From fa7adbaa1425bc4786a2b4ab1c95630f1b21d096 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 01/25] draft ccd vignette --- .gitignore | 1 + DESCRIPTION | 3 +++ vignettes/.gitignore | 2 ++ vignettes/ccd.Rmd | 19 +++++++++++++++++++ 4 files changed, 25 insertions(+) create mode 100644 vignettes/.gitignore create mode 100644 vignettes/ccd.Rmd diff --git a/.gitignore b/.gitignore index e4c203a..43d3ebe 100644 --- a/.gitignore +++ b/.gitignore @@ -5,3 +5,4 @@ .DS_Store .quarto docs +inst/doc diff --git a/DESCRIPTION b/DESCRIPTION index 697e77c..6657e5e 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -18,9 +18,12 @@ LinkingTo: RcppThread Suggests: infoxtr, + knitr, pc, Rcpp, RcppThread, + rmarkdown, spEDM Config/roxygen2/markdown: TRUE Config/roxygen2/version: 8.0.0 +VignetteBuilder: knitr diff --git a/vignettes/.gitignore b/vignettes/.gitignore new file mode 100644 index 0000000..097b241 --- /dev/null +++ b/vignettes/.gitignore @@ -0,0 +1,2 @@ +*.html +*.R diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd new file mode 100644 index 0000000..6a40e0a --- /dev/null +++ b/vignettes/ccd.Rmd @@ -0,0 +1,19 @@ +--- +title: "ccd" +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{ccd} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + comment = "#>" +) +``` + +```{r setup} +library(coupling) +``` From 1f24513a0efc6433f8fdb1f1c42a3f7202fcc7c8 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 02/25] draft ccd vignette --- _pkgdown.yml | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/_pkgdown.yml b/_pkgdown.yml index 15cd5bd..bf66769 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -13,7 +13,7 @@ navbar: articles: # text: Vignettes # menu: - # - text: Coupling Coordination Degree Models + # - text: Coupling Coordination Degree Models and Metacoupling Analysis # href: articles/ccd.html home: From f39cfff2a44f55906710faf11720e9f6a86b182a Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 03/25] draft ccd vignette --- .Rbuildignore | 1 + build-vignettes.md | 9 +++++++++ 2 files changed, 10 insertions(+) create mode 100644 build-vignettes.md diff --git a/.Rbuildignore b/.Rbuildignore index 3f92db2..f5253e2 100644 --- a/.Rbuildignore +++ b/.Rbuildignore @@ -5,3 +5,4 @@ ^docs$ ^pkgdown$ ^cran-comments\.md$ +^build-vignettes\.md$ diff --git a/build-vignettes.md b/build-vignettes.md new file mode 100644 index 0000000..28a8666 --- /dev/null +++ b/build-vignettes.md @@ -0,0 +1,9 @@ +``` r +.prebuild_vignettes = \(name){ + out = paste0("vignettes/",name,".Rmd") + inp = paste0(out,".orig") + knitr::knit(inp,out) +} + +.prebuild_vignettes("ccd") +``` From 7242e58fe63ce1b6cbce87f296fb64909d0e6378 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 04/25] draft ccd vignette --- _pkgdown.yml | 2 +- vignettes/ccd.Rmd | 14 +++++++++----- 2 files changed, 10 insertions(+), 6 deletions(-) diff --git a/_pkgdown.yml b/_pkgdown.yml index bf66769..9f8a541 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -13,7 +13,7 @@ navbar: articles: # text: Vignettes # menu: - # - text: Coupling Coordination Degree Models and Metacoupling Analysis + # - text: Coupling Coordination Degree Model and Metacoupling Analysis # href: articles/ccd.html home: diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 6a40e0a..7ac1e79 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -1,5 +1,9 @@ --- -title: "ccd" +title: "Coupling Coordination Degree Model and Metacoupling Analysis" +author: "Wenbo Lyu" +date: | + | Last update: 2026-05-11 + | Last run: `r Sys.Date()` output: rmarkdown::html_vignette vignette: > %\VignetteIndexEntry{ccd} @@ -10,10 +14,10 @@ vignette: > ```{r, include = FALSE} knitr::opts_chunk$set( collapse = TRUE, - comment = "#>" + message = FALSE, + comment = "##", + fig.path = "man/figures/ccd/" ) ``` -```{r setup} -library(coupling) -``` +# Introduction \ No newline at end of file From 05b9f3bbc4b523cef0e93f310527c6bb54a3a7ac Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 05/25] draft ccd vignette --- vignettes/ccd.Rmd | 78 ++++++++++++++++++++++++++++++++++++++++++++++- 1 file changed, 77 insertions(+), 1 deletion(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 7ac1e79..882171d 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -20,4 +20,80 @@ knitr::opts_chunk$set( ) ``` -# Introduction \ No newline at end of file +# Introduction + +The **Coupling Coordination Degree (CCD) model** is widely used to quantify the coupling and coordinated development among multiple subsystems. Originating from physics, it has been extensively applied in regional and human–environment systems. + +## Coupling Degree + +Given *n* normalized subsystem indicators $U_i$, the classical coupling degree is defined as: + +$$ +C = \left[ \frac{\prod_{i=1}^{n} U_i}{\left( \frac{1}{n} \sum_{i=1}^{n} U_i \right)^n} \right]^{\frac{1}{n}} +$$ + +Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. + +## Modified Coupling Degree + +To address these issues, alternative formulations have been proposed by modifying the functional form of the coupling degree. + +### Wang-type formulation + +The Wang-type modification