average values of the regression coefficients over a period of 24 h both on weekdays and on weekends and used the natural breaks (Jenks) method to visualize the grading of categories, in which the differences between categories are significant, while the differences within classes are small [
59,
60]. The boundary of the classification of each factor was manually set to zero to distinguish positive and negative differences, which can intuitively reflect the enhancement or the restraint of various effects on the city’s vibrancy. The spatial distributions of the estimated coefficients of the indicators are shown from
Figure 4,
Figure 5,
Figure 6,
Figure 7,
Figure 8,
Figure 9,
Figure 10 and
Figure 11. These figures show that the average value of the regression coefficient of the same index may have positive or negative differences to varying degrees among the different TAZs. In addition, these figures indicate that the effects of the same factors exhibit significant spatial variations that cannot be generalized in this research. Moreover, the influences of the same index on the weekdays and weekends are different, but the same indicators on weekdays and weekends for each TAZ have a similar trend overall. Hence, the reasons for the spatial differences in the variables depend much more on the characteristics of each TAZ.
In terms of the form of the urban transportation network, the regions that are positively correlated with urban vibrancy are focused mainly in central Shenzhen. In the process of urban construction, Shenzhen has always emphasized the construction of multi-centre urban development structures, which are the main clusters of urban functions. A good road network is needed as a skeleton to support the flow of the population to these places. The degree of integration mainly measures the development of the urban road network, describes the centrality of roads, and indicates the potential of roads as destinations.
Figure 4 demonstrates that a region with a high degree of integration exhibits a high accessibility. For multiple central regions undertaking important urban functions, enhancing the degree of integration of the road network can significantly improve the urban vibrancy in those regions. In contrast, the places that display negative effects of integration on vibrancy are mostly ecological control areas, which usually have fewer people and facilities.
For the degree of functional mixing (
Figure 5), the weekends have larger values than the weekdays, which is consistent with the results of the temporal dimensional analysis. With the exception of passive–active weekdays, improving the functional diversity can achieve better urban vibrancy. The mixing degree is significantly positively correlated with urban vibrancy in some regions, such as the Futian Central Business District (CBD). In the downtown areas of Nanshan and Luohu, the degree of functional mixing has negative impacts. This finding is inconsistent with the scenario mentioned in many studies in which an increase in the mixing degree of core functions can effectively improve the urban vibrancy. One of the main reasons for this is that there are some key functions of planning in these areas, and crowd gathering is mainly attributed to these key functions rather than other functions.
As shown in
Figure 6, the positive and negative influences of the living (residence) function on different local areas are not identical. For the living function, the number of TAZs with positive effects on weekends is higher than that on weekdays, which is in accordance with the results of the change in the trend of the temporal dimension coefficient. In addition, the negative effects of the living function on urban vibrancy are focused in the ecological control areas of Shenzhen that contain important sources of water, mountains, green space and ecological environments; in these areas, excessive development is prohibited, and few residential areas and urban residents exist. In contrast, the positive effects of residence throughout Shenzhen are similar; this finding reveals that the residential land use is basically distributed for citizens of Shenzhen.
From the spatial distribution of the traffic function shown in
Figure 7, the influence of traffic is very obvious; the effects in the city centre and sub-centres are negative, and those outside the downtown areas are positive. This is because centres usually contain more companies, businesses and other important functional areas that are spatially separated from the surrounding main living areas. The main function of the city centre to attract a gathering population is the demand to work, especially on weekdays. The demand to travel to areas in the city centre relies more on transportation to reach these areas. Hence, the relationship between traffic and vibrancy in these areas is positive. In contrast, for each core region, the facilities are relatively complete in the vicinity of residential areas; as a result, the residents have no need to spend excessive amounts of money on transportation to travel to other places. Moreover, traffic facilities can introduce congestion and noise. Therefore, the traffic function in these areas has a negative impact.
The influence of the commerce function on urban vibrancy is positive in most areas of Shenzhen, particularly in the central regions (
Figure 8). This finding shows that the commerce function plays an important role in enhancing urban vibrancy in prosperous and important areas. However, fewer crowds gather in remote areas, that is, less accessible and less developed areas or ecologically controlled areas; thus, the effect of the commerce function on the vibrancy of these areas is negative. The spatial distribution of the influence of commerce suggests that the spatial heterogeneity of POIs coincide with the supply for commerce and business that would lead to differential facilities to attract and retain human activity.
The influence of the leisure function on urban vibrancy contrasts with that of the commerce function in many areas except major central districts (
Figure 9). The reason is that commercial consumption is not well developed in relatively remote regions. However, as a result of the natural ecological environment, these places have many famous tourist attractions. Therefore, the leisure function attracts the flow of the population and enhances urban vibrancy. The most apparent places in Shenzhen are some areas in Yantian, Longhua, southwestern Nanshan and Dapeng, which have many famous tourist attractions.
With regard to the influences of the geographical conditions on urban vibrancy, the distance to the city centre shows a negative correlation with vibrancy in many TAZs (
Figure 10). This correlation shows that the vibrancy is higher closer to the city centre, that is, the greater the distance is from the city centre, the lower the vibrancy is. However, in some areas, the distance to the city centre is still positively correlated with the vibrancy. Most of these areas are ecological control areas, where the determinants of vibrancy are natural conditions more than geographical location factors.
The influence of the distance to the airport on vibrancy is mostly negative, indicating that a smaller distance to the airport correlates to a higher city vibrancy (
Figure 11). In general, the areas with negative effects are focused mainly in multiple core regions, suggesting that the residents in these areas have a higher demand for foreign travel. Yantian suffers from an ageing problem; hence, the residents have few opportunities and demand to travel outside the city. The greater is the distance from the airport, the more positive is the vibrancy of the city. Notably, in the city centre, the effect of the distance from the airport is positive because the distance from the airport is not the most important or significant factor of vibrancy.