## 4 Empirical Analysis
### Results Analysis and Discussion
#### 4.2.3 Convergence Analysis
It can thus be seen that, although there exist certain convergence characteristics among the regions' _ITE_, the convergence period takes a long time. Therefore, the provinces with low _ITE_ need to take a long time to catch up to the provinces with high _ITE_. (2) The conditional \(\beta\)-convergence model selection and result analysis  
In line with previous studies, this study selected the level of economic development (_led_), government intervention (_gi_), the scale of transport industry development (_tids_), technological advancement (_ta_), traffic intensity (_ti_) and residents' per capita transport consumption expenditure (_ptse_) as conditional variables that may exert an influence over the convergence of condition \(\beta\) in China's regional integrated transport efficiency [3; 41; 58; 59; 60]. Regarding the data processing of these conditional variables, each province's Gross Domestic Product (GDP) was used to express its level of economic development. The ratio of the local government's fiscal expenditure on transport to the gross value of production was used as a proxy to measure the government's degree of intervention in the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**LM\_Error** & **Robust LM\_Error** & **LM\_Lag** & **Robust LM\_Lag** \\ _(\(p\) Value)_ & _(\(p\) Value)_ & _(\(p\) Value)_ & _(\(p\) Value)_ \\ \hline
9.263 & 7.381 & 5.279 & 4.814 \\ (0.023) & (0.0014) & (0.034) & (0.0038) \\ \hline \hline \end{tabular} Note: The \(p\)-value is significant at the 1% level.  
\end{table} 
Table 6: Spatial correlation tests for the absolute \(\beta\)-convergence model. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\beta\) & **Spatial Residual Item** & **Goodness of** & **Maximum** & **Convergence** & **Half Life** \\ (\(t\) Value) & **(\(t\) Value)** & **Fit** & **Likelihood** & **Speed\%** & **Cycle** \\ \hline \(-0.1057\)*** & 0.274 *** & 0.768 & 342.191 & 1.39 & 49.8 \\ (\(-4.2603\)) & (2.961) & & & & \\ \hline \hline \end{tabular} Note: *** indicates a 1% level of significance.  
\end{table} 
Table 7: Estimation results of the absolute \(\beta\)-convergence SEM model for _ITE_s. development of the public transport economy. The scale of development of the transport industry was expressed via the ratio of the value added by the transport industry to GDP. Technological progress was mainly reflected in the efficiency of energy use, which was expressed by the ratio of the value added by the transport industry to the amount of energy this industry consumed. These conditional variables were used to show the level of transport technology innovation and application effect of energy saving technology. Transport intensity was expressed as the ratio of conversion turnover to GDP. Residents' per capita transport consumption expenditure reflects the demand for transport. Therefore, as it affects transport outputs, it was also considered as an external factor that may affect integrated transport efficiency. The statistical descriptions of these indicators are shown in Table 8.  
Similar to the process of discerning absolute \(\beta\)-convergence, the condition \(\beta\)-convergence model of the panel data was checked and estimated using Matlab software. The results are shown in Table 9.  
From the spatial diagnosis results in Table 10, we can see that the LM_Error, LM_Lag and Robust LM_Error failed the 1% significance test, but the Robust LM_Lag passed it, indicating that the SLM established under the condition of the convergence of \(ITE\) was more accurate than the SEM. Therefore, the conditional \(\beta\)-convergence characteristics of \(ITE\) were queried using by Formula (7). The estimated results are shown in Table 10.