hierbase (version 0.1.2)

advance_hierarchy: Hierarchical Testing

Description

Hierarchical testing for a given build-in test function.

Usage

advance_hierarchy(
  x,
  y,
  dendr,
  test = c("QF", "hdi", "hdi.logistic", "F", "logistic"),
  clvar = NULL,
  alpha = 0.05,
  global.test = TRUE,
  hier.adj = FALSE,
  mt.adj = c("dpBF", "none"),
  agg.method = c("Tippett", "Stouffer"),
  verbose = FALSE,
  sort.parallel = TRUE,
  parallel = c("no", "multicore", "snow"),
  ncpus = 1L,
  cl = NULL
)

Arguments

x

a matrix or list of matrices for multiple data sets. The matrix or matrices have to be of type numeric and are required to have column names / variable names. The rows and the columns represent the observations and the variables, respectively.

y

a vector, a matrix with one column, or list of the aforementioned objects for multiple data sets. The vector, vectors, matrix, or matrices have to be of type numeric.

dendr

the output of one of the functions cluster_vars or cluster_positions.

test

a character string naming a 'build-in' group test function. See the 'Details' section.

clvar

a matrix or list of matrices of control variables.

alpha

the significant level at which the FWER is controlled.

global.test

a logical value indicating whether the global test should be performed.

hier.adj

a logical value indicating whether the p-values can only increase when going down some given branch. Strong FWER control holds as well if the argument is set to FALSE which is the default option.

mt.adj

type of multiple testing correction to be used; either "dpBF" (depth-wise Bonferroni multiple adjustment) or "none" (no adjustment). See the 'Details' section.

agg.method

a character string naming an aggregation method which aggregates the p-values over the different data sets for a given cluster; either "Tippett" (Tippett's rule) or "Stouffer" (Stouffer's rule). This argument is only relevant if multiple data sets are specified in the function call.

verbose

a logical value indicating whether the progress of the computation should be printed in the console.

sort.parallel

a logical indicating whether the blocks should be sorted with respect to the size of the block. This can reduce the run time for parallel computation.

parallel

type of parallel computation to be used. See the 'Details' section.

ncpus

number of processes to be run in parallel.

cl

an optional parallel or snow cluster used if parallel = "snow". If not supplied, a cluster on the local machine is created.

Value

The returned value is an object of class "hierBase", consisting a data.frame with the result of the hierarchical testing.

The data.frame has the following columns:

block

NA or the name of the block if the significant cluster is a subcluster of the block or is the block itself.

p.value

The p-value of the significant cluster.

significant.cluster

The column names of the members of the significant cluster.

There is a print method for this class; see print.hierBase.

Details

Hierarchical testing is performed by going top down through the hierarchical tree. Testing in some branch only continues if at least one child of a given cluster is significant. The function advance_hierarchy requires the output of one of the functions cluster_vars or cluster_positions as an input (argument dendr).

The user can choose one of the 'build-in' group test functions that is applied to every group which is tested. The default is test = "QF" (inference for quadratic functionals in linear regression; see function QF in the R package SIHR). Alternatively, there are "hdi" (de-biased Lasso for linear regression; see function lasso.proj in the R package hdi), "hdi.logistic" (de-biased Lasso for logistic regression; see function lasso.proj in the R package hdi), "F" (classical partial F-Test for low-dimensional data; see function anova), and "logistic" (likelihood ratio test for logistic regression for low-dimensional data; see function anova).

If one of the 'build-in' group test functions "QF", "hdi", or "hdi.logistic" is applied and control variables are specified using the argument clvar, then those variables are included in the model, there is an L1-penalty in the Lasso imposed on them, and obviously those covariates are not tested in the hierarchical procedure.

The user can specify which hierarchical multiple testing adjustment for the hierarchical procedure is applied. The default is "dpBF" (depth-wise Bonferroni multiple adjustment). Alternatively, the user can choose "none" (no adjustment). The hierarchical multiple testing adjustment "dpBF" guarantees strong family-wise error control if the group test, which is applied for testing a given group, controls the type I error.

If the argument block was supplied for the building of the hierarchical tree (i.e. in the function call of either cluster_vars or cluster_positions), i.e. the second level of the hierarchical tree was given, the hierarchical testing step can be run in parallel across the different blocks by specifying the arguments parallel and ncpus. There is an optional argument cl if parallel = "snow". There are three possibilities to set the argument parallel: parallel = "no" for serial evaluation (default), parallel = "multicore" for parallel evaluation using forking, and parallel = "snow" for parallel evaluation using a parallel socket cluster. It is recommended to select RNGkind("L'Ecuyer-CMRG") and set a seed to ensure that the parallel computing of the package hierbase is reproducible. This way each processor gets a different substream of the pseudo random number generator stream which makes the results reproducible if the arguments (as sort.parallel and ncpus) remain unchanged. See the vignette or the reference for more details.

Note that if Tippett's aggregation method is applied for multiple data sets, then very small p-values are set to machine precision. This is due to rounding in floating point arithmetic.

References

Meinshausen, N. (2008). Hierarchical testing of variable importance. Biometrika, 95(2), 265-278. Renaux, C., Buzdugan, L., Kalisch, M., and B<U+00FC>hlmann, P. (2020). Hierarchical inference for genome-wide association studies: a view on methodology with software. Computational Statistics, 35(1), 1-40.

See Also

cluster_vars, cluster_positions, and run_hierarchy.

Examples

# NOT RUN {
## Low-dimensonal example
n <- 100
p <- 50
library(MASS)
set.seed(3)
x <- mvrnorm(n, mu = rep(0, p), Sigma = diag(p))
colnames(x) <- paste0("Var", 1:p)
beta <- rep(0, p)
beta[c(5, 20, 46)] <- 1
y <- x %*% beta + rnorm(n)

dendr1 <- cluster_vars(x = x)
set.seed(76)
sign.clusters1 <- advance_hierarchy(x = x, y = y, dendr = dendr1,
                                    test = "F")

## High-dimensional example
if (FALSE) {
  n <- 50
  p <- 80
  library(MASS)
  set.seed(3)
  x <- mvrnorm(n, mu = rep(0, p), Sigma = diag(p))
  colnames(x) <- paste0("Var", 1:p)
  beta <- rep(0, p)
  beta[c(5, 20, 46)] <- 1
  y <- x %*% beta + rnorm(n)
 
  dendr1 <- cluster_vars(x = x)
  set.seed(76)
  sign.clusters1 <- advance_hierarchy(x = x, y = y, dendr = dendr1,
                                    test = "QF")

  ## With block
  # I.e. second level of the hierarchical tree is specified by 
  # the user. This would allow to run the code in parallel; see the 'Details'
  # section.
  # The column names of the data frame block are optional.

  block <- data.frame("var.name" = paste0("Var", 1:p),
                      "block" = rep(c(1, 2), each = p/2))
  dendr2 <- cluster_vars(x = x, block = block)
  set.seed(76)
  sign.clusters2 <- advance_hierarchy(x = x, y = y, dendr = dendr2,
                                      test = "QF")
 
  # Access part of the return object or result
  sign.clusters2[, "block"]
  sign.clusters2[, "p.value"]
  # Column names or variable names of the significant cluster in the first row.
  sign.clusters2[[1, "significant.cluster"]]
}

# }