rSpearman | R Documentation |
Spearman's rank correlation coefficient between sim
and obs
, with treatment of missing values.
rSpearman(sim, obs, ...)
## Default S3 method:
rSpearman(sim, obs, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
rSpearman(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
rSpearman(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
rSpearman(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 |
numeric value to be added to both |
It is a wrapper to the cor
function.
The Spearman's rank correlation coefficient is a nonparametric measure of rank correlation (statistical dependence between the rankings of two variables).
It assesses how well the relationship between two variables can be described using a monotonic function.
The Spearman correlation between two variables is equal to the Pearson correlation between the rank values of those two variables.
However, while Pearson's correlation assesses linear relationships, Spearman's correlation assesses monotonic relationships (whether linear or not).
If there are no repeated data values, a perfect Spearman correlation of +1 or -1 occurs when each of the variables is a perfect monotone function of the other.
Spearman's rank correlation coefficient between sim
and obs
.
If sim
and obs
are matrixes, the returned value is a vector, with the Spearman's rank correlation coefficient between each column of sim
and obs
.
obs
and sim
has 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/Spearman%27s_rank_correlation_coefficient
Spearman, C. (1961). The Proof and Measurement of Association Between Two Things. In J. J. Jenkins and D. G. Paterson (Eds.), Studies in individual differences: The search for intelligence (pp. 45-58). Appleton-Century-Crofts. doi:10.1037/11491-005
cor
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
rSpearman(sim, obs)
obs <- 1:10
sim <- 2:11
rSpearman(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 'rSpearman' for the "best" (unattainable) case
rSpearman(sim=sim, obs=obs)
##################
# Example 3: rSpearman 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)
rSpearman(sim=sim, obs=obs)
##################
# Example 4: rSpearman 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.
rSpearman(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
rSpearman(sim=lsim, obs=lobs)
##################
# Example 5: rSpearman 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
rSpearman(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)
rSpearman(sim=lsim, obs=lobs)
##################
# Example 6: rSpearman 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
rSpearman(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
rSpearman(sim=lsim, obs=lobs)
##################
# Example 7: rSpearman 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
rSpearman(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)
rSpearman(sim=lsim, obs=lobs)
##################
# Example 8: rSpearman 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)}
rSpearman(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
rSpearman(sim=sim1, obs=obs1)
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