Compute the FR coefficient on two vectors based exactly on Gamma2.

Description

This function computes the unidimensional graph prediction coefficient between two vectors xvec and yvec.

Usage

FRpredcor(xvec, yvec, tiemethod = "average")

Arguments

Value

In the case simple = TRUE, function returns the value of the FR standardized coefficient.

Note

Auxiliary function with no checks for NA, etc.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. and Holmes, S (2020) Practical observations and applications of the robust prediction coefficient.

See Also

xicor FRpredcorhalf

Examples

# Compute  the coefficient and compare to the xi coefficient
simulCompare <- function(n = 20, B = 1000)
{
 diffs<- rep(0,B)
 xvec <- 1:n
 for (i in 1:B)
 {
   yvec <- runif(n)
   diffs[i] <- FRpredcor(xvec, yvec) - xicor(xvec, yvec)
 }
 return(diffs)
 }

 simulcompare1K <- simulCompare()
 summary(simulcompare1K)

Compute the FR half coefficient on two vectors based on half Gamma 2.

Description

This function computes the unidimensional ranked half graph prediction coefficient between two vectors xvec and yvec.

Usage

FRpredcorhalf(xvec, yvec, tiemethod = "average")

Arguments

Value

In the case simple = TRUE, function returns the value of the FR standardized coefficient.

Note

Auxiliary function with no checks for NA, etc.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. and Holmes, S (2020) Practical observations and applications of the robust prediction coefficient.

See Also

xicor FRpredcor

Examples

# Compute  the coefficient and compare to the xi coefficient
simulCompare <- function(n = 20, B = 1000)
{
 diffsim <- rep(0,B)
 xvec <- 1:n
 for (i in 1:B)
 {
   yvec <- sample(n,n)
   diffsim[i] <- FRpredcorhalf(xvec,yvec)-xicor(xvec,yvec)
 }
 return(diffsim)
 }

 compare1K <- simulCompare()
 summary(compare1K)

Inverse function to wholebinary returns the number from its expansion

Description

Inverse function to wholebinary returns the number from its expansion

Usage

backdec(rmat, sgn)

Arguments

Note

It may be necessary to make a new version of this using special functions for large integers.

Auxiliary function that takes avector and produces a single number through a Borel isomorphism using the wholebinary and backdec functions.

Description

Auxiliary function that takes avector and produces a single number through a Borel isomorphism using the wholebinary and backdec functions.

Usage

borelmerge(xvec)

Arguments

Value

produces a single real number by converting each element

Compute the cross rank coefficient xi on two vectors.

Description

This function computes the xi coefficient between two vectors x and y.

Usage

calculateXI(xvec, yvec, simple = TRUE)

Arguments

Value

In the case simple = TRUE, function returns the value of the xi coefficient, If simple = FALSE is chosen, the function returns a list:

xi

The xi coefficient

fr

rearranged rank of yvec

CU

mean(gr*(1-gr))

Note

Auxiliary function with no checks for NA, etc.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. (2020) A New Coefficient Of Correlation, <arXiv:1909.10140>.

See Also

xicor

Examples

# Compute one of the coefficients
library("psychTools")
data(peas)
calculateXI(peas$parent,peas$child)
calculateXI(peas$child,peas$parent)

Take fractionary part and make its binary expansion Auxiliary function used in expanding real numbers

Description

Take fractionary part and make its binary expansion Auxiliary function used in expanding real numbers

Usage

fracbinary(x)

Arguments

Value

Binary expansion of length 31 of the decimal input

Note

this implementation uses the built-in function intToBits

Compute the generalized cross rank increment correlation coefficient gxi.

Description

This function computes the generalized xi coefficient between two matrices xmat and ymat. There is a limitation on the size of the matrices, for the time being, xmat and ymat can only have 31 columns. If they are wider than 31, there is the option of using a dimension reduction technique to bring the number of columns down to 31, the first 31 components are then used. The function encodes the data using a binary expansion and then calls xicor on the vectors, so some of the arguments relevant for xicor can be specified, such as pvalue.

