sda (version 1.0.2)

centroids: Group Centroids, (Pooled) Variances, and Powers of the Pooled Correlation Matrix

Description

centroids computes group centroids and optionally the pooled mean and pooled variance, the group specific variances, and powers of the pooled correlation matrix.

Usage

centroids(x, L, mean.pooled=FALSE, var.pooled=TRUE, var.groups=FALSE, 
  powcor.pooled=FALSE, alpha=1, shrink=FALSE, verbose=TRUE)

Arguments

x

A matrix containing the data set. Note that the rows are sample observations and the columns are variables.

L

A factor with the group labels.

mean.pooled

Estimate the pooled mean.

var.pooled

Estimate the pooled variances.

var.groups

Estimate all group-specific variances.

powcor.pooled

Estimate pooled correlation matrix (taken to the power of alpha).

alpha

exponent for the pooled correlation matrix (default: alpha=1).

shrink

Use empirical or shrinkage estimator.

verbose

Provide some messages while computing.

Value

• centroids returns a list with the following components:
• samples
  a vector containing the samples sizes in each group,
• means
  the empirical group means,
• mean.pooled
  the pooled empirical mean,
• var.pooled
  a vector containing the pooled variances,
• var.groups
  a matrix containing the group-specific variances, and
• powcor.pooled
  a matrix containing the pooled correlation matrix to the power of alpha (if all correlations are zero a vector only 1s is returned to save space).
• alpha
  exponent for the pooled correlation matrix.

Details

If option shrink=TRUE then the shrinkage estimators var.shrink from Opgen-Rhein and Strimmer (2007) and cor.shrink from Sch"afer and Strimmer (2005) are used.

See Also

var.shrink, powcor.shrink.

Examples

# load sda library
library("sda")

## prepare data set
data(iris) # good old iris data
X = as.matrix(iris[,1:4])
Y = iris[,5]

## estimate centroids and empirical pooled variances
centroids(X, Y)

## show pooled mean
centroids(X, Y, mean.pooled=TRUE)

## compute group-specific variances
centroids(X, Y, var.groups=TRUE)

## and inverse pooled correlation
centroids(X, Y, var.groups=TRUE, powcor.pooled=TRUE, alpha=-1)

## use shrinkage estimator for variances and correlations
centroids(X, Y, var.groups=TRUE, powcor.pooled=TRUE, alpha=-1, shrink=TRUE)