Title:	Reduced-Rank Regression
Version:	0.1-13
Description:	Multivariate regression methodologies including classical reduced-rank regression (RRR) studied by Anderson (1951) <doi:10.1214/aoms/1177729580> and Reinsel and Velu (1998) <doi:10.1007/978-1-4757-2853-8>, reduced-rank regression via adaptive nuclear norm penalization proposed by Chen et al. (2013) <doi:10.1093/biomet/ast036> and Mukherjee et al. (2015) <doi:10.1093/biomet/asx080>, robust reduced-rank regression (R4) proposed by She and Chen (2017) <doi:10.1093/biomet/asx032>, generalized/mixed-response reduced-rank regression (mRRR) proposed by Luo et al. (2018) <doi:10.1016/j.jmva.2018.04.011>, row-sparse reduced-rank regression (SRRR) proposed by Chen and Huang (2012) <doi:10.1080/01621459.2012.734178>, reduced-rank regression with a sparse singular value decomposition (RSSVD) proposed by Chen et al. (2012) <doi:10.1111/j.1467-9868.2011.01002.x> and sparse and orthogonal factor regression (SOFAR) proposed by Uematsu et al. (2019) <doi:10.1109/TIT.2019.2909889>.
Depends:	R (≥ 3.4.0)
Imports:	ggplot2, glmnet, MASS, Rcpp (≥ 0.12.0)
LinkingTo:	Rcpp, RcppArmadillo
License:	GPL (≥ 3)
Encoding:	UTF-8
RoxygenNote:	7.2.0
NeedsCompilation:	yes
Packaged:	2022-06-15 15:49:54 UTC; wenjie
Author:	Kun Chen [aut, cre], Wenjie Wang [aut], Jun Yan [ctb]
Maintainer:	Kun Chen <kun.chen@uconn.edu>
Repository:	CRAN
Date/Publication:	2022-06-16 06:40:02 UTC

Mixed-response reduced-rank regression with rank selected by cross validation

Description

Mixed-response reduced-rank regression with rank selected by cross validation

Usage

cv.mrrr(
  Y,
  X,
  is.pca = NULL,
  offset = NULL,
  ctrl.id = c(),
  family = list(gaussian(), binomial(), poisson()),
  familygroup = NULL,
  maxrank = min(ncol(Y), ncol(X)),
  penstr = list(),
  init = list(),
  control = list(),
  nfold = 5,
  foldid = NULL,
  nlam = 20,
  warm = FALSE
)

Arguments

Value

S3 mrrr object, a list containing

Examples

## Not run: 
library(rrpack)
simdata <- rrr.sim3(n = 100, p = 30, q.mix = c(5, 20, 5),
                    nrank = 2, mis.prop = 0.2)
Y <- simdata$Y
Y_mis <- simdata$Y.mis
X <- simdata$X
X0 <- cbind(1,X)
C <- simdata$C
family <- simdata$family
familygroup <- simdata$familygroup
svdX0d1 <- svd(X0)$d[1]
init1 = list(kappaC0 = svdX0d1 * 5)
offset = NULL
control = list(epsilon = 1e-4, sv.tol = 1e-2, maxit = 2000,
               trace = FALSE, gammaC0 = 1.1, plot.cv = TRUE,
               conv.obj = TRUE)
fit.cv.mrrr <- cv.mrrr(Y_mis, X, family = family,
                       familygroup = familygroup,
                       maxrank = 20,
                       penstr = list(penaltySVD = "rankCon",
                                     lambdaSVD = c(1 : 6)),
                       control = control, init = init1,
                       nfold = 10, nlam = 50)
summary(fit.cv.mrrr)
coef(fit.cv.mrrr)
fit.mrrr <- fit.cv.mrrr$fit

## plot(svd(fit.mrrr$coef[- 1,])$d)
plot(C ~ fit.mrrr$coef[- 1, ])
abline(a = 0, b = 1)

## End(Not run)

Reduced-rank regression with rank selected by cross validation

Description

Reduced-rank regression with rank selected by cross validation

Usage

cv.rrr(
  Y,
  X,
  nfold = 10,
  maxrank = min(dim(Y), dim(X)),
  norder = NULL,
  coefSVD = FALSE
)

Arguments

Value

a list containing rr estimates from cross validation

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_cv <- with(mydata, cv.rrr(Y, X, nfold = 10, maxrank = 10))
summary(rfit_cv)
coef(rfit_cv)

Sparse orthognal factor regression tuned by cross validation

Description

Sparse orthognal factor regression tuned by cross validation

Usage

cv.sofar(
  Y,
  X,
  nrank = 1,
  su = NULL,
  sv = NULL,
  nfold = 5,
  norder = NULL,
  modstr = list(),
  control = list(),
  screening = FALSE
)

Arguments

Details

The model parameters can be specified through argument modstr. The available elements include

• mu: parameter in the augmented Lagrangian function.

• mugamma: increament of mu along iterations to speed up computation.

• WA: weight matrix for A.

• WB: weight matrix for B.

• Wd: weight matrix for d.

• wgamma: power parameter in constructing adaptive weights.

The model fitting can be controled through argument control. The avilable elements include

• nlam: number of lambda triplets to be used.

• lam.min.factor: set the smallest lambda triplets as a fraction of the estimation lambda.max triplets.

• lam.max.factor: set the largest lambda triplets as a multiple of the estimation lambda.max triplets.

• lam.AB.factor: set the relative penalty level between A/B and D.

• penA,penB,penD: if TRUE, penalty is applied.

• lamA: sequence of tuning parameters for A.

• lamB: sequence of tuning parameters for B.

• lamD: sequence of tuning parameters for d.

• methodA: penalty for penalizing A.

• methodB: penalty for penalizing B.

• epsilon: convergence tolerance.

• maxit: maximum number of iterations.

• innerEpsilon: convergence tolerance for inner subroutines.

• innerMaxit: maximum number of iterations for inner subroutines.

• sv.tol: tolerance for singular values.

Row-sparse reduced-rank regression tuned by cross validation

Description

Row-sparse reduced-rank regression tuned by cross validation

Usage

cv.srrr(
  Y,
  X,
  nrank = 1,
  method = c("glasso", "adglasso"),
  nfold = 5,
  norder = NULL,
  A0 = NULL,
  V0 = NULL,
  modstr = list(),
  control = list()
)

Arguments

Details

Model parameters controlling the model fitting can be specified through argument modstr. The available elements include

• lamA: tuning parameter sequence.

• nlam: number of tuning parameters; no effect if lamA is specified.

• minLambda: minimum lambda value, no effect if lamA is specified.

• maxLambda: maxmum lambda value, no effect if lamA is specified.

• WA: adaptive weights. If NULL, the weights are constructed