adjusts the coupling function to reduce nonlinearity and improve interpretability: + +$$ +C = \frac{2 \sqrt{U_1 U_2}}{U_1 + U_2} +$$ + +and can be extended to the general form: + +$$ +C = \frac{n \left( \prod_{i=1}^{n} U_i \right)^{1/n}}{\sum_{i=1}^{n} U_i} +$$ + +This formulation replaces the power structure with a ratio between the geometric mean and arithmetic mean, leading to more stable behavior. + +### Fan-type formulation + +The Fan-type modification further revises the coupling structure by directly transforming the classical expression: + +\[ +C = \sqrt{1 - \frac{\sum_{i=1}^{n} (U_i - \bar{U})^2}{n \bar{U}^2}} +\] + +where \( \bar{U} = \frac{1}{n} \sum_{i=1}^{n} U_i \). + +This formulation emphasizes **dispersion-based consistency**, making the coupling degree more sensitive to imbalance among subsystems. + +## Comprehensive Development Index + +The overall development level is defined as: + +$$ +T = \sum_{i=1}^{n} \alpha_i U_i +$$ + +where $\alpha_i$ are weights with $\sum \alpha_i = 1$. + +## Coordination Degree + +The CCD integrates interaction and development: + +$$ +D = \sqrt{C \times T} +$$ + +where +- $C$ measures coupling degree +- $T$ measures development level +- $D$ reflects coordinated development + +## Metacoupling Perspective + +The CCD framework can be extended under the **metacoupling framework**, distinguishing: +- **Intracoupling** +- **Pericoupling** +- **Telecoupling** + +This enables cross-scale analysis of spatial interactions. \ No newline at end of file From 6383f2c57545d05119786443b71d4673eebc9186 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 06/25] draft ccd vignette --- vignettes/ccd.Rmd | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 882171d..f755e0a 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -22,7 +22,7 @@ knitr::opts_chunk$set( # Introduction -The **Coupling Coordination Degree (CCD) model** is widely used to quantify the coupling and coordinated development among multiple subsystems. Originating from physics, it has been extensively applied in regional and human–environment systems. +The **Coupling Coordination Degree (CCD) model** is widely used to quantify the degree of coupling and coordinated development among multiple subsystems. Originating from physics, it has been extensively applied in regional and human–environment systems. ## Coupling Degree @@ -32,11 +32,11 @@ $$ C = \left[ \frac{\prod_{i=1}^{n} U_i}{\left( \frac{1}{n} \sum_{i=1}^{n} U_i \right)^n} \right]^{\frac{1}{n}} $$ -Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. +Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. To address these issues, alternative formulations have been proposed by modifying the functional form of the coupling degree. ## Modified Coupling Degree -To address these issues, alternative formulations have been proposed by modifying the functional form of the coupling degree. + ### Wang-type formulation @@ -96,4 +96,5 @@ The CCD framework can be extended under the **metacoupling framework**, distingu - **Pericoupling** - **Telecoupling** -This enables cross-scale analysis of spatial interactions. \ No newline at end of file +This enables cross-scale analysis of coupling. + From 29e10370a5d314107b9f31c24119519bd7872746 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 07/25] draft ccd vignette --- vignettes/ccd.Rmd | 40 ++++++++++++++++------------------------ 1 file changed, 16 insertions(+), 24 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index f755e0a..d9381cf 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -26,7 +26,7 @@ The **Coupling Coordination Degree (CCD) model** is widely used to quantify the ## Coupling Degree -Given *n* normalized subsystem indicators $U_i$, the classical coupling degree is defined as: +Given *n* normalized subsystem indicators $U_i$, the standard coupling degree $C$ is defined as: $$ C = \left[ \frac{\prod_{i=1}^{n} U_i}{\left( \frac{1}{n} \sum_{i=1}^{n} U_i \right)^n} \right]^{\frac{1}{n}} @@ -36,36 +36,18 @@ Although widely used, this formulation may suffer from **scale sensitivity and o ## Modified Coupling Degree - - -### Wang-type formulation - -The Wang-type modification adjusts the coupling function to reduce nonlinearity and improve interpretability: +### Modification by $\text{wang et al}^{[1]}$. $$ -C = \frac{2 \sqrt{U_1 U_2}}{U_1 + U_2} +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}}} $$ -and can be extended to the general form: +### Modification by $\text{fan et al}^{[2]}$. $$ -C = \frac{n \left( \prod_{i=1}^{n} U_i \right)^{1/n}}{\sum_{i=1}^{n} U_i} +C = 1-2\sqrt{\frac{n\sum_{i=1}^n U_i^2 - \left(\sum_{i=1}^n U_i\right)^2}{n^2}} $$ -This formulation replaces the power structure with a ratio between the geometric mean and arithmetic mean, leading to more stable behavior. - -### Fan-type formulation - -The Fan-type modification further revises the coupling structure by directly transforming the classical expression: - -\[ -C = \sqrt{1 - \frac{\sum_{i=1}^{n} (U_i - \bar{U})^2}{n \bar{U}^2}} -\] - -where \( \bar{U} = \frac{1}{n} \sum_{i=1}^{n} U_i \). - -This formulation