ccc: Concordance correlation coefficient

In yardstick: Tidy Characterizations of Model Performance

Concordance correlation coefficient

Description

Calculate the concordance correlation coefficient.

Usage

ccc(data, ...)

## S3 method for class 'data.frame'
ccc(
  data,
  truth,
  estimate,
  bias = FALSE,
  na_rm = TRUE,
  case_weights = NULL,
  ...
)

ccc_vec(truth, estimate, bias = FALSE, na_rm = TRUE, case_weights = NULL, ...)

Arguments

data	A data.frame containing the columns specified by the truth and estimate arguments.
...	Not currently used.
truth	The column identifier for the true results (that is numeric). This should be an unquoted column name although this argument is passed by expression and supports quasiquotation (you can unquote column names). For ⁠_vec()⁠ functions, a numeric vector.
estimate	The column identifier for the predicted results (that is also numeric). As with truth this can be specified different ways but the primary method is to use an unquoted variable name. For ⁠_vec()⁠ functions, a numeric vector.
bias	A logical; should the biased estimate of variance be used (as is Lin (1989))?
na_rm	A logical value indicating whether NA values should be stripped before the computation proceeds.
case_weights	The optional column identifier for case weights. This should be an unquoted column name that evaluates to a numeric column in data. For ⁠_vec()⁠ functions, a numeric vector, hardhat::importance_weights(), or hardhat::frequency_weights().

Details

ccc() is a metric of both consistency/correlation and accuracy, while metrics such as rmse() are strictly for accuracy and metrics such as rsq() are strictly for consistency/correlation

CCC is a metric that should be maximized. The output ranges from -1 to 1, with 1 indicating perfect agreement.

The formula for CCC is:

\text{CCC} = \frac{2 \cdot \text{cov}(\text{truth}, \text{estimate})}{\text{var}(\text{truth}) + \text{var}(\text{estimate}) + (\bar{\text{truth}} - \bar{\text{estimate}})^2}

Value

A tibble with columns .metric, .estimator, and .estimate and 1 row of values.

For grouped data frames, the number of rows returned will be the same as the number of groups.

For ccc_vec(), a single numeric value (or NA).

Author(s)

Max Kuhn

References

Lin, L. (1989). A concordance correlation coefficient to evaluate reproducibility. Biometrics, 45 (1), 255-268.

Nickerson, C. (1997). A note on "A concordance correlation coefficient to evaluate reproducibility". Biometrics, 53(4), 1503-1507.

See Also

All numeric metrics

Other numeric metrics: gini_coef(), huber_loss(), huber_loss_pseudo(), iic(), mae(), mape(), mase(), mpe(), msd(), mse(), poisson_log_loss(), rmse(), rmse_relative(), rpd(), rpiq(), rsq(), rsq_trad(), smape()

Other consistency metrics: rpd(), rpiq(), rsq(), rsq_trad()

Other accuracy metrics: huber_loss(), huber_loss_pseudo(), iic(), mae(), mape(), mase(), mpe(), msd(), mse(), poisson_log_loss(), rmse(), rmse_relative(), smape()

Examples

# Supply truth and predictions as bare column names
ccc(solubility_test, solubility, prediction)

library(dplyr)

set.seed(1234)
size <- 100
times <- 10

# create 10 resamples
solubility_resampled <- bind_rows(
  replicate(
    n = times,
    expr = sample_n(solubility_test, size, replace = TRUE),
    simplify = FALSE
  ),
  .id = "resample"
)

# Compute the metric by group
metric_results <- solubility_resampled |>
  group_by(resample) |>
  ccc(solubility, prediction)

metric_results

# Resampled mean estimate
metric_results |>
  summarise(avg_estimate = mean(.estimate))
# Using a different value of 'bias'... if you are adding the metric to a
# metric set, you can create a new metric function with the updated argument
# value:

ccc_bias <- metric_tweak("ccc_bias", ccc, bias = TRUE)
multi_metrics <- metric_set(ccc, ccc_bias)
multi_metrics(solubility_test, solubility, prediction)

yardstick documentation built on April 8, 2026, 1:06 a.m.