# canonRho: Generalized canonical correlation, estimating alpha, beta,... In generalCorr: Generalized Correlations, Causal Paths and Portfolio Selection

 canonRho R Documentation

## 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 `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.