emphasizes **dispersion-based consistency**, making the coupling degree more sensitive to imbalance among subsystems. - ## Comprehensive Development Index The overall development level is defined as: @@ -78,7 +60,7 @@ where $\alpha_i$ are weights with $\sum \alpha_i = 1$. ## Coordination Degree -The CCD integrates interaction and development: +The coordination degree $D$ integrates interaction and development: $$ D = \sqrt{C \times T} @@ -98,3 +80,13 @@ The CCD framework can be extended under the **metacoupling framework**, distingu This enables cross-scale analysis of coupling. + +## References + +[1] Wang, S., Kong, W., Ren, L. and ZHI, D., 2021. Research on misuses and modification of coupling coordination degree model in China. Journal of Natural Resources, 36, 793-810. https://doi.org/10.31497/zrzyxb.20210319 + +[2] Fan, D., Ke, H. and Cao, R., 2024. Modification and improvement of coupling coordination degree model. Stat. Decis, 40, 41-46. https://doi.org/10.13546/j.cnki.tjyjc.2024.22.007 + +[3] Tang, P., Huang, J., Zhou, H., Fang, C., Zhan, Y., Huang, W., 2021. Local and telecoupling coordination degree model of urbanization and the eco-environment based on RS and GIS: A case study in the Wuhan urban agglomeration. Sustainable Cities and Society 75, 103405. https://doi.org/10.1016/j.scs.2021.103405 + +[4] Li, Y., Jia, N., Zheng, L., Yin, C., Chen, K., Sun, N., Jiang, A., Wang, M., Chen, R., Zhou, Z., 2026. A meta-coupling analysis between three-dimensional urbanization and ecosystem services in China’s urban agglomerations. Communications Earth & Environment 7. https://doi.org/10.1038/s43247-025-03047-w From 5643a5608620d1bab621e8ab9ec6b7e176cd1a22 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 08/25] draft ccd vignette --- vignettes/ccd.Rmd | 8 ++++++-- 1 file changed, 6 insertions(+), 2 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index d9381cf..812ba34 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -32,18 +32,22 @@ $$ C = \left[ \frac{\prod_{i=1}^{n} U_i}{\left( \frac{1}{n} \sum_{i=1}^{n} U_i \right)^n} \right]^{\frac{1}{n}} $$ -Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. To address these issues, alternative formulations have been proposed by modifying the functional form of the coupling degree. +Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. To address these issues, several formulations have been proposed by modifying the functional form of the coupling degree. ## Modified Coupling Degree ### Modification by $\text{wang et al}^{[1]}$. +**First**, Wang et al. introduce a formulation that incorporates pairwise differences among subsystems while normalizing their relative magnitudes: + $$ 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}}} $$ ### Modification by $\text{fan et al}^{[2]}$. +**Alternatively**, Fan et al. propose a simplified structure derived from variance-like dispersion, which directly captures the imbalance among subsystem indicators: + $$ C = 1-2\sqrt{\frac{n\sum_{i=1}^n U_i^2 - \left(\sum_{i=1}^n U_i\right)^2}{n^2}} $$ @@ -60,7 +64,7 @@ where $\alpha_i$ are weights with $\sum \alpha_i = 1$. ## Coordination Degree -The coordination degree $D$ integrates interaction and development: +The coordination degree $D$ integrates interaction $C$ and development $T$: $$ D = \sqrt{C \times T} From 21e42e1edb122f8bb11bcc87d67413c109660c4d Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 09/25] draft ccd vignette --- vignettes/ccd.Rmd | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 812ba34..c3bc987 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -77,7 +77,7 @@ where ## Metacoupling Perspective -The CCD framework can be extended under the **metacoupling framework**, distinguishing: +The CCD framework can be extended under the $\text{metacoupling framework}^{[3,4]}$, distinguishing: - **Intracoupling** - **Pericoupling** - **Telecoupling** From e888cead048151ec6935d728af683278b51fa232 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 10/25] draft ccd vignette --- vignettes/ccd.Rmd | 1 + 1 file changed, 1 insertion(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index c3bc987..7bb0dfe 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -78,6 +78,7 @@ where ## Metacoupling Perspective The CCD framework can be extended under the $\text{metacoupling framework}^{[3,4]}$, distinguishing: + - **Intracoupling** - **Pericoupling** - **Telecoupling** From 4adaf3e4a774f9c86bd4dc9e80604dfe0ae34752 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 11/25] draft ccd vignette --- vignettes/ccd.Rmd | 15 +++++++++++++++ 1 file changed, 15 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 7bb0dfe..9ed1b1f 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -85,6 +85,21 @@ The CCD framework can be extended under the $\text{metacoupling framework}^{[3,4 This enables cross-scale analysis of coupling. +# Example Cases + +## Install necessary packages and load data + +```{r install_pkgs, eval = FALSE, echo = TRUE} +install.packages(c("sdsfun", "coupling", "tmap"), dep = TRUE) +``` + +Load the `gzma` dataset from the `sdsfun` package: + +```{r load_data} +gzma = sf::read_sf(system.file('extdata/gzma.gpkg',package = 'sdsfun')) +gzma +``` + ## References From dfc43e9254b65f64a59eeca680d722808ad081cf Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 12/25] draft ccd vignette --- vignettes/ccd.Rmd | 7 +++++++ 1 file changed, 7 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 9ed1b1f..007a6ef 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -100,6 +100,13 @@ gzma = sf::read_sf(system.file('extdata/gzma.gpkg',package = 'sdsfun')) gzma ``` +Normalize the `*_Score` columns: + +```{r normalize_score} +dt = apply(sf::st_drop_geometry(gzma), 2, + \(.x) (.x - min(.x)) / (max(.x) - min(.x))) +head(dt) +``` ## References From 5e801519f4a845ccdf2921d7055979faae9a3d3e Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 13/25] draft ccd vignette --- vignettes/ccd.Rmd | 14 ++++++++++++++ 1 file changed, 14 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 007a6ef..86f2bf7 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -108,6 +108,20 @@ dt = apply(sf::st_drop_geometry(gzma), 2, head(dt) ``` +## Analysis of coupling coordination degree + +```{r ccd_standard} +ccd_standard = coupling::ccd(dt) +``` + +```{r ccd_wang} +ccd_wang = coupling::ccd(dt, method = "wang") +``` + +```{r ccd_fan} +ccd_fan = coupling::ccd(dt, method = "fan") +``` + ## 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 From 78c7e5e4fbe1f6669d6b08611bdb7c0f4fc5ae8c Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 14/25] draft ccd vignette --- vignettes/ccd.Rmd | 5 ++++- 1 file changed, 4 insertions(+), 1 deletion(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 86f2bf7..9550120 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -90,7 +90,7 @@ This enables cross-scale analysis of coupling. ## Install necessary packages and load data ```{r install_pkgs, eval = FALSE, echo = TRUE} -install.packages(c("sdsfun", "coupling", "tmap"), dep = TRUE) +install.packages(c("sdsfun", "coupling", "ggplot2"), dep = TRUE) ``` Load the `gzma` dataset from the `sdsfun` package: @@ -112,14 +112,17 @@ head(dt) ```{r ccd_standard} ccd_standard = coupling::ccd(dt) +head(ccd_standard) ``` ```{r ccd_wang} ccd_wang = coupling::ccd(dt, method = "wang") +head(ccd_wang) ``` ```{r ccd_fan} ccd_fan = coupling::ccd(dt, method = "fan") +head(ccd_fan) ``` ## References From 56771020f2f38e03f84235e89f9dbc423a9fc08c Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 15/25] draft ccd vignette --- vignettes/ccd.Rmd | 16 +++++++++++++++- 1 file changed, 15 insertions(+), 1 deletion(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 9550120..72087e4 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -90,7 +90,7 @@ This enables cross-scale analysis of coupling. ## Install necessary packages and load data ```{r install_pkgs, eval = FALSE, echo = TRUE} -install.packages(c("sdsfun", "coupling", "ggplot2"), dep = TRUE) +install.packages(c("sdsfun", "coupling", "tidyr", "dplyr", "ggplot2"), dep = TRUE) ``` Load the `gzma` dataset from the `sdsfun` package: @@ -125,6 +125,20 @@ ccd_fan = coupling::ccd(dt, method = "fan") head(ccd_fan) ``` +```{r fig_ccd, fig.width=6.5,fig.height=2.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 1**. SURD decomposition results between climatic and topographic factors and npp.")} +ccd_df = do.call(cbind, list(ccd_standard, ccd_wang, ccd_fan)) +names(ccd_df) = paste0(rep(c("standard", "wang", "fan"), each = 2), + "_", rep(c("C", "D"), times = 3)) +fig1 = ccd_df |> + sf::st_set_geometry(sf::st_geometry(gzma)) |> + tidyr::pivot_longer(-geometry, names_to = "var", values_to = "val") |> + dplyr::mutate(var = factor(var, levels = names(ccd_df))) |> + ggplot2::ggplot() + + ggplot2::geom_sf(ggplot2::aes(fill = val), color = "grey40", lwd = 0.15) + + ggplot2::facet_wrap(~var, ncol = 2) +fig1 + ggview::canvas(4.5,6.8) +``` + ## 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 From e18ccce490656d6b09a262a5e06d7d6d164a7f37 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 16/25] draft ccd vignette --- vignettes/ccd.Rmd | 20 +++++++++++++++++--- 1 file changed, 17 insertions(+), 3 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 72087e4..b29d1ca 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -125,7 +125,7 @@ ccd_fan = coupling::ccd(dt, method = "fan") head(ccd_fan) ``` -```{r fig_ccd, fig.width=6.5,fig.height=2.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 1**. SURD decomposition results between climatic and topographic factors and npp.")} +```{r fig_ccd,fig.width=4.5,fig.height=6.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 1**. Spatial distribution of CCD components across three estimation methods. Panels display component C and component D derived from the standard, Wang, and Fan methods, respectively.")