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System Evaluation Functions for Coupling and Obstacle Analysis

Source: R/eval_system.R
system_evaluation.Rd

These functions provide tools for system-level evaluation in multi-indicator systems:

  • coupling_degree(): Computes coupling degree, coordination index, and coupling coordination degree for subsystems.

  • obstacle_degree(): Computes obstacle degrees for secondary indicators to identify key constraints in the system, enabling batch processing with tidyverse for grouping and summarization.

Usage

coupling_degree(data, w = NULL, id_cols = NULL, type = "standard")

obstacle_degree(data, w = NULL, id_cols = NULL, scaled = FALSE)

Arguments

data

A data frame with normalized scores (usually in [0, 1]) as columns.

w

Optional vector of weights for indicators or subsystems; defaults to equal weights if NULL.

id_cols

Optional character vector of column names in data to preserve as identifiers (not used in calculations).

type

Either "standard" for the standard coupling formula (results concentrated near 1) or "adjusted" for the revised formula (results more uniformly distributed in [0, 1]), as proposed by Wang Shujia, Kong Wei, et al. in "Misconceptions and Corrections of Domestic Coupling Coordination Degree Models, Journal of Natural Resources, 2021, 36(3): 793–810 (In Chinese)"

scaled

Logical. Whether to perform row normalization on obstacle degrees (default FALSE).

Value

A tibble depending on the function:

coupling_degree

A tibble with columns:

  • ID: Identifier columns specified by id_cols (if provided).

  • coupling: Coupling Degree (range 0-1).

  • coord: Coordination Index (range 0-1).

  • coupling_coord: Coupling Coordination Degree (range 0-1).

obstacle_degree

A tibble with:

  • ID: Identifier columns specified by id_cols (if provided).

  • Columns for secondary indicator obstacle degrees (O_{ij} = (1 - X_{ij}) * w_{ij}).

Suitable for grouping and summarizing (e.g., with tidyverse) to compute primary indicator obstacle degrees (\( U_i \)).

Examples

# Sample normalized subsystem scores
df = data.frame(
  ID = LETTERS[1:6],
  s1 = c(0.0162, 0.1782, 0.5490, 0.6730, 0.0207, 0.9875),
  s2 = c(0.2720, 0.6824, 0.0593, 0.4812, 0.8891, 0.5573),
  s3 = c(0.2655, 0.3721, 0.5729, 0.9082, 0.2017, 0.8984)
)
# Coupling Degree Analysis
coupling_degree(df, id_cols = "ID")        # Equal weights
#> # A tibble: 6 × 4
#>   ID    coupling coord coupling_coord
#>   <chr>    <dbl> <dbl>          <dbl>
#> 1 A        0.571 0.185          0.325
#> 2 B        0.867 0.411          0.597
#> 3 C        0.674 0.394          0.515
#> 4 D        0.967 0.687          0.815
#> 5 E        0.418 0.370          0.393
#> 6 F        0.971 0.814          0.889
coupling_degree(df, c(0.4, 0.3, 0.3), id_cols = "ID",
                type = "adjusted")         # "adjusted" coupling degree
#> # A tibble: 6 × 4
#>   ID    coupling coord coupling_coord
#>   <chr>    <dbl> <dbl>          <dbl>
#> 1 A        0.447 0.168          0.274
#> 2 B        0.501 0.388          0.440
#> 3 C        0.455 0.409          0.432
#> 4 D        0.669 0.686          0.678
#> 5 E        0.175 0.336          0.242
#> 6 F        0.715 0.832          0.771
# Obstacle Degree Analysis
obstacle_degree(df, id_cols = "ID")        # Equal weights
#> # A tibble: 6 × 4
#>   ID         s1     s2     s3
#>   <chr>   <dbl>  <dbl>  <dbl>
#> 1 A     0.328   0.243  0.245 
#> 2 B     0.274   0.106  0.209 
#> 3 C     0.150   0.314  0.142 
#> 4 D     0.109   0.173  0.0306
#> 5 E     0.326   0.0370 0.266 
#> 6 F     0.00417 0.148  0.0339
obstacle_degree(df, c(0.4, 0.3, 0.3), id_cols = "ID")
#> # A tibble: 6 × 4
#>   ID         s1     s2     s3
#>   <chr>   <dbl>  <dbl>  <dbl>
#> 1 A     0.394   0.218  0.220 
#> 2 B     0.329   0.0953 0.188 
#> 3 C     0.180   0.282  0.128 
#> 4 D     0.131   0.156  0.0275
#> 5 E     0.392   0.0333 0.239 
#> 6 F     0.00500 0.133  0.0305