update ccd vignette

vignettes/ccd.Rmd

@@ -3,7 +3,7 @@ title: "Coupling Coordination Degree Model and Metacoupling Analysis"
 author: "Wenbo Lyu"
 date: |
   | Last update: 2026-05-12
-  | Last run: `r Sys.Date()`
+  | Last run: 2026-05-12
 output: rmarkdown::html_vignette
 vignette: >
   %\VignetteIndexEntry{ccd}
@@ -29,15 +29,15 @@ Although widely used, this formulation may suffer from **scale sensitivity and o
 
 ## Modified Coupling Degree
 
-### Modification by $\text{wang et al}^{[1]}$.
+### Modification by $\text{wang}^{[1]}$.
 
 **First**, Wang et al. introduce a formulation that incorporates pairwise differences among subsystems while normalizing their relative magnitudes:
 
 $$
 C = \sqrt{\left[1-\frac{\sum\limits_{i>j,j=1}^{n-1} \sqrt{\left(U_i-U_j\right)^2}}{\sum_{m=1}^{n-1}m}\right] \times \left(\prod_{i=1}^n \frac{U_i}{\text{max} U_i}\right)^{\frac{1}{n-1}}}
 $$
 
-### Modification by $\text{fan et al}^{[2]}$.
+### Modification by $\text{fan}^{[2]}$.
 
 **Alternatively**, Fan et al. propose a simplified structure derived from variance-like dispersion, which directly captures the imbalance among subsystem indicators:
 
@@ -206,7 +206,7 @@ fig1
 
 ## A Meta-Coupling Analysis
 
-Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Pericoupling among neighboring units are further weighted using an inverse distance scheme. The calculation of the coupling coordination degree adopts the formulation proposed by $\text{wang et al}^{[1]}$.
+Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Pericoupling among neighboring units are further weighted using an inverse distance scheme. The calculation of the coupling coordination degree adopts the formulation proposed by $\text{wang}^{[1]}$.
 
 
 ``` r
@@ -260,10 +260,17 @@ fig2
 
 ## References
 
-[1] Wang, S., Kong, W., Ren, L. and ZHI, D., 2021. Research on misuses and modification of coupling coordination degree model in China. Journal of Natural Resources, 36, 793-810. https://doi.org/10.31497/zrzyxb.20210319
+1. Wang, S., Kong, W., Ren, L. and ZHI, D., 2021. Research on misuses and modification of coupling coordination degree model in China. Journal of Natural Resources, 36, 793-810. [https://doi.org/10.31497/zrzyxb.20210319][1]
 
-[2] Fan, D., Ke, H. and Cao, R., 2024. Modification and improvement of coupling coordination degree model. Stat. Decis, 40, 41-46. https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007
+2. Fan, D., Ke, H. and Cao, R., 2024. Modification and improvement of coupling coordination degree model. Stat. Decis, 40, 41-46. [https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007][2]
 
-[3] Tang, P., Huang, J., Zhou, H., Fang, C., Zhan, Y., Huang, W., 2021. Local and telecoupling coordination degree model of urbanization and the eco-environment based on RS and GIS: A case study in the Wuhan urban agglomeration. Sustainable Cities and Society 75, 103405. https://doi.org/10.1016/j.scs.2021.103405
+3. Tang, P., Huang, J., Zhou, H., Fang, C., Zhan, Y., Huang, W., 2021. Local and telecoupling coordination degree model of urbanization and the eco-environment based on RS and GIS: A case study in the Wuhan urban agglomeration. Sustainable Cities and Society 75, 103405. [https://doi.org/10.1016/j.scs.2021.103405][3]
 
-[4] Li, Y., Jia, N., Zheng, L., Yin, C., Chen, K., Sun, N., Jiang, A., Wang, M., Chen, R., Zhou, Z., 2026. A meta-coupling analysis between three-dimensional urbanization and ecosystem services in China’s urban agglomerations. Communications Earth & Environment 7. https://doi.org/10.1038/s43247-025-03047-w
+4. Li, Y., Jia, N., Zheng, L., Yin, C., Chen, K., Sun, N., Jiang, A., Wang, M., Chen, R., Zhou, Z., 2026. A meta-coupling analysis between three-dimensional urbanization and ecosystem services in China’s urban agglomerations. Communications Earth & Environment 7. [https://doi.org/10.1038/s43247-025-03047-w][4]
+
+ 
+
+[1]: https://doi.org/10.31497/zrzyxb.20210319
+[2]: https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007
+[3]: https://doi.org/10.1016/j.scs.2021.103405
+[4]: https://doi.org/10.1038/s43247-025-03047-w

vignettes/ccd.Rmd.orig

@@ -36,15 +36,15 @@ Although widely used, this formulation may suffer from **scale sensitivity and o
 
 ## Modified Coupling Degree
 
-### Modification by $\text{wang et al}^{[1]}$.
+### Modification by $\text{wang}^{[1]}$.
 
 **First**, Wang et al. introduce a formulation that incorporates pairwise differences among subsystems while normalizing their relative magnitudes:
 
 $$
 C = \sqrt{\left[1-\frac{\sum\limits_{i>j,j=1}^{n-1} \sqrt{\left(U_i-U_j\right)^2}}{\sum_{m=1}^{n-1}m}\right] \times \left(\prod_{i=1}^n \frac{U_i}{\text{max} U_i}\right)^{\frac{1}{n-1}}}
 $$
 
-### Modification by $\text{fan et al}^{[2]}$.
+### Modification by $\text{fan}^{[2]}$.
 
 **Alternatively**, Fan et al. propose a simplified structure derived from variance-like dispersion, which directly captures the imbalance among subsystem indicators:
 
@@ -157,7 +157,7 @@ fig1
 
 ## A Meta-Coupling Analysis
 
-Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Pericoupling among neighboring units are further weighted using an inverse distance scheme. The calculation of the coupling coordination degree adopts the formulation proposed by $\text{wang et al}^{[1]}$.
+Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Pericoupling among neighboring units are further weighted using an inverse distance scheme. The calculation of the coupling coordination degree adopts the formulation proposed by $\text{wang}^{[1]}$.
 