} ccd_df = do.call(cbind, list(ccd_standard, ccd_wang, ccd_fan)) names(ccd_df) = paste0(rep(c("standard", "wang", "fan"), each = 2), "_", rep(c("C", "D"), times = 3)) @@ -135,8 +135,22 @@ fig1 = ccd_df |> dplyr::mutate(var = factor(var, levels = names(ccd_df))) |> ggplot2::ggplot() + ggplot2::geom_sf(ggplot2::aes(fill = val), color = "grey40", lwd = 0.15) + - ggplot2::facet_wrap(~var, ncol = 2) -fig1 + ggview::canvas(4.5,6.8) + ggplot2::scale_fill_gradientn( + name = "degree", + colors = c("#ffffcc", "#d9f0a3", "#addd8e", + "#78c679", "#31a354", "#006837") + ) + + ggplot2::facet_wrap(~var, ncol = 2) + + ggplot2::theme_bw(base_family = "serif") + + ggplot2::theme( + panel.grid = ggplot2::element_blank(), + axis.text = ggplot2::element_blank(), + axis.ticks = ggplot2::element_blank(), + strip.text = ggplot2::element_text(face = "bold", size = 15), + legend.title = ggplot2::element_text(size = 16.5), + legend.text = ggplot2::element_text(size = 15) + ) +fig1 ``` ## References From 2be4bb966f42ad7db5ade2f07a6230b178ae7d8f Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 17/25] draft ccd vignette --- vignettes/ccd.Rmd | 2 ++ 1 file changed, 2 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index b29d1ca..3691365 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -93,6 +93,8 @@ This enables cross-scale analysis of coupling. install.packages(c("sdsfun", "coupling", "tidyr", "dplyr", "ggplot2"), dep = TRUE) ``` +The `gzma` dataset represents the *Data of Social Space Quality in Guangzhou Metropolitan Areas of China (2010)*. It contains multiple indicators describing urban social space conditions. In particular, four key variables correspond to subsystem scores, including population stability (`PS_Score`), educational level (`EL_Score`), occupational hierarchy (`OH_Score`), and income level (`IL_Score `). + Load the `gzma` dataset from the `sdsfun` package: ```{r load_data} From 2c210f4335cf2dd21830f83ccbe282d311de146f Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 18/25] draft ccd vignette --- vignettes/ccd.Rmd | 6 ++++++ 1 file changed, 6 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 3691365..0f38fef 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -155,6 +155,12 @@ fig1 = ccd_df |> fig1 ``` +## A Meta-Coupling Analysis + +Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Spatial interactions among neighboring units are further weighted using an inverse distance scheme. The calculation of the coupling coordination degree adopts the formulation proposed by $\text{wang et al}^{[1]}$. + + + ## 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 From c591b8cd456ec0e11aff6c75ba239090bdcfa78f Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 19/25] draft ccd vignette --- vignettes/ccd.Rmd | 16 +++++++++++++--- 1 file changed, 13 insertions(+), 3 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 0f38fef..18727f1 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -157,9 +157,19 @@ fig1 ## A Meta-Coupling Analysis -Due to data limitations, here we focus on **peri-coupling** based on a Queen contiguity structure. Spatial interactions 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 $\text{wang et al}^{[1]}$. + +```{r peri_coupling} +nb = sdsfun::spdep_nb(gzma) +swm_peri = sdsfun::inverse_distance_swm(gzma) +for (i in seq_len(nrow(gzma))) { + swm_peri[i, seq_len(nrow(gzma))[-nb[[i]]]] = 0 +} +swm_peri = apply(swm_peri, 1, \(.x) .x / sum(.x)) + +mc_wang = coupling::metacoupling(dt, swm_peri = swm_peri, method = "wang") +head(mc_wang) +``` ## References From feac687f919dbc05fee51ef091aafaa3a2a181c8 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 20/25] draft ccd vignette --- vignettes/ccd.Rmd | 27 +++++++++++++++++++++++++++ 1 file changed, 27 insertions(+) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 18727f1..813256d 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -171,6 +171,33 @@ mc_wang = coupling::metacoupling(dt, swm_peri = swm_peri, method = "wang") head(mc_wang) ``` +```{r fig_metacoupling,fig.width=4.5,fig.height=4.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 2**. Spatial distribution of intra- and pericoupling CCD components based on the Wang formulation. Panels display coupling degree (C) and coordination degree (D) for intra- and pericoupling, respectively.")} +fig2 = mc_wang |> + dplyr::select(dplyr::all_of(c("Intra_C", "Intra_D", "Peri_C", "Peri_D"))) |> + sf::st_set_geometry(sf::st_geometry(gzma)) |> + tidyr::pivot_longer(-geometry, names_to = "var", values_to = "val") |> + dplyr::mutate(var = factor(var, + levels = c("Intra_C", "Intra_D", "Peri_C", "Peri_D"))) |> + ggplot2::ggplot() + + ggplot2::geom_sf(ggplot2::aes(fill = val), color = "grey40", lwd = 0.15) + + ggplot2::scale_fill_gradientn( + name = "degree", + colors = c("#ffffcc", "#d9f0a3", "#addd8e", + "#78c679", "#31a354", "#006837") + ) + + ggplot2::facet_wrap(~var, ncol = 2) + + ggplot2::theme_bw(base_family = "serif") + + ggplot2::theme( + panel.grid = ggplot2::element_blank(), + axis.text = ggplot2::element_blank(), + axis.ticks = ggplot2::element_blank(), + strip.text = ggplot2::element_text(face = "bold", size = 15), + legend.title = ggplot2::element_text(size = 16.5), + legend.text = ggplot2::element_text(size = 15) + ) +fig2 + ggview::canvas(4.5,4.5) +``` + ## 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 From 