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

In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

Generalized canonical correlation, estimating alpha, beta, rho.

Description

What exactly is generalized? Canonical correlations start with Rij, a symmetric matrix of Pearson correlation coefficients based on linear relations. This function starts with a more general non-symmetric R*ij produced by gmcmtx0() as an input. This is a superior measure of dependence, allowing for nonlinear dependencies. It generalizes Hotelling's derivation for the nonlinear case. 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 our 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

A	eigenvalue computing matrix for Generalized canonical correlations
rho	Generalized canonical correlation coefficient
bet	RHS coefficient vector
alp	LHS coefficient vector

Note

This function calls kern,

Author(s)

Prof. H. D. Vinod, Economics Dept., Fordham University, NY.

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.

See Also

See gmcmtx0.

Examples

## Not run: 
set.seed(99)
mtx2=matrix(sample(1:25),nrow=5)
g1=gmcmtx0(mtx2)
canonRho(g1,verbo=TRUE)

## End(Not run)#' 

generalCorr documentation built on Oct. 10, 2023, 1:06 a.m.