Normalized Gini coefficient

Compute the normalized Gini coefficient, which measures the ranking ability of a regression model based on the Lorenz curve. This metric is useful for evaluating models that predict risk or loss costs, such as insurance pricing models.

Usage

gini_coef(data, ...)

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

gini_coef_vec(truth, estimate, 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.

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().

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 gini_coef_vec(), a single numeric value (or NA).

Details

The normalized Gini coefficient is a metric that should be maximized. The output ranges from 0 to 1, with 1 indicating perfect ranking ability where predicted values perfectly rank the true values.

The Gini coefficient is calculated from the Lorenz curve, which plots the cumulative proportion of the total truth values against the cumulative proportion of observations when sorted by predicted values. The raw Gini is the area between the Lorenz curve and the diagonal line of equality. The normalized Gini divides this by the maximum possible Gini (achieved when observations are sorted by the true values).

The formula is:

$$\text{Normalized Gini} = \frac{G(\text{estimate})}{G(\text{truth})}$$

where \(G(x)\) is the Gini coefficient when sorting by \(x\).

Note that gini_coef() is a regression metric based on ranking, distinct from gain_capture() which is a classification metric.

Unlike many other metrics, gini_coef() is not symmetric with respect to truth and estimate. The estimate values determine the sorting order, while the truth values are accumulated along the Lorenz curve. Swapping them will produce different results.

When the true values are constant (zero variance), the Gini coefficient is undefined and NA is returned with a warning.

See also

All numeric metrics

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

Examples

# Supply truth and predictions as bare column names
gini_coef(solubility_test, solubility, prediction)
#> # A tibble: 1 × 3
#>   .metric   .estimator .estimate
#>   <chr>     <chr>          <dbl>
#> 1 gini_coef standard       0.935

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) |>
  gini_coef(solubility, prediction)

metric_results
#> # A tibble: 10 × 4
#>    resample .metric   .estimator .estimate
#>    <chr>    <chr>     <chr>          <dbl>
#>  1 1        gini_coef standard       0.929
#>  2 10       gini_coef standard       0.946
#>  3 2        gini_coef standard       0.940
#>  4 3        gini_coef standard       0.945
#>  5 4        gini_coef standard       0.946
#>  6 5        gini_coef standard       0.923
#>  7 6        gini_coef standard       0.931
#>  8 7        gini_coef standard       0.921
#>  9 8        gini_coef standard       0.951
#> 10 9        gini_coef standard       0.936

# Resampled mean estimate
metric_results |>
  summarise(avg_estimate = mean(.estimate))
#> # A tibble: 1 × 1
#>   avg_estimate
#>          <dbl>
#> 1        0.937