69bbc07414cb661602bc20fd306b09827a50f1aa Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 00:00:01 +0800 Subject: [PATCH 21/25] draft ccd vignette --- vignettes/ccd.Rmd | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 813256d..71f0de3 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -2,7 +2,7 @@ title: "Coupling Coordination Degree Model and Metacoupling Analysis" author: "Wenbo Lyu" date: | - | Last update: 2026-05-11 + | Last update: 2026-05-12 | Last run: `r Sys.Date()` output: rmarkdown::html_vignette vignette: > @@ -195,7 +195,7 @@ fig2 = mc_wang |> legend.title = ggplot2::element_text(size = 16.5), legend.text = ggplot2::element_text(size = 15) ) -fig2 + ggview::canvas(4.5,4.5) +fig2 ``` ## References From dccc661e96adb499b903b173c2bb192e467ae742 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Thu, 18 Jun 2026 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z#Y(sy+X2}l3lc~OMD2q)RCurY3D4QWe<7Q_aPz~}8f!o`9Q^1%uxE$}|Fdmh;(uO= mJihmTUihE&_B|eDYsyounB6 literal 0 HcmV?d00001 diff --git a/vignettes/ccd.Rmd b/vignettes/ccd.Rmd index 71f0de3..3e66cc9 100644 --- a/vignettes/ccd.Rmd +++ b/vignettes/ccd.Rmd @@ -11,14 +11,7 @@ vignette: > %\VignetteEncoding{UTF-8} --- -```{r, include = FALSE} -knitr::opts_chunk$set( - collapse = TRUE, - message = FALSE, - comment = "##", - fig.path = "man/figures/ccd/" -) -``` + # Introduction @@ -89,7 +82,8 @@ This enables cross-scale analysis of coupling. ## Install necessary packages and load data -```{r install_pkgs, eval = FALSE, echo = TRUE} + +``` r install.packages(c("sdsfun", "coupling", "tidyr", "dplyr", "ggplot2"), dep = TRUE) ``` @@ -97,37 +91,90 @@ The `gzma` dataset represents the *Data of Social Space Quality in Guangzhou Met Load the `gzma` dataset from the `sdsfun` package: -```{r load_data} + +``` r gzma = sf::read_sf(system.file('extdata/gzma.gpkg',package = 'sdsfun')) gzma +## Simple feature collection with 118 features and 4 fields +## Geometry type: POLYGON +## Dimension: XY +## Bounding box: xmin: 113.1485 ymin: 22.94659 xmax: 113.5628 ymax: 23.33026 +## Geodetic CRS: WGS 84 +## # A tibble: 118 × 5 +## PS_Score EL_Score OH_Score IL_Score geom +## +## 1 7.21 4.64 4.75 2.64 ((113.2797 23.13359, 113.2715 23.13413, 113.2682 23.13371, … +## 2 3.55 3.81 3.91 4.06 ((113.2519 23.15353, 113.2497 23.15545, 113.254 23.15774, 1… +## 3 7.94 4.69 4.86 3.31 ((113.2815 23.12902, 113.2749 23.12969, 113.2732 23.12523, … +## 4 8.22 4.93 4.92 3.74 ((113.3098 23.12458, 113.3046 23.12448, 113.3026 23.12642, … +## 5 7.84 4.74 4.98 4.69 ((113.3099 23.11566, 113.3087 23.11542, 113.2957 23.11531, … +## 6 8.12 5.13 4.98 3.92 ((113.2864 23.13354, 113.2863 23.135, 113.2884 23.1375, 113… +## 7 8.30 5.18 4.87 3.77 ((113.2797 23.13359, 113.2799 23.13956, 113.274 23.14182, 1… +## 8 5.14 4.43 4.41 4.13 ((113.3013 23.16168, 113.2985 23.16208, 113.296 23.16051, 1… +## 9 5.92 4.18 4.37 2.29 ((113.2631 23.12832, 113.2586 23.12813, 113.2592 23.12228, … +## 10 6.99 4.32 4.24 2.72 ((113.2747 23.12164, 113.2727 23.12362, 113.2732 23.12523, … +## # ℹ 108 more rows ``` Normalize the `*_Score` columns: -```{r normalize_score} + +``` r dt = apply(sf::st_drop_geometry(gzma), 2, \(.x) (.x - min(.x)) / (max(.x) - min(.x))) head(dt) +## PS_Score EL_Score OH_Score IL_Score +## 1 0.8179733 0.3246648 0.6590316 0.1308531 +## 2 0.3020233 0.1318888 0.4046987 0.5173794 +## 3 0.9209903 0.3353516 0.6921477 0.3141320 +## 4 0.9604095 0.3914758 0.7099999 0.4316421 +## 5 0.9061589 0.3473603 0.7297774 0.6909494 +## 6 0.9456379 0.4391423 0.7304117 0.4792905 ``` ## Analysis of coupling coordination degree -```{r ccd_standard} + +``` r ccd_standard = coupling::ccd(dt) head(ccd_standard) +## C D +## 1 0.8051958 0.6237105 +## 2 0.8914577 0.5497290 +## 3 0.8999423 0.7134825 +## 4 0.9346128 0.7632959 +## 5 0.9440912 0.7944703 +## 6 0.9519923 0.7858001 ``` -```{r ccd_wang} + +``` r ccd_wang = coupling::ccd(dt, method = "wang") head(ccd_wang) +## C D +## 1 0.4722274 0.4776480 +## 2 0.6211236 0.4588675 +## 3 0.5375842 0.5514412 +## 4 0.5861986 0.6045044 +## 5 0.6640321 0.6662930 +## 6 0.6319211 0.6402164 ``` -```{r ccd_fan} + +``` r ccd_fan = coupling::ccd(dt, method = "fan") head(ccd_fan) +## C D +## 1 0.4593785 0.4711049 +## 2 0.7164548 0.4928249 +## 3 0.4915051 0.5272784 +## 4 0.5399620 0.5801746 +## 5 0.5951898 0.6308098 +## 6 0.5907777 0.6190239 ``` -```{r fig_ccd,fig.width=4.5,fig.height=6.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 1**. Spatial distribution of CCD components across three estimation methods. Panels display component C and component D derived from the standard, Wang, and Fan methods, respectively.")