rPearson | R Documentation |
Pearson correlation coefficient between sim
and obs
, with treatment of missing values.
rPearson(sim, obs, ...)
## Default S3 method:
rPearson(sim, obs, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'matrix'
rPearson(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'data.frame'
rPearson(sim, obs, na.rm=TRUE, fun=NULL, ...,
epsilon.type=c("none", "Pushpalatha2012", "otherFactor", "otherValue"),
epsilon.value=NA)
## S3 method for class 'zoo'
rPearson(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 Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data.
It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between -1 and 1.
As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.
The correlation coefficient ranges from -1 to 1. An absolute value of exactly 1 implies that a linear equation describes the relationship between sim
and obs
perfectly, with all data points lying on a line.
The correlation sign is determined by the regression slope: a value of +1 implies that all data points lie on a line for which sim
increases as obs
increases, and vice versa for -1.
A value of 0 implies that there is no linear dependency between the variables.
Pearson correlation coefficient between sim
and obs
.
If sim
and obs
are matrixes, the returned value is a vector, with the Pearson 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/Pearson_correlation_coefficient
Pearson, K. (1920). Notes on the history of correlation. Biometrika, 13(1), 25-45. doi:10.2307/2331722.
Schober, P.; Boer, C.; Schwarte, L.A. (2018). Correlation coefficients: appropriate use and interpretation. Anesthesia and Analgesia, 126(5), 1763-1768. doi:10.1213/ANE.0000000000002864.
cor
##################
# Example 1: basic ideal case
obs <- 1:10
sim <- 1:10
rPearson(sim, obs)
obs <- 1:10
sim <- 2:11
rPearson(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 'rPearson' for the "best" (unattainable) case
rPearson(sim=sim, obs=obs)
##################
# Example 3: rPearson 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)
rPearson(sim=sim, obs=obs)
##################
# Example 4: rPearson 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.
rPearson(sim=sim, obs=obs, fun=log)
# Verifying the previous value:
lsim <- log(sim)
lobs <- log(obs)
rPearson(sim=lsim, obs=lobs)
##################
# Example 5: rPearson 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
rPearson(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)
rPearson(sim=lsim, obs=lobs)
##################
# Example 6: rPearson 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
rPearson(sim=sim, obs=obs, fun=log, epsilon.type="otherValue", epsilon.value=eps)
# Verifying the previous value:
lsim <- log(sim+eps)
lobs <- log(obs+eps)
rPearson(sim=lsim, obs=lobs)
##################
# Example 7: rPearson 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
rPearson(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)
rPearson(sim=lsim, obs=lobs)
##################
# Example 8: rPearson 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)}
rPearson(sim=sim, obs=obs, fun=fun1)
# Verifying the previous value, with the epsilon value following Pushpalatha2012
sim1 <- sqrt(sim+1)
obs1 <- sqrt(obs+1)
rPearson(sim=sim1, obs=obs1)
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