corpcor (version 1.6.9)

pcor.shrink: Shrinkage Estimates of Partial Correlation and Partial Variance

Description

The functions pcor.shrink and pvar.shrink compute shrinkage estimates of partial correlation and partial variance, respectively.

Usage

pcor.shrink(x, lambda, w, verbose=TRUE)
pvar.shrink(x, lambda, lambda.var, w, verbose=TRUE)

Arguments

x

a data matrix

lambda

the correlation shrinkage intensity (range 0-1). If lambda is not specified (the default) it is estimated using an analytic formula from Sch\"afer and Strimmer (2005) - see cor.shrink. For lambda=0 the empirical correlations are recovered.

lambda.var

the variance shrinkage intensity (range 0-1). If lambda.var is not specified (the default) it is estimated using an analytic formula from Opgen-Rhein and Strimmer (2007) - see details below. For lambda.var=0 the empirical variances are recovered.

w

optional: weights for each data point - if not specified uniform weights are assumed (w = rep(1/n, n) with n = nrow(x)).

verbose

report progress while computing (default: TRUE)

Value

pcor.shrink returns the partial correlation matrix. Attached to this matrix are the standardized partial variances (i.e. PVAR/VAR) that can be retrieved using attr under the attribute "spv".

pvar.shrink returns the partial variances.

Details

The partial variance \(var(X_k | rest)\) is the variance of \(X_k\) conditioned on the remaining variables. It equals the inverse of the corresponding diagonal entry of the precision matrix (see Whittaker 1990).

The partial correlations \(corr(X_k, X_l | rest)\) is the correlation between \(X_k\) and \(X_l\) conditioned on the remaining variables. It equals the sign-reversed entries of the off-diagonal entries of the precision matrix, standardized by the the squared root of the associated inverse partial variances.

Note that using pcor.shrink(x) much faster than cor2pcor(cor.shrink(x)).

For details about the shrinkage procedure consult Sch\"afer and Strimmer (2005), Opgen-Rhein and Strimmer (2007), and the help page of cov.shrink.

References

Opgen-Rhein, R., and K. Strimmer. 2007. Accurate ranking of differentially expressed genes by a distribution-free shrinkage approach. Statist. Appl. Genet. Mol. Biol. 6:9. <DOI:10.2202/1544-6115.1252>

Sch\"afer, J., and K. Strimmer. 2005. A shrinkage approach to large-scale covariance estimation and implications for functional genomics. Statist. Appl. Genet. Mol. Biol. 4:32. <DOI:10.2202/1544-6115.1175>

Whittaker J. 1990. Graphical Models in Applied Multivariate Statistics. John Wiley, Chichester.

See Also

invcov.shrink, cov.shrink, cor2pcor

Examples

# NOT RUN {
# load corpcor library
library("corpcor")

# generate data matrix
p = 50
n = 10
X = matrix(rnorm(n*p), nrow = n, ncol = p)


# partial variance
pv = pvar.shrink(X)
pv

# partial correlations (fast and recommend way)
pcr1 = pcor.shrink(X)

# other possibilities to estimate partial correlations
pcr2 = cor2pcor( cor.shrink(X) )


# all the same
sum((pcr1 - pcr2)^2)

# }