} + +``` r ccd_df = do.call(cbind, list(ccd_standard, ccd_wang, ccd_fan)) names(ccd_df) = paste0(rep(c("standard", "wang", "fan"), each = 2), "_", rep(c("C", "D"), times = 3)) @@ -155,11 +202,14 @@ fig1 = ccd_df |> fig1 ``` +![**Figure 1**. Spatial distribution of CCD components across three estimation methods. Panels display component C and component D derived from the standard, Wang, and Fan methods, respectively.](../man/figures/ccd/fig_ccd-1.png) + ## 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 $\text{wang et al}^{[1]}$. -```{r peri_coupling} + +``` r nb = sdsfun::spdep_nb(gzma) swm_peri = sdsfun::inverse_distance_swm(gzma) for (i in seq_len(nrow(gzma))) { @@ -169,9 +219,17 @@ swm_peri = apply(swm_peri, 1, \(.x) .x / sum(.x)) mc_wang = coupling::metacoupling(dt, swm_peri = swm_peri, method = "wang") head(mc_wang) +## Intra_C Intra_D Peri_C Peri_D Tele_C Tele_D +## 1 0.4722274 0.4776480 0.7414392 0.7507625 0 0 +## 2 0.6211236 0.4588675 0.6712215 0.5061883 0 0 +## 3 0.5375842 0.5514412 0.4539894 0.4644758 0 0 +## 4 0.5861986 0.6045044 0.6692548 0.6808108 0 0 +## 5 0.6640321 0.6662930 0.6880871 0.6870927 0 0 +## 6 0.6319211 0.6402164 0.6064480 0.6032699 0 0 ``` -```{r fig_metacoupling,fig.width=4.5,fig.height=4.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 2**. Spatial distribution of intra- and pericoupling CCD components based on the Wang formulation. Panels display coupling degree (C) and coordination degree (D) for intra- and pericoupling, respectively.")} + +``` r fig2 = mc_wang |> dplyr::select(dplyr::all_of(c("Intra_C", "Intra_D", "Peri_C", "Peri_D"))) |> sf::st_set_geometry(sf::st_geometry(gzma)) |> @@ -198,6 +256,8 @@ fig2 = mc_wang |> fig2 ``` +![**Figure 2**. Spatial distribution of intra- and pericoupling CCD components based on the Wang formulation. Panels display coupling degree (C) and coordination degree (D) for intra- and pericoupling, respectively.](../man/figures/ccd/fig_metacoupling-1.png) + ## 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 diff --git a/vignettes/ccd.Rmd.orig b/vignettes/ccd.Rmd.orig new file mode 100644 index 0000000..71f0de3 --- /dev/null +++ b/vignettes/ccd.Rmd.orig @@ -0,0 +1,209 @@ +--- +title: "Coupling Coordination Degree Model and Metacoupling Analysis" +author: "Wenbo Lyu" +date: | + | Last update: 2026-05-12 + | Last run: `r Sys.Date()` +output: rmarkdown::html_vignette +vignette: > + %\VignetteIndexEntry{ccd} + %\VignetteEngine{knitr::rmarkdown} + %\VignetteEncoding{UTF-8} +--- + +```{r, include = FALSE} +knitr::opts_chunk$set( + collapse = TRUE, + message = FALSE, + comment = "##", + fig.path = "man/figures/ccd/" +) +``` + +# Introduction + +The **Coupling Coordination Degree (CCD) model** is widely used to quantify the degree of coupling and coordinated development among multiple subsystems. Originating from physics, it has been extensively applied in regional and human–environment systems. + +## Coupling Degree + +Given *n* normalized subsystem indicators $U_i$, the standard coupling degree $C$ is defined as: + +$$ +C = \left[ \frac{\prod_{i=1}^{n} U_i}{\left( \frac{1}{n} \sum_{i=1}^{n} U_i \right)^n} \right]^{\frac{1}{n}} +$$ + +Although widely used, this formulation may suffer from **scale sensitivity and over-amplification effects** due to the power structure. To address these issues, several formulations have been proposed by modifying the functional form of the coupling degree. + +## Modified Coupling Degree + +### Modification by $\text{wang et al}^{[1]}$. + +**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 $\text{fan et al}^{[2]}$. + +**Alternatively**, Fan et al. propose a simplified structure derived from variance-like dispersion, which directly captures the imbalance among subsystem indicators: + +$$ +C = 1-2\sqrt{\frac{n\sum_{i=1}^n U_i^2 - \left(\sum_{i=1}^n U_i\right)^2}{n^2}} +$$ + +## Comprehensive Development Index + +The overall development level is defined as: + +$$ +T = \sum_{i=1}^{n} \alpha_i U_i +$$ + +where $\alpha_i$ are weights with $\sum \alpha_i = 1$. + +## Coordination Degree + +The coordination degree $D$ integrates interaction $C$ and development $T$: + +$$ +D = \sqrt{C \times T} +$$ + +where +- $C$ measures coupling degree +- $T$ measures development level +- $D$ reflects coordinated development + +## Metacoupling Perspective + +The CCD framework can be extended under the $\text{metacoupling framework}^{[3,4]}$, distinguishing: + +- **Intracoupling** +- **Pericoupling** +- **Telecoupling** + +This enables cross-scale analysis of coupling. + +# Example Cases + +## Install necessary packages and load data + +```{r install_pkgs, eval = FALSE, echo = TRUE} +install.packages(c("sdsfun", "coupling", "tidyr", "dplyr", "ggplot2"), dep = TRUE) +``` + +The `gzma` dataset represents the *Data of Social Space Quality in Guangzhou Metropolitan Areas of China (2010)*. It contains multiple indicators describing urban social space conditions. In particular, four key variables correspond to subsystem scores, including population stability (`PS_Score`), educational level (`EL_Score`), occupational hierarchy (`OH_Score`), and income level (`IL_Score `). + +Load the `gzma` dataset from the `sdsfun` package: + +```{r load_data} +gzma = sf::read_sf(system.file('extdata/gzma.gpkg',package = 'sdsfun')) +gzma +``` + +Normalize the `*_Score` columns: + +```{r normalize_score} +dt = apply(sf::st_drop_geometry(gzma), 2, + \(.x) (.x - min(.x)) / (max(.x) - min(.x))) +head(dt) +``` + +## Analysis of coupling coordination degree + +```{r ccd_standard} +ccd_standard = coupling::ccd(dt) +head(ccd_standard) +``` + +```{r ccd_wang} +ccd_wang = coupling::ccd(dt, method = "wang") +head(ccd_wang) +``` + +```{r ccd_fan} +ccd_fan = coupling::ccd(dt, method = "fan") +head(ccd_fan) +``` + +```{r fig_ccd,fig.width=4.5,fig.height=6.