Usage

genxicor(xmat, ymat)

Arguments

Value

Function returns the value of the genxi coefficient. Since by default the option pvalue=TRUE is chosen, the function returns a list:

xi

The value of the xi coefficient.

sd

The standard deviation.

pval

The test p-value.

Note

This version does not use a seed as argument, if reproducibility is an issue, set a seed before calling the function.

The p-value of rejecting independence is set to TRUE.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. (2022) <arXiv:2211.04702>

Examples

example_joint_calc = function(n,x=runif(n),y=runif(n),ep=runif(n)) {
u = (x + y + ep) %% 1
v = ((x + y)/2 + ep) %% 1
w = (4*x/3 + 2*y/3 + ep) %% 1
z = (2*x/3 + y/3 + ep) %% 1
q = cbind(u,v,w,z)
p = cbind(x,y)
c1 = genxicor(u, p)
c2 = genxicor(v, p)
c3 = genxicor(w, p)
c4 = genxicor(z, p)
c5 = genxicor(q, p)
return(list(marg1 = c1$xi, marg2 = c2$xi, marg3 = c3$xi, 
marg4 = c4$xi, joint = c5$xi, p1 = c1$pval, p2 = c2$pval, p3 = c3$pval,
p4 = c4$pval, p5 = c5$pval))
}
result1 <- example_joint_calc(n=10)

Computes the binary expansion of a number

Description

If the argument x is a real number the decimal portion is dropped.

Usage

numbinary(x)

Arguments

Value

the output is a binary vector of length 31

Take a matrix of two numbers given in their binary expansion one in each of the two rows and return the interleaving of the two numbers

Description

Take a matrix of two numbers given in their binary expansion one in each of the two rows and return the interleaving of the two numbers

Usage

weave(rmat, sgn)

Arguments

Encodes a number as a two row binary matrix and its sign

Description

Auxiliary function used for generating expansion of a number, the binary expansion of length nc of the integer part is the first row and the binary expansion of length nc of the fractional part is the second row of the matrix. The sign as appended into the final list object which the function returns.

Usage

wholebinary(x, nc = 31)

Arguments

Value

This function generates a list with a binary matrix rmat with two rows and the sign sgn in a separate entry of the list.

Compute the cross rank increment correlation coefficient xi.

Description

This function computes the xi coefficient between two vectors x and y, possibly all coefficients for a matrix. If only one coefficient is computed it can be used to test independence using a Monte Carlo permutation test or through an asymptotic approximation test.

Usage

xicor(
  x,
  y = NULL,
  pvalue = FALSE,
  ties = TRUE,
  method = "asymptotic",
  nperm = 1000,
  factor = FALSE
)

Arguments

Value

In the case pvalue=FALSE, function returns the value of the xi coefficient, if the input is a matrix, a matrix of coefficients is returned. In the case pvalue=TRUE is chosen, the function returns a list:

xi

The value of the xi coefficient.

sd

The standard deviation.

pval

The test p-value.

Note

Dataset peas no longer available in psych, we are now using psychTools.

This version does not use a seed as argument, if reproducibility is an issue, set a seed before calling the function.

Author(s)

Sourav Chatterjee, Susan Holmes

References

Chatterjee, S. (2020) <arXiv:1909.10140>.

See Also

dcov

Examples

##---- Should be DIRECTLY executable !! ----
library("psychTools")
data(peas)
# Visualize       the peas data
library(ggplot2)
ggplot(peas,aes(parent,child)) +
geom_count() + scale_radius(range=c(0,5)) +
       xlim(c(13.5,24))+ylim(c(13.5,24))+       coord_fixed() +
       theme(legend.position="bottom")
# Compute one of the coefficients
xicor(peas$parent,peas$child,pvalue=TRUE)
xicor(peas$child,peas$parent)
# Compute all the coefficients
xicor(peas)