| FitRDeltaQSym {Correlplot} | R Documentation |
Approximation of a correlation matrix with column adjustment and symmetric low rank factorization
Description
Program FitRDeltaQSym calculates a low rank factorization for a correlation matrix. It adjusts for column effects, and the approximation is therefore asymmetric.
Usage
FitRDeltaQSym(R, W = NULL, nd = 2, eps = 1e-10, delta = 0, q = colMeans(R),
itmax.inner = 1000, itmax.outer = 1000, verbose = FALSE)
Arguments
R |
A correlation matrix |
W |
A weight matrix (optional) |
nd |
The rank of the low rank approximation |
eps |
The convergence criterion |
delta |
Initial value for the scalar adjustment (zero by default) |
q |
Initial values for the column adjustments (random by default) |
itmax.inner |
Maximum number of iterations for the inner loop of the algorithm |
itmax.outer |
Maximum number of iterations for the outer loop of the algorithm |
verbose |
Print information or not |
Details
Program FitRDeltaQSym implements an iterative algorithm for the low rank factorization of the correlation matrix. It decomposes the correlation matrix as R = delta J + 1 q' + G G' + E. The approximation of R is ultimately asymmetric, but the low rank factorization used for biplotting (G G') is symmetric.
Value
A list object with fields:
delta |
The final scalar adjustment |
Rhat |
The final approximation to the correlation matrix |
C |
The matrix of biplot vectors |
rmse |
The root mean squared error |
q |
The final column adjustments |
Author(s)
Jan Graffelman (jan.graffelman@upc.edu)
References
Graffelman, J. and De Leeuw, J. (2023) Improved approximation and visualization of the correlation matrix. The American Statistician pp. 1–20. Available online as latest article doi:10.1080/00031305.2023.2186952
See Also
Examples
data(HeartAttack)
X <- HeartAttack[,1:7]
X[,7] <- log(X[,7])
colnames(X)[7] <- "logPR"
R <- cor(X)
W <- matrix(1, 7, 7)
diag(W) <- 0
out.sym <- FitRDeltaQSym(R, W, eps=1e-6)
Rhat <- out.sym$Rhat