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 1**. Spatial distribution of CCD components across three estimation methods. Panels display component C and component D derived from the standard, Wang, and Fan methods, respectively.")} +ccd_df = do.call(cbind, list(ccd_standard, ccd_wang, ccd_fan)) +names(ccd_df) = paste0(rep(c("standard", "wang", "fan"), each = 2), + "_", rep(c("C", "D"), times = 3)) +fig1 = ccd_df |> + sf::st_set_geometry(sf::st_geometry(gzma)) |> + tidyr::pivot_longer(-geometry, names_to = "var", values_to = "val") |> + dplyr::mutate(var = factor(var, levels = names(ccd_df))) |> + ggplot2::ggplot() + + ggplot2::geom_sf(ggplot2::aes(fill = val), color = "grey40", lwd = 0.15) + + ggplot2::scale_fill_gradientn( + name = "degree", + colors = c("#ffffcc", "#d9f0a3", "#addd8e", + "#78c679", "#31a354", "#006837") + ) + + ggplot2::facet_wrap(~var, ncol = 2) + + ggplot2::theme_bw(base_family = "serif") + + ggplot2::theme( + panel.grid = ggplot2::element_blank(), + axis.text = ggplot2::element_blank(), + axis.ticks = ggplot2::element_blank(), + strip.text = ggplot2::element_text(face = "bold", size = 15), + legend.title = ggplot2::element_text(size = 16.5), + legend.text = ggplot2::element_text(size = 15) + ) +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 $\text{wang et al}^{[1]}$. + +```{r peri_coupling} +nb = sdsfun::spdep_nb(gzma) +swm_peri = sdsfun::inverse_distance_swm(gzma) +for (i in seq_len(nrow(gzma))) { + swm_peri[i, seq_len(nrow(gzma))[-nb[[i]]]] = 0 +} +swm_peri = apply(swm_peri, 1, \(.x) .x / sum(.x)) + +mc_wang = coupling::metacoupling(dt, swm_peri = swm_peri, method = "wang") +head(mc_wang) +``` + +```{r fig_metacoupling,fig.width=4.5,fig.height=4.5,fig.dpi=300,fig.cap=knitr::asis_output("**Figure 2**. Spatial distribution of intra- and pericoupling CCD components based on the Wang formulation. Panels display coupling degree (C) and coordination degree (D) for intra- and pericoupling, respectively.")} +fig2 = mc_wang |> + dplyr::select(dplyr::all_of(c("Intra_C", "Intra_D", "Peri_C", "Peri_D"))) |> + sf::st_set_geometry(sf::st_geometry(gzma)) |> + tidyr::pivot_longer(-geometry, names_to = "var", values_to = "val") |> + dplyr::mutate(var = factor(var, + levels = c("Intra_C", "Intra_D", "Peri_C", "Peri_D"))) |> + ggplot2::ggplot() + + ggplot2::geom_sf(ggplot2::aes(fill = val), color = "grey40", lwd = 0.15) + + ggplot2::scale_fill_gradientn( + name = "degree", + colors = c("#ffffcc", "#d9f0a3", "#addd8e", + "#78c679", "#31a354", "#006837") + ) + + ggplot2::facet_wrap(~var, ncol = 2) + + ggplot2::theme_bw(base_family = "serif") + + ggplot2::theme( + panel.grid = ggplot2::element_blank(), + axis.text = ggplot2::element_blank(), + axis.ticks = ggplot2::element_blank(), + strip.text = ggplot2::element_text(face = "bold", size = 15), + legend.title = ggplot2::element_text(size = 16.5), + legend.text = ggplot2::element_text(size = 15) + ) +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 + +[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 + +[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 + +[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 From a6fa9dae65c78d96ecbb3fcef6b04dfef5b6ed15 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Fri, 19 Jun 2026 00:00:01 +0800 Subject: [PATCH 23/25] new suggesting dependences --- DESCRIPTION | 2 ++ 1 file changed, 2 insertions(+) diff --git a/DESCRIPTION b/DESCRIPTION index 6657e5e..0f6b827 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -17,12 +17,14 @@ LinkingTo: Rcpp, RcppThread Suggests: + gdverse, infoxtr, knitr, pc, Rcpp, RcppThread, rmarkdown, + sdsfun, spEDM Config/roxygen2/markdown: TRUE Config/roxygen2/version: 8.0.0 From fce4e6c189c273b76aa0fdb5ab2588661c9a00d9 Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Fri, 19 Jun 2026 00:00:01 +0800 Subject: [PATCH 24/25] new suggesting dependences --- DESCRIPTION | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/DESCRIPTION b/DESCRIPTION index 0f6b827..84ef0f3 100644 --- a/DESCRIPTION +++ b/DESCRIPTION @@ -26,6 +26,6 @@ Suggests: rmarkdown, sdsfun, spEDM +VignetteBuilder: knitr Config/roxygen2/markdown: TRUE Config/roxygen2/version: 8.0.0 -VignetteBuilder: knitr From 7155abb9f69e183e2c0df5aba30fdd2c18d5d97c Mon Sep 17 00:00:00 2001 From: SpatLyu Date: Fri, 19 Jun 2026 00:00:01 +0800 Subject: [PATCH 25/25] show vignette in pkg website --- _pkgdown.yml | 8 ++++---- 1 file changed, 4 insertions(+), 4 deletions(-) diff --git a/_pkgdown.yml b/_pkgdown.yml index 9f8a541..73a5e36 100644 --- a/_pkgdown.yml +++ b/_pkgdown.yml @@ -11,10 +11,10 @@ navbar: bg: custom components: articles: - # text: Vignettes - # menu: - # - text: Coupling Coordination Degree Model and Metacoupling Analysis - # href: articles/ccd.html + text: Vignettes + menu: + - text: Coupling Coordination Degree Model and Metacoupling Analysis + href: articles/ccd.html home: title: |