clusterGroupBound: Hierarchical structure group tests in linear model
In hdi: High-Dimensional Inference

Description Usage Arguments Value Author(s) References See Also Examples

Computes confidence intervals for the l1-norm of groups of linear regression coefficients in a hierarchical clustering tree.

clusterGroupBound(x, y, method = "average",
                  dist = as.dist(1 - abs(cor(x))), alpha = 0.05,
                  eps = 0.1, hcloutput, nsplit = 11,
                  s = min(10, ncol(x) - 1),
                  silent = FALSE, setseed = TRUE, lpSolve = TRUE)

`x`	numeric design matrix of the regression n p* with p columns for p predictor variables and n rows corresponding to n observations.
`y`	numeric response variable of length n.
`method`	a `character` string; the method used for constructing the hierarchical clustering tree (default: `"average"` for “average linkage”) via `hclust`. Alternatively, you can provide your own hierarchical clustering through the optional argument `hcloutput`.
`dist`	a distance matrix can be specified on which the hierarchical clustering will be based (see `dist`). The default option is that the distance between variables will be calculated as 1 less the absolute correlation matrix. Alternatively, you can provide your own hierarchical clustering through the optional argument `hcloutput`.
`alpha`	numeric level in (0, 1) at which the test / confidence intervals are to be constructed.
`eps`	a level of eps*alpha is used and the values of different splits are aggregated using the (1-eps) quantile. See reference below for more details.
`hcloutput`	optionally, the value of a `hclust()` call. If it is provided, the arguments `dist` and `method` are ignored.
`nsplit`	the number of data splits used.
`s`	the dimensionality of the projection that is used. Lower values lead to faster computation and if n > 50, then `s` is set to 50 if left unspecified, to avoid lengthy computations.
`silent`	logical enabling progress output.
`setseed`	a logical; if this is true (recommended), then the same random seeds are used for all groups, which makes the confidence intervals simultaneously valid over all groups of variables tested.
`lpSolve`	logical; only set it to false if `lpSolve()` is not working on the current machine: setting it to false will result in much slower computations; only use on small problems.

Returns a list with components

`groupNumber`	The index of the group tested in the original hierarchical clustering tree
`members`	A list containing the variables that belong into each testes group
`noMembers`	A vector containing the number of members in each group
`lowerBound`	The lower bound on the l1-norm in each group
`position`	The position on the x-axis of each group (used for plotting)
`leftChild`	Gives the index of the group that corresponds to the left child node in the tested tree (negative values correspond to leaf nodes)
`rightChild`	Same as `leftCHild` for the right child of each node
`isLeaf`	Logical vector. Is `TRUE` for a group if it is a leaf node in the tested tree or if both child nodes have a zero lower bound on their group l1-norm

Nicolai Meinshausen

Meinshausen, N. (2015); JRSS B, see groupBound.

Use groupBound to compute the lower bound for selected groups of variables whereas you use this clusterGroupBound to test all groups in a hierarchical clustering tree.

## Create a regression problem with correlated design (n = 10, p = 3):
## a block of size 2 and a block of size 1, within-block correlation is 0.99

set.seed(29)
p   <- 3
n   <- 10

Sigma <- diag(p)
Sigma[1,2] <- Sigma[2,1] <- 0.99

x <- matrix(rnorm(n * p), nrow = n) %*% chol(Sigma)

## Create response with active variable 1
beta    <- rep(0, p)
beta[1] <- 5

y  <- as.numeric(x %*% beta + rnorm(n))

out <- clusterGroupBound(x, y, nsplit = 4) ## use larger value for nsplit!

## Plot and print the hierarchical group-test
plot(out)
print(out)
out$members
out$lowerBound