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rrr

Multivariate reduced-rank linear regression

Description

Produce solution paths of reduced-rank estimators and adaptive nuclear norm penalized estimators; compute the degrees of freeom of the RRR estimators and select a solution via certain information criterion.

Usage

rrr(Y, X, penaltySVD = c("rank", "ann"),
    ic.type = c("GIC","AIC","BIC","BICP","GCV"),
    df.type = c("exact","naive"), maxrank = min(dim(Y), dim(X)),
    modstr = list(), control = list())

Arguments

`Y`	a matrix of response (n by q)
`X`	a matrix of covariate (n by p)
`penaltySVD`	‘rank’: rank-constrainted estimation; ‘ann’: adaptive nuclear norm estimation.
`ic.type`	the information criterion to be used; currently supporting ‘AIC’, ‘BIC’, ‘BICP’, ‘GCV’, and ‘GIC’.
`df.type`	‘exact’: the exact degrees of freedoms based on SURE theory; ‘naive’: the naive degress of freedoms based on counting number of free parameters
`maxrank`	an integer of maximum desired rank.
`modstr`	a list of model parameters controlling the model fitting
`control`	a list of parameters for controlling the fitting process: ‘sv.tol’ controls the tolerence of singular values; ‘qr.tol’ controls the tolerence of QR decomposition for the LS fit

Details

Model parameters can be specified through argument modstr. The available include

gamma: A scalar power parameter of the adaptive weights in penalty == "ann".
nlambda: The number of lambda values; no effect if penalty == "count".
lambda: A vector of user-specified rank values if penalty == "count" or a vector of penalty values if penalty == "ann".

The available elements for argument control include

sv.tol: singular value tolerence.
qr.tol: QR decomposition tolerence.

Value

S3 rrr object, a list consisting of

`call`	original function call
`Y`	input matrix of response
`X`	input matrix of covariate
`A`	right singular matri x of the least square fitted matrix
`Ad`	a vector of squared singular values of the least square fitted matrix
`coef.ls`	coefficient estimate from LS
`Spath`	a matrix, each column containing shrinkage factors of the singular values of a solution; the first four objects can be used to recover all reduced-rank solutions
`df.exact`	the exact degrees of freedom
`df.naive`	the naive degrees of freedom
`penaltySVD`	the method of low-rank estimation
`sse`	a vecotr of sum of squard errors
`ic`	a vector of information criterion
`coef`	estimated coefficient matrix
`U`	estimated left singular matrix such that XU/sqrtn is orthogonal
`V`	estimated right singular matrix that is orthogonal
`D`	estimated singular value matrix such that C = UDVt
`rank`	estimated rank

References

Chen, K., Dong, H. and Chan, K.-S. (2013) Reduced rank regression via adaptive nuclear norm penalization. Biometrika, 100, 901–920.

Examples

library(rrpack)
p <- 50; q <- 50; n <- 100; nrank <- 3
mydata <- rrr.sim1(n, p, q, nrank, s2n = 1, sigma = NULL,
                   rho_X = 0.5, rho_E = 0.3)
rfit <- with(mydata, rrr(Y, X, maxrank = 10))
summary(rfit)
coef(rfit)
plot(rfit)

rrpack

Reduced-Rank Regression

v0.1-11

GPL (>= 3)

Authors

Kun Chen [aut, cre] (<https://orcid.org/0000-0003-3579-5467>), Wenjie Wang [ctb] (<https://orcid.org/0000-0003-0363-3180>), Jun Yan [ctb] (<https://orcid.org/0000-0003-4401-7296>)

Initial release

2019-11-09

rrr