ApplyFwerCor: Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix.

Description

Applies multiple testing procedures controlling (asymptotically) the FWER for tests on a correlation matrix. Methods are described in Chapter 5 of Roux (2018).

Usage

ApplyFwerCor(
  data,
  alpha = NULL,
  stat_test = "empirical",
  method = "Sidak",
  Nboot = 1000,
  stepdown = TRUE,
  vect = FALSE,
  logical = stepdown,
  arr.ind = FALSE
)

Arguments

data

matrix of observations

alpha

level of multiple testing (used if logical=TRUE)

stat_test

'empirical': \(\sqrt{n}*abs(corr)\)
'fisher': \(\sqrt{n-3}*1/2*\log( (1+corr)/(1-corr) )\)
'student': \(\sqrt{n-2}*abs(corr)/\sqrt(1-corr^2)\)
'2nd.order': \(\sqrt{n}*mean(Y)/sd(Y)\) with \(Y=(X_i-mean(X_i))(X_j-mean(X_j))\)

method

choice between 'Bonferroni', 'Sidak', 'BootRW', 'MaxTinfty'

Nboot

number of iterations for Monte-Carlo of bootstrap quantile evaluation

stepdown

logical, if TRUE a stepdown procedure is applied

vect

if TRUE returns a vector of adjusted p-values, corresponding to vectorize(cor(data)); if FALSE, returns an array containing the adjusted p-values for each entry of the correlation matrix

logical

if TRUE, returns either a vector or a matrix where each element is equal to TRUE if the corresponding null hypothesis is rejected, and to FALSE if it is not rejected if stepdown=TRUE and logical=FALSE, returns a list of successive p-values.

arr.ind

if TRUE, returns the indexes of the significant correlations, with repspect to level alpha

Value

Returns either

logicals indicating if the corresponding correlation is significant if logical=TRUE, 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.

References

Bonferroni, C. E. (1935). Il calcolo delle assicurazioni su gruppi di teste. Studi in onore del professore salvatore ortu carboni, 13-60.

Drton, M., & Perlman, M. D. (2007). Multiple testing and error control in Gaussian graphical model selection. Statistical Science, 22(3), 430-449.

Romano, J. P., & Wolf, M. (2005). Exact and approximate stepdown methods for multiple hypothesis testing. Journal of the American Statistical Association, 100(469), 94-108.

Roux, M. (2018). Graph inference by multiple testing with application to Neuroimaging, Ph.D., Universit<U+00E9> Grenoble Alpes, France, https://tel.archives-ouvertes.fr/tel-01971574v1.

<U+0160>id<U+00E1>k, Z. (1967). Rectangular confidence regions for the means of multivariate normal distributions. Journal of the American Statistical Association, 62(318), 626-633.

Examples

Run this code

# NOT RUN {
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)
# adjusted p-values
(res <- ApplyFwerCor(data,stat_test='empirical',method='Bonferroni',stepdown=FALSE))
# significant correlations, level alpha:
alpha <- 0.05
whichCor(res<alpha)
# }