ww_willmott_d: Willmott's d and related values

In waywiser: Ergonomic Methods for Assessing Spatial Models

Willmott's d and related values

Description

These functions calculate Willmott's d value, a proposed replacement for R2 which better differentiates between types and magnitudes of possible covariations. Additional functions calculate systematic and unsystematic components of MSE and RMSE; the sum of the systematic and unsystematic components of MSE equal total MSE (though the same is not true for RMSE).

Usage

ww_willmott_d(data, ...)

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

ww_willmott_d_vec(truth, estimate, na_rm = TRUE, ...)

ww_willmott_d1(data, ...)

## S3 method for class 'data.frame'
ww_willmott_d1(data, truth, estimate, na_rm = TRUE, ...)

ww_willmott_d1_vec(truth, estimate, na_rm = TRUE, ...)

ww_willmott_dr(data, ...)

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

ww_willmott_dr_vec(truth, estimate, na_rm = TRUE, ...)

ww_systematic_mse(data, ...)

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

ww_systematic_mse_vec(truth, estimate, na_rm = TRUE, ...)

ww_unsystematic_mse(data, ...)

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

ww_unsystematic_mse_vec(truth, estimate, na_rm = TRUE, ...)

ww_systematic_rmse(data, ...)

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

ww_systematic_rmse_vec(truth, estimate, na_rm = TRUE, ...)

ww_unsystematic_rmse(data, ...)

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

ww_unsystematic_rmse_vec(truth, estimate, na_rm = TRUE, ...)

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.

Details

Values of d and d1 range from 0 to 1, with 1 indicating perfect agreement. Values of dr range from -1 to 1, with 1 similarly indicating perfect agreement. Values of RMSE are in the same units as truth and estimate, while values of MSE are in squared units. truth and estimate must be the same length. This function is not explicitly spatial and as such can be applied to data with any number of dimensions and any coordinate reference system.

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 ⁠_vec()⁠ functions, a single value (or NA).

References

Willmott, C. J. 1981. "On the Validation of Models". Physical Geography 2(2), pp 184-194, doi: 10.1080/02723646.1981.10642213.

Willmott, C. J. 1982. "Some Comments on the Evaluation of Model Performance". Bulletin of the American Meteorological Society 63(11), pp 1309-1313, doi: 10.1175/1520-0477(1982)063<1309:SCOTEO>2.0.CO;2.

Willmott C. J., Ackleson S. G., Davis R. E., Feddema J. J., Klink K. M., Legates D. R., O’Donnell J., Rowe C. M. 1985. "Statistics for the evaluation of model performance." Journal of Geophysical Research 90(C5): 8995–9005, doi: 10.1029/jc090ic05p08995

Willmott, C. J., Robeson, S. M., and Matsuura, K. "A refined index of model performance". International Journal of Climatology 32, pp 2088-2094, doi: 10.1002/joc.2419.

See Also

Other agreement metrics: ww_agreement_coefficient()

Other yardstick metrics: ww_agreement_coefficient(), ww_global_geary_c(), ww_global_moran_i(), ww_local_geary_c(), ww_local_getis_ord_g(), ww_local_moran_i()

Examples

x <- c(6, 8, 9, 10, 11, 14)
y <- c(2, 3, 5, 5, 6, 8)

ww_willmott_d_vec(x, y)
ww_willmott_d1_vec(x, y)
ww_willmott_dr_vec(x, y)
ww_systematic_mse_vec(x, y)
ww_unsystematic_mse_vec(x, y)
ww_systematic_rmse_vec(x, y)
ww_unsystematic_rmse_vec(x, y)

example_df <- data.frame(x = x, y = y)
ww_willmott_d(example_df, x, y)
ww_willmott_d1(example_df, x, y)
ww_willmott_dr(example_df, x, y)
ww_systematic_mse(example_df, x, y)
ww_unsystematic_mse(example_df, x, y)
ww_systematic_rmse(example_df, x, y)
ww_unsystematic_rmse(example_df, x, y)

waywiser documentation built on April 16, 2025, 1:10 a.m.