Appendix for Chapter 4
Appendix 4.A. Effects of Different Visibility Projects on the Risk of Deprivatization, Urban Bus Sector, 1996–2016. Cox Proportional Hazard Models
(1) | (2) | |
---|---|---|
Whole Sample | 20 Cities with BRT | |
Hazard Ratio | Hazard Ratio | |
BRT construction | 6.727Footnote *** (2.121) | 48.695Footnote ** (85.384) |
City title application | 3.799Footnote *** (0.724) | 0.996 (0.560) |
New type bus | 4.238Footnote *** (0.862) | 2.370 (1.522) |
Fiscal health Bus per capita | 0.989 (0.010) 0.956 (0.093) | 8.983 (15.021) 6.343 (10.452) |
Annual bus change GDP per capita | 1.255 (0.430) 1.005 (0.002) | 0.066 (0.151) 1.016 (0.012) |
Log pseudolikelihood | −437.08 | −10.564 |
N | 1,811 | 144 |
Notes:
* p≤ 0.10, **p≤ 0.05, ***p≤ 0.01. Robust standard errors in parentheses.
Appendix 4.B. Effects of Different Visibility Projects on the Risk of Deprivatization, Urban Bus Sector, 1996–2016. Cox Proportional Hazard Models
(1) | (2) | (3) | |
---|---|---|---|
Coefficients | Coefficients | Coefficients | |
City title application | 1.080Footnote *** (0.144) | 1.159Footnote *** (0.159) | 1.092Footnote *** (0.164) |
New type bus | 1.610Footnote *** (0.162) | 1.658Footnote *** (0.171) | 1.640Footnote *** (0.170) |
Fiscal health Bus per capita | −0.009 (0.012) 0.035 (0.052) | −0.003 (0.011) −0.137 (0.145) | |
Annual bus change GDP per capita | 0.018 (0.115) 0.004Footnote * (0.002) | ||
Log pseudolikelihood | −708.29 | −570.62 | −561.62 |
N | 2,472 | 1,987 | 1,870 |
Notes:
* p≤ 0.10, **p≤ 0.05, ***p≤ 0.01. Robust standard errors in parentheses.
Appendix 4.C. Test of Proportional-Hazards Assumption, Model Specification 3 in Figure 4.2
As shown here, all of the variables are not significant either collectively or individually, thus supporting the assumption of proportional hazards.
rho | chi2 | Df | Prob>chi2 | |
---|---|---|---|---|
City title application | −0.03202 | 0.11 | 1 | 0.7380 |
New type bus | −0.04863 | 0.34 | 1 | 0.5583 |
Fiscal health | −0.08621 | 0.22 | 1 | 0.6357 |
Bus per capita | 0.18505 | 2.16 | 1 | 0.1414 |
Annual bus change | −0.10404 | 0.26 | 1 | 0.6128 |
GDP per capita | −0.15068 | 2.26 | 1 | 0.1327 |
Global test | n.a. | 3.99 | 6 | 0.6783 |
Note: robust variance−covariance matrix used.
Appendix 4.D. Cox–Snell Residual Plot for Model Specification 3 in Figure 4.2

As shown in the figure, I plot the Nelson–Aalen cumulative hazard function against the Cox–Snell residuals to check for general model fit. If the hazard function follows the 45-degree line, then it approximately has an exponential distribution with a hazard rate of 1, meaning the model fits the data well. As shown in the plot, the hazard function follows the 45-degree line closely except for very large values of time. The large values of time are mostly likely due to censored data, a common phenomenon in survival data. Overall, we can conclude that the model has an approximately exponential distribution with a hazard rate of 1 and that the main model fits the data well.
Appendix 4.E. Cox Proportional Hazard Model with Three-year Frequency
Hazard ratio | Hazard ratio | ||
---|---|---|---|
City title application Three-year frequency | 2.324Footnote *** (0.268) | Fiscal health | 0.994 (0.012) |
New type bus Three-year frequency | 1.879Footnote *** (0.195) | Bus per capita | 0.889 (0.112) |
Annual bus replacement GDP per capita | 1.480 (0.636) 1.005 (0.003) | ||
Log pseudolikelihood | −397.96 | ||
N | 1,664 |
Notes:
* p≤ 0.10, **p≤ 0.05, ***p≤ 0.01. Robust standard errors in parentheses.
Appendix 4.F. Frailty Model and Logit Model
Cox frailty model | Logit model, random effects, panel data | |
---|---|---|
Hazard Ratio | Coefficient | |
City title application | 7.090Footnote *** (2.814) | 2.018Footnote *** (0.280) |
New type bus | 3.889Footnote *** (1.363) | 2.159Footnote *** (0.238) |
Fiscal health Bus per capita | 0.839 (0.141) 0.920 (0.162) | −0.012 (0.029) −0.174 (0.229) |
Annual bus change GDP per capita | 1.102 (0.816) 1.061Footnote * (0.034) | 1.432 (0.551) 1.005Footnote ** (0.003) |
Log pseudolikelihood | −413.62 | −387.36 |
N | 2,112 | 1,667 |
Notes:
* p≤ 0.10, **p≤ 0.05, ***p≤ 0.01. Robust standard errors in parentheses.
Appendix 4.G. Effects of Different Visibility Projects on the Risk of Deprivatization, Urban Bus Sector, 1996–2016. Cox Proportional Hazard Models. With Leadership Tenure
Hazard ratio | Hazard ratio | ||
---|---|---|---|
City title application | 4.011Footnote *** (0.803) | Fiscal health | 0.988 (0.012) |
New type bus | 4.667Footnote *** (0.994) | Bus per capita | 0.906 (0.098) |
Secretary tenure Secretary tenure Squared term | 1.078 (0.201) 1.002 (0.022) | Annual bus change GDP per capita | 1.431 (0.055) 1.005Footnote * (0.003) |
Mayor tenure Mayor tenure Squared term | 0.873 (0.161) 1.008 (0.025) | Log pseudolikelihood N | −387.29 1666 |
Notes:
* p≤ 0.10, **p≤ 0.05, ***p≤ 0.01. Robust standard errors in parentheses.