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 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 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 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 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 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 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 data.frame
ww_unsystematic_rmse(data, truth, estimate, na_rm = TRUE, ...)
ww_unsystematic_rmse_vec(truth, estimate, na_rm = TRUE, ...)Arguments
- data
A
data.framecontaining the columns specified by thetruthandestimatearguments.- ...
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, anumericvector.- estimate
The column identifier for the predicted results (that is also
numeric). As withtruththis can be specified different ways but the primary method is to use an unquoted variable name. For_vec()functions, anumericvector.- na_rm
A
logicalvalue indicating whetherNAvalues should be stripped before the computation proceeds.
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).
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.
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)
#> [1] 0.5421558
ww_willmott_d1_vec(x, y)
#> [1] 0.2926829
ww_willmott_dr_vec(x, y)
#> [1] -0.1724138
ww_systematic_mse_vec(x, y)
#> [1] 0.2238443
ww_unsystematic_mse_vec(x, y)
#> [1] 23.60949
ww_systematic_rmse_vec(x, y)
#> [1] 0.4731218
ww_unsystematic_rmse_vec(x, y)
#> [1] 4.85896
example_df <- data.frame(x = x, y = y)
ww_willmott_d(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 willmott_d standard 0.542
ww_willmott_d1(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 willmott_d1 standard 0.293
ww_willmott_dr(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 willmott_dr standard -0.172
ww_systematic_mse(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 systematic_mse standard 0.224
ww_unsystematic_mse(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 unsystematic_mse standard 23.6
ww_systematic_rmse(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 systematic_rmse standard 0.473
ww_unsystematic_rmse(example_df, x, y)
#> # A tibble: 1 × 3
#> .metric .estimator .estimate
#> <chr> <chr> <dbl>
#> 1 unsystematic_rmse standard 4.86