ApplyFdrCor: Applies multiple testing procedures built to control...
In TestCor: FWER and FDR Controlling Procedures for Multiple Correlation Tests

Description Usage Arguments Value References See Also Examples

Applies multiple testing procedures built to control (asymptotically) the FDR for correlation testing. Some have no theoretical proofs for tests on a correlation matrix.

ApplyFdrCor(
  data,
  alpha = 0.05,
  stat_test = "empirical",
  method = "LCTnorm",
  Nboot = 1000,
  vect = FALSE,
  arr.ind = FALSE
)

`data`	matrix of observations
`alpha`	level of multiple testing
`stat_test`	'empirical' √{n}abs(corr)* 'fisher' √{n-3}1/2\log( (1+corr)/(1-corr) ) 'student' √{n-2}abs(corr)/√(1-corr^2)* '2nd.order' √{n}mean(Y)/sd(Y)* with Y=(X_i-mean(X_i))(X_j-mean(X_j))
`method`	choice between 'LCTnorm' and 'LCTboot' developped by Cai & Liu (2016), 'BH', traditional Benjamini-Hochberg's procedure Benjamini & Hochberg (1995)'s and 'BHboot', Benjamini-Hochberg (1995)'s procedure with bootstrap evaluation of p-values
`Nboot`	number of iterations for bootstrap p-values evaluation
`vect`	if TRUE returns a vector of TRUE/FALSE values, corresponding to `vectorize(cor(data))`; if FALSE, returns an array containing rows and columns of significant correlations
`arr.ind`	if TRUE, returns the indexes of the significant correlations, with repspect to level alpha

Returns either

logicals indicating if the corresponding correlation is significant, as a vector or a matrix depending on vect,
an array containing indexes \lbrace(i,j),\,i<j\rbrace for which correlation between variables i and j is significant, if arr.ind=TRUE.

Benjamini, Y., & Hochberg, Y. (1995). Controlling the false discovery rate: a practical and powerful approach to multiple testing. Journal of the royal statistical society. Series B (Methodological), 289-300.

Cai, T. T., & Liu, W. (2016). Large-scale multiple testing of correlations. Journal of the American Statistical Association, 111(513), 229-240.

Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Université Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

ApplyFwerCor

LCTnorm, LCTboot, BHCor, BHBootCor

n <- 100
p <- 10
corr_theo <- diag(1,p)
corr_theo[1,3] <- 0.5
corr_theo[3,1] <- 0.5
data <- MASS::mvrnorm(n,rep(0,p),corr_theo)
res <- ApplyFdrCor(data,stat_test='empirical',method='LCTnorm')
# significant correlations, level alpha:
alpha <- 0.05
whichCor(res<alpha)