| fix_cor {seqgendiff} | R Documentation |
Fixes an invalid target correlation.
Description
Shrinks the target correlation using a uniform scaling factor so that the overall correlation matrix is positive semi-definite. The method is described in detail in Gerard (2020).
Usage
fix_cor(design_perm, target_cor, num_steps = 51)
Arguments
design_perm |
A numeric design matrix whose rows are to be permuted (thus controlling the amount by which they are correlated with the surrogate variables). The rows index the samples and the columns index the variables. The intercept should not be included (though see Section "Unestimable Components"). |
target_cor |
A numeric matrix of target correlations between the
variables in |
num_steps |
The number of steps between 0 and 1 to take in the
grid search for the shrinkage factor. The step-size would be
|
Details
Let W = cor(design_perm). Let R = target_cor.
Then the overall correlation matrix is:
\left(
\begin{array}{cc}
W & R\\
R' & I_K
\end{array}
\right).
This function applies a multiplicative scaling factor to R until
the above matrix is positive semi-definite. That is, it finds a
between 0 and 1 such that
\left(
\begin{array}{cc}
W & aR\\
aR' & I_K
\end{array}
\right)
is positive semi-definite.
Value
A matrix of correlations the same dimension as target_cor.
Actually, the returned matrix is a * target_cor, where a
was determined to make the overall correlation matrix positive
semi-definite.
Author(s)
David Gerard
References
Gerard, D (2020). "Data-based RNA-seq simulations by binomial thinning." BMC Bioinformatics. 21(1), 206. doi:10.1186/s12859-020-3450-9.
Examples
n <- 10
design_perm <- matrix(rep(c(0, 1), length.out = n))
target_cor <- matrix(seq(1, 0, length.out = 10), nrow = 1)
new_cor <- seqgendiff:::fix_cor(design_perm = design_perm, target_cor = target_cor)
new_cor / target_cor
## In the case of one observed covariate, the requirement is just that
## the sum of squared correlations is less than or equal to one.
sum(target_cor ^ 2)
sum(new_cor ^ 2)