cor0.test: Test of Vanishing (Partial) Correlation

In GeneNet: Modeling and Inferring Gene Networks

Description

cor0.test computes a p-value for the two-sided test with the null hypothesis H0: rho == 0 versus the alternative hypothesis HA: rho != 0.

If method="student" is selected then the statistic t=r*sqrt((kappa-1)/(1-r*r)) is considered which under H0 is student-t distributed with df=kappa-1. This method is exact.

If method="dcor0" is selected then the p-value is computed directly from the null distribution of the (partial) correlation (see dcor0). This method is also exact.

If method="ztransform" is selected then the p-value is computed using the z-transform (see z.transform), i.e. using a suitable chosen normal distribution. This method returns approximate p-values.

Usage

cor0.test(r, kappa, method=c("student", "dcor0", "ztransform"))

Arguments

r	observed correlation
kappa	degree of freedom of the null-distribution
method	method used to compute the p-value

Value

A p-value.

Author(s)

Juliane Sch\"afer and Korbinian Strimmer (https://strimmerlab.github.io).

See Also

dcor0, kappa2n, z.transform.

Examples

# load GeneNet library
library("GeneNet")

# covariance matrix
m.cov <- rbind(
 c(3,1,1,0),
 c(1,3,0,1),
 c(1,0,2,0),
 c(0,1,0,2)
)

# compute partial correlations
m.pcor <- cor2pcor(m.cov)
m.pcor

# corresponding p-values 
# assuming a sample size of 25, i.e. kappa=22
kappa2n(22, 4)
cor0.test(m.pcor, kappa=22)
cor0.test(m.pcor, kappa=22) < 0.05

# p-values become smaller with larger r 
cor0.test(0.7, 12)
cor0.test(0.8, 12)
cor0.test(0.9, 12)

# comparison of various methods
cor0.test(0.2, 45, method="student")
cor0.test(0.2, 45, method="dcor0")
cor0.test(0.2, 45, method="ztransform")

Example output

Loading required package: corpcor
Loading required package: longitudinal
Loading required package: fdrtool
           [,1]       [,2]        [,3]        [,4]
[1,]  1.0000000  0.4000000  0.43852901 -0.17541160
[2,]  0.4000000  1.0000000 -0.17541160  0.43852901
[3,]  0.4385290 -0.1754116  1.00000000  0.07692308
[4,] -0.1754116  0.4385290  0.07692308  1.00000000
[1] 25
           [,1]       [,2]       [,3]       [,4]
[1,] 0.00000000 0.05860001 0.03633173 0.42338215
[2,] 0.05860001 0.00000000 0.42338215 0.03633173
[3,] 0.03633173 0.42338215 0.00000000 0.72719831
[4,] 0.42338215 0.03633173 0.72719831 0.00000000
      [,1]  [,2]  [,3]  [,4]
[1,]  TRUE FALSE  TRUE FALSE
[2,] FALSE  TRUE FALSE  TRUE
[3,]  TRUE FALSE  TRUE FALSE
[4,] FALSE  TRUE FALSE  TRUE
[1] 0.007722282
[1] 0.001024829
[1] 2.771608e-05
[1] 0.1826482
[1] 0.1826482
[1] 0.183714

GeneNet documentation built on Nov. 15, 2021, 1:07 a.m.