 ```{r peri_coupling}
 nb = sdsfun::spdep_nb(gzma)
@@ -200,10 +200,17 @@ fig2
 
 ## References
 
-[1] Wang, S., Kong, W., Ren, L. and ZHI, D., 2021. Research on misuses and modification of coupling coordination degree model in China. Journal of Natural Resources, 36, 793-810. https://doi.org/10.31497/zrzyxb.20210319
+1. Wang, S., Kong, W., Ren, L. and ZHI, D., 2021. Research on misuses and modification of coupling coordination degree model in China. Journal of Natural Resources, 36, 793-810. [https://doi.org/10.31497/zrzyxb.20210319][1]
 
-[2] Fan, D., Ke, H. and Cao, R., 2024. Modification and improvement of coupling coordination degree model. Stat. Decis, 40, 41-46. https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007
+2. Fan, D., Ke, H. and Cao, R., 2024. Modification and improvement of coupling coordination degree model. Stat. Decis, 40, 41-46. [https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007][2]
 
-[3] Tang, P., Huang, J., Zhou, H., Fang, C., Zhan, Y., Huang, W., 2021. Local and telecoupling coordination degree model of urbanization and the eco-environment based on RS and GIS: A case study in the Wuhan urban agglomeration. Sustainable Cities and Society 75, 103405. https://doi.org/10.1016/j.scs.2021.103405
+3. Tang, P., Huang, J., Zhou, H., Fang, C., Zhan, Y., Huang, W., 2021. Local and telecoupling coordination degree model of urbanization and the eco-environment based on RS and GIS: A case study in the Wuhan urban agglomeration. Sustainable Cities and Society 75, 103405. [https://doi.org/10.1016/j.scs.2021.103405][3]
 
-[4] Li, Y., Jia, N., Zheng, L., Yin, C., Chen, K., Sun, N., Jiang, A., Wang, M., Chen, R., Zhou, Z., 2026. A meta-coupling analysis between three-dimensional urbanization and ecosystem services in China’s urban agglomerations. Communications Earth & Environment 7. https://doi.org/10.1038/s43247-025-03047-w
+4. Li, Y., Jia, N., Zheng, L., Yin, C., Chen, K., Sun, N., Jiang, A., Wang, M., Chen, R., Zhou, Z., 2026. A meta-coupling analysis between three-dimensional urbanization and ecosystem services in China’s urban agglomerations. Communications Earth & Environment 7. [https://doi.org/10.1038/s43247-025-03047-w][4]
+
+ 
+
+[1]: https://doi.org/10.31497/zrzyxb.20210319
+[2]: https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007
+[3]: https://doi.org/10.1016/j.scs.2021.103405
+[4]: https://doi.org/10.1038/s43247-025-03047-w