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 Schaefer and Strimmer (2005)
- see var.shrink .
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)
and the help page of cov.shrink
.
pcor.shrink
returns the partial correlation matrix.
pvar.shrink
returns the partial variances.
Juliane Schaefer (http://www.stat.math.ethz.ch/~schaefer/) and Korbinian Strimmer (http://strimmerlab.org).
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)