Lin's Concordance Correlation Coefficient (CCC)

Computes Lin's Concordance Correlation Coefficient (CCC) between observed and predicted values. Also returns Pearson's correlation coefficient and root mean squared error (RMSE). If the input is a grouped data frame (grouped_df), the function will return results for each group.

Usage

ccc(data, real, predito)

Arguments

data: A data frame containing the columns for observed and predicted values.
real: The column name (unquoted) corresponding to the observed values.
predito: The column name (unquoted) corresponding to the predicted values.

Value

A data frame with the following columns:

r: Pearson correlation coefficient
ccc: Lin's Concordance Correlation Coefficient
rmse: Root mean squared error

Details

The CCC is defined as:

$$\rho_c = \frac{2 \cdot \text{Cov}(x, y)}{\text{Var}(x) + \text{Var}(y) + (\bar{x} - \bar{y})^2}$$

where:

$\text{Cov}(x, y)$ is the covariance between observed and predicted values
$\text{Var}(x)$ and $\text{Var}(y)$ are the variances of the observed and predicted values
$\bar{x}$ and $\bar{y}$ are the means of the observed and predicted values

Examples

library(dplyr)
#> 
#> Attaching package: 'dplyr'
#> The following object is masked from 'package:pliman':
#> 
#>     %>%
#> The following objects are masked from 'package:stats':
#> 
#>     filter, lag
#> The following objects are masked from 'package:base':
#> 
#>     intersect, setdiff, setequal, union
library(pliman)
df <- data.frame(
  group = rep(c("A", "B"), each = 5),
  real = c(1:5, 2:6),
  predicted = c(1.1, 2, 2.9, 4.1, 5, 2.2, 3.1, 4, 4.8, 6.1)
)

# Without grouping
ccc(df, real, predicted)
#>          r       ccc      rmse
#> 1 0.997498 0.9970678 0.1140175

# With grouping
df |>
  group_by(group) |>
  ccc(real, predicted)
#> # A tibble: 2 × 4
#>   group     r   ccc   rmse
#>   <chr> <dbl> <dbl>  <dbl>
#> 1 A     0.999 0.999 0.0775
#> 2 B     0.996 0.995 0.141