mae | R Documentation |
Mean absolute error between sim
and obs
, in the same units of them, with treatment of missing values.
mae(sim, obs, ...)
## Default S3 method:
mae(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
mae(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
mae(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
mae(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
sim |
numeric, zoo, matrix or data.frame with simulated values |
obs |
numeric, zoo, matrix or data.frame with observed values |
na.rm |
a logical value indicating whether 'NA' should be stripped before the computation proceeds. |
fun |
function to be applied to The first argument MUST BE a numeric vector with any name (e.g., |
... |
arguments passed to |
epsilon.type |
argument used to define a numeric value to be added to both It is was designed to allow the use of logarithm and other similar functions that do not work with zero values. Valid values of 1) "none": 2) "Pushpalatha2012": one hundredth (1/100) of the mean observed values is added to both 3) "otherFactor": the numeric value defined in the 4) "otherValue": the numeric value defined in the |
epsilon.value |
-) when |
mae = \frac{1}{N} \sum_{i=1}^N { \left|S_i - O_i) \right| }
Mean absolute error between sim
and obs
.
If sim
and obs
are matrixes, the returned value is a vector, with the mean absolute error between each column of sim
and obs
.
obs
and sim
have to have the same length/dimension
The missing values in obs
and sim
are removed before the computation proceeds, and only those positions with non-missing values in obs
and sim
are considered in the computation
Mauricio Zambrano Bigiarini <mzb.devel@gmail.com>
https://en.wikipedia.org/wiki/Mean_absolute_error
Willmott, C.J.; Matsuura, K. (2005). Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance, Climate Research, 30, 79-82, doi:10.3354/cr030079.
Chai, T.; Draxler, R.R. (2014). Root mean square error (RMSE) or mean absolute error (MAE)? - Arguments against avoiding RMSE in the literature, Geoscientific Model Development, 7, 1247-1250. doi:10.5194/gmd-7-1247-2014.
Hodson, T.O. (2022). Root-mean-square error (RMSE) or mean absolute error (MAE): when to use them or not, Geoscientific Model Development, 15, 5481-5487, doi:10.5194/gmd-15-5481-2022.
pbias
, pbiasfdc
, mse
, rmse
, ubRMSE
, nrmse
, ssq
, gof
, ggof
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
mae(sim, obs)
obs <- 1:10
sim <- 2:11
mae(sim, obs)
##################
# Example 2:
# Loading daily streamflows of the Ega River (Spain), from 1961 to 1970
data(EgaEnEstellaQts)
obs <- EgaEnEstellaQts
# Generating a simulated daily time series, initially equal to the observed series
sim <- obs
# Computing the 'mae' for the "best" (unattainable) case
mae(sim=sim, obs=obs)
##################
# Example 3: mae for simulated values equal to observations plus random noise
# on the first half of the observed values.
# This random noise has more relative importance for ow flows than
# for medium and high flows.
# Randomly changing the first 1826 elements of 'sim', by using a normal distribution
# with mean 10 and standard deviation equal to 1 (default of 'rnorm').
sim[1:1826] <- obs[1:1826] + rnorm(1826, mean=10)
ggof(sim, obs)
mae(sim=sim, obs=obs)
##################
# Example 4: mae for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' during computations.
mae(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
mae(sim=lsim, obs=lobs)
##################
# Example 5: mae for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and adding the Pushpalatha2012 constant
# during computations
mae(sim=sim, obs=obs, fun=log, epsilon.type="Pushpalatha2012")
# Verifying the previous value, with the epsilon value following Pushpalatha2012
eps <- mean(obs, na.rm=TRUE)/100
lsim <- log(sim+eps)
lobs <- log(obs+eps)
mae(sim=lsim, obs=lobs)
##################
# Example 6: mae for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and adding a user-defined constant
# during computations
eps <- 0.01
mae(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
mae(sim=lsim, obs=lobs)
##################
# Example 7: mae for simulated values equal to observations plus random noise
# on the first half of the observed values and applying (natural)
# logarithm to 'sim' and 'obs' and using a user-defined factor
# to multiply the mean of the observed values to obtain the constant
# to be added to 'sim' and 'obs' during computations
fact <- 1/50
mae(sim=sim, obs=obs, fun=log, epsilon.type="otherFactor", epsilon.value=fact)
# Verifying the previous value:
eps <- fact*mean(obs, na.rm=TRUE)
lsim <- log(sim+eps)
lobs <- log(obs+eps)
mae(sim=lsim, obs=lobs)
##################
# Example 8: mae for simulated values equal to observations plus random noise
# on the first half of the observed values and applying a
# user-defined function to 'sim' and 'obs' during computations
fun1 <- function(x) {sqrt(x+1)}
mae(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
mae(sim=sim1, obs=obs1)
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