shrinkTEGS: Default shrinkage estimation of covariance matrices

In SourceSet: A Graphical Model Approach to Identify Primary Genes in Perturbed Biological Pathways

Default shrinkage estimation of covariance matrices

Description

The function adds a small quantity to the diagonals of covariance matrix estimates to regularize them.

Usage

shrinkTEGS(s, s1, s2, param = list(probs = 0.05, type = "min"))

Arguments

s	covariance matrix estimte in the pooled sample
s1	sample covariance matrix estimate in class 1
s2	sample covariance matrix estimate in class 2
param	list of parameters: lamda: a vector of lambdas (to be supplied only if some custom lambdas are to be used) type: minimum (min), maximum (max) or optimal (opt) probs: the numeric value of probability with value in [0,1]

Details

To determine the quantity to add to the diagonals of covariance matrices, the function:

• finds the distributions of the sample variances of the p variables in the two classes and in the pooled sample

• computes the probs percentile of each of these distributions

• use the minimum, maximum or optimal (one for each matrix) (type)

Value

The function returns a list of shrink covariance matrices.

Note

It should be stressed that the default parameters for TEGS shrink estimator allow to compare the log likelihood criterion among distributions if the testMeanVariance is performed.

References

Huang, Y.-T. and Lin, X. (2013). Gene set analysis using variance component tests. BMC Bioinformatics, 14(1), 210.

See Also

testMeanVariance, parameters

Examples

if(require(mvtnorm)){

  ## Generate two random samples of size 50 from two multivariate normal distributions
  # sample size
  n<-50
  # true parameters of class 1 and class 2
  param.class1<-simulation$condition1
  param.class2<-simulation$condition2$`5`$`2`
  # simulated dataset
  data.class1<-rmvnorm(n = n,mean =param.class1$mu ,sigma =param.class1$S)
  data.class2<-rmvnorm(n = n,mean =param.class2$mu ,sigma=param.class2$S)
  data<-rbind(data.class1,data.class2)
  classes<-c(rep(1,nrow(data.class1)),rep(2,nrow(data.class2)))

  ## estimated parameters: maximum likelihood estimate
  s<-cov(data)
  s1<-cov(data.class1)
  s2<-cov(data.class2)

  ## default parameters:
  # use the minimum of median variances distributions of the three supplied covariance matrices
  def.shrink<-shrinkTEGS(s,s1,s2)
  def.shrink$lambda

  ## use customize lamdas
  def.shrink<-shrinkTEGS(s,s1,s2,param = list(lambda=c(0.1,0.2,0.3)))
  def.shrink$lambda

  # use for each covariance matrix the 0.4 percentile of its variances distributions
  def.shrink<-shrinkTEGS(s,s1,s2,param = list(type="opt",probs=0.4))
  def.shrink$lambda
}

SourceSet documentation built on Nov. 21, 2022, 5:06 p.m.