canonRho: Generalized canonical correlation, estimating alpha, beta, rho.

Description

This function uses data on two sets of column vectors. LHS set [x1, x2 .. xr] has r=nLHS number of columns with coefficients alpha and the larger RHS set [xr+1, xr+2, .. xp] has nRHS=(p-r) columns and RHS coefficients beta. Must arrange the sets so that the larger set in on RHS with coefficients beta estimated first from an eigenvector of the problem A* beta = rho^2 beta where A* is a partitioning of generalized matrix of (non-symmetric) correlation coefficients.

Usage

canonRho(mtx, nLHS = 2, sgn = 1, verbo = FALSE, ridg = c(0, 0))

Arguments

mtx

Input matrix of generalized correlation coefficients R*

nLHS

number of columns in the LHS set, default=2

sgn

preferred sign of coefficients default=1 for positive, use sgn= -1 if prior knowledge suggests that negative signs of coefficients are more realistic

verbo

logical, verbo=FALSE default means do not print results

ridg

two regularization constants added before computing matrix inverses of S11 and S22, respectively, with default=c(0,0). Some suggest ridg=c(0.01,0.01) for stable results

Value

eigenvalue computing matrix for Generalized canonical correlations

rho

Generalized canonical correlation coefficient

bet

RHS coefficient vector

alp

LHS coefficient vector

References

Vinod, H. D. 'Matrix Algebra Topics in Statistics and Economics Using R', Chapter 4 in 'Handbook of Statistics: Computational Statistics with R', Vol.32, co-editors: M. B. Rao and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2014, pp. 143-176.

Vinod, H. D. 'Canonical ridge and econometrics of joint production,' Journal of Econometrics, vol. 4, 147--166.

Vinod, H. D. 'New exogeneity tests and causal paths,' Chapter 2 in 'Handbook of Statistics: Conceptual Econometrics Using R', Vol.32, co-editors: H. D. Vinod and C.R. Rao. New York: North Holland, Elsevier Science Publishers, 2019, pp. 33-64.

Examples

Run this code

# NOT RUN {
# }
# NOT RUN {
set.seed(99)
mtx2=matrix(sample(1:25),nrow=5)
g1=gmcmtx0(mtx2)
canonRho(g1,verbo=TRUE)
# }
# NOT RUN {
#' 
# }