## 4 Empirical Analysis
### Results Analysis and Discussion
#### 4.2.2 Spatial Autocorrelation Test and Aggregation Results  
The analysis of spatial autocorrelation based on the [PERSON]'s I index formed the basis of our spatial convergence analysis. The [PERSON]'s I values, estimated by OpenGeoDa (1.2.0) software, are shown in Table 4. The [PERSON]'s I indexes during 2009-2016 were found to be greater than zero, indicating a positive spatial autocorrelation between the integrated transport efficiency of the 31 studied provinces. The relevant statistics (\(Z\) values are all greater than 1.96; \(p\) values are all less than 0.05) passed the significance test pertaining to spatial autocorrelation. The \(Z\)-test, which rejected the null hypothesis that the spatial distribution of China's provincial transport efficiency presents a completely random distribution, and further demonstrates the correctness of the [PERSON]'s I results. Furthermore, the existence of spatial autocorrelation indicates that a spatial econometric model could be used to analyze the extent of the necessity for spatial convergence for regional integrated transport efficiency. The integrated transport efficiency of the 31 studied provinces demonstrates significant spatial agglomeration characteristics, indicating that the convergence of integrated transport efficiency that considers spatial effects is both empirically valid and applicable in the current context. In addition,  
Figure 5: Division of the three economic zones. Figure 6: Changes of \(ITE\) in the three economic regions during 2009–2016. the Moran's I Index during 2009-2014 was decreasing, indicating that the spatial autocorrelation of positive transport efficiency weakened over time, and that the interaction between neighboring provinces decreased. However, the value of the Moran's I index gradually increased from 2014 to 2015, with a growing trend of a mutual influence of integrated transport efficiency between adjacent provinces. According to changes in the Moran's I Index, which were generally experienced during 2009-2016, and taking 2009, 2011, 2014 and 2016 as key nodes containing further significant changes, we analyzed and compared the specific changes and spatial aggregation of China's regional _ITE_ by constructing Moran scatter plots to further understand the spatial distribution characteristics. To clearly show the distribution of each province in the Moran scatter plots, we represent each province by numbering them. As shown in Figure 7, the first quadrant shows provinces with a high level of _ITE_ that are adjacent to other provinces with a high value (H-H aggregation). The second quadrant highlights provinces with a low _ITE_ that are surrounded by provinces with a high level of efficiency, and where the difference in efficiency between neighboring provinces is quite marked (L-H aggregation). The third quadrant illustrates less efficient provinces that are adjacent to other low-value provinces (L-L aggregation). The fourth quadrant shows provinces with a high level of _ITE_ that are bordered by provinces with a lower level (H-L aggregation). In Figure 7, we can see that, in 2009 and 2011, most of the provinces were distributed in the third quadrant and the least were found in the fourth quadrant, indicating that the _ITE_ was mainly characterized by L-L aggregation. Furthermore, the provinces with L-L aggregation features mostly belonged to the western part of China (such as Yunnan (25); Tibet (26); Qinghai (30); Qinghai (31); etc.). However, the points in the third quadrant of 2014 and 2016 show a decreasing trend, which indicated that low-low characteristics of transport efficiency aggregation gradually weakened. In 2014 and 2016, the aggregation features mainly include high aggregation and low aggregation, reflecting a general improvement in _ITE_ and further confirming the spatial aggregation characteristics of China's regional _ITE_.