predictor_assessment | R Documentation |
Provide 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 |
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}
A statistic depending on the function used.
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()
library(sticRs)
sim= rnorm(n = 5,mean = 1,sd = 1)
obs= rnorm(n = 5,mean = 1,sd = 1)
RMSE(sim,obs)
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