| pcor.shrink {corpcor} | R Documentation |
The functions pcor.shrink and pvar.shrink compute shrinkage estimates
of partial correlation and partial variance, respectively.
pcor.shrink(x, lambda, w, protect=0, verbose=TRUE) pvar.shrink(x, lambda, lambda.var, w, protect=0, verbose=TRUE)
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 Schaefer 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)). |
protect |
the fraction of correlation components protected against excessive individual component risk (default: 0, no limited translation) |
verbose |
report progress while computing (default: TRUE) |
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 Schaefer and Strimmer (2005),
Opgen-Rhein and Strimmer (2007), and the help page of cov.shrink.
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.
Juliane Schaefer (http://www.stat.math.ethz.ch/~schaefer/) and Korbinian Strimmer (http://strimmerlab.org).
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. (http://www.bepress.com/sagmb/vol6/iss1/art9/)
Schaefer, 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. (http://www.bepress.com/sagmb/vol4/iss1/art32/)
Whittaker J. 1990. Graphical Models in Applied Multivariate Statistics. John Wiley, Chichester.
invcov.shrink, cov.shrink, cor2pcor
# 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)