predictor_assessment.RdProvide several metrics to assess the quality of the predictions of a model (see note) against observations.
R2(sim, obs, na.action = stats::na.omit) SS_res(sim, obs, na.rm = T) RMSE(sim, obs, na.rm = T) nRMSE(sim, obs, na.rm = T) MAE(sim, obs, na.rm = T) ABS(sim, obs, na.rm = T) MSE(sim, obs, na.rm = T) EF(sim, obs, na.rm = T) NSE(sim, obs, na.rm = T) Bias(sim, obs, na.rm = T) MAPE(sim, obs, na.rm = T) FVU(sim, obs, na.rm = T) RME(sim, obs, na.rm = T)
| sim | Simulated values |
|---|---|
| obs | Observed values |
| na.action | A function which indicates what should happen when the data contain NAs. |
| na.rm | Boolean. Remove |
A statistic depending on the function used.
The statistics for model quality can differ between sources. Here is a
short description of each statistic and its equation (see html version
for LATEX):
R2(): coefficient of determination, computed using stats::lm() on obs~sim.
SS_res(): residual sum of squares (see notes).
RMSE(): Root Mean Squared Error, computed as
$$RMSE = \sqrt{\frac{\sum_1^n(\hat{y_i}-y_i)^2}{n}}$$
NSE(): Nash-Sutcliffe Efficiency, alias of EF, provided for user convenience.
nRMSE(): Normalized Root Mean Squared Error, also denoted as CV(RMSE), and computed as:
$$nRMSE = \frac{RMSE}{\hat{y}}\cdot100$$
MAE(): Mean Absolute Error, computed as:
$$MAE = \frac{\sum_1^n(\left|\hat{y_i}-y_i\right|)}{n}$$
ABS(): Mean Absolute Bias, which is an alias of MAE()
FVU(): Fraction of variance unexplained, computed as:
$$FVU = \frac{SS_{res}}{SS_{tot}}$$
MSE(): Mean squared Error, computed as:
$$MSE = \frac{1}{n}\sum_{i=1}^n(Y_i-\hat{Y_i})^2$$
EF(): Model efficiency, also called Nash-Sutcliffe efficiency (NSE). This statistic is
related to the FVU as \(EF= 1-FVU\). It is also related to the \(R^2\)
because they share the same equation, except SStot is applied relative to the
identity function (i.e. 1:1 line) instead of the regression line. It is computed
as: $$EF = 1-\frac{SS_{res}}{SS_{tot}}$$
Bias(): Modelling bias, simply computed as:
$$Bias = \frac{\sum_1^n(\hat{y_i}-y_i)}{n}$$
MAPE(): Mean Absolute Percent Error, computed as:
$$MAPE = \frac{\sum_1^n(\frac{\left|\hat{y_i}-y_i\right|}{y_i})}{n}$$
RME(): Relative mean error (\
$$RME = \frac{\sum_1^n(\frac{\hat{y_i}-y_i}{y_i})}{n}$$
\(SS_{res}\) is the residual sum of squares and \(SS_{tot}\) the total sum of squares. They are computed as: $$SS_{res} = \sum_{i=1}^n (y_i - \hat{y_i})^2$$ $$SS_{tot} = \sum_{i=1}^{n}\left(y_{i}-\bar{y}\right)^2$$ Also, it should be noted that \(y_i\) refers to the observed values and \(\hat{y_i}\) to the predicted values, and \(\bar{y}\) to the mean value of observations.
This function was inspired from the evaluate() function
from the SticsEvalR package. This function is used by stics_eval()
#> [1] 1.815465