R squared - traditional — rsq

Calculate the coefficient of determination using the traditional definition of R squared using sum of squares. For a measure of R squared that is strictly between (0, 1), see rsq().

rsq_trad(data, ...)

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

rsq_trad_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 rsq_trad_vec(), a single numeric value (or NA).

Details

The two estimates for the coefficient of determination, rsq() and rsq_trad(), differ by their formula. The former guarantees a value on (0, 1) while the latter can generate inaccurate values when the model is non-informative (see the examples). Both are measures of consistency/correlation and not of accuracy.

References

Kvalseth. Cautionary note about \(R^2\). American Statistician (1985) vol. 39 (4) pp. 279-285.

Author

Max Kuhn

Examples

# Supply truth and predictions as bare column names
rsq_trad(solubility_test, solubility, prediction)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 rsq_trad standard       0.879

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) %>%
  rsq_trad(solubility, prediction)

metric_results
#> # A tibble: 10 × 4
#>    resample .metric  .estimator .estimate
#>    <chr>    <chr>    <chr>          <dbl>
#>  1 1        rsq_trad standard       0.870
#>  2 10       rsq_trad standard       0.878
#>  3 2        rsq_trad standard       0.891
#>  4 3        rsq_trad standard       0.913
#>  5 4        rsq_trad standard       0.889
#>  6 5        rsq_trad standard       0.857
#>  7 6        rsq_trad standard       0.872
#>  8 7        rsq_trad standard       0.852
#>  9 8        rsq_trad standard       0.915
#> 10 9        rsq_trad standard       0.883

# Resampled mean estimate
metric_results %>%
  summarise(avg_estimate = mean(.estimate))
#> # A tibble: 1 × 1
#>   avg_estimate
#>          <dbl>
#> 1        0.882
# With uninformitive data, the traditional version of R^2 can return
# negative values.
set.seed(2291)
solubility_test$randomized <- sample(solubility_test$prediction)
rsq(solubility_test, solubility, randomized)
#> # A tibble: 1 × 3
#>   .metric .estimator .estimate
#>   <chr>   <chr>          <dbl>
#> 1 rsq     standard     0.00199
rsq_trad(solubility_test, solubility, randomized)
#> # A tibble: 1 × 3
#>   .metric  .estimator .estimate
#>   <chr>    <chr>          <dbl>
#> 1 rsq_trad standard       -1.01

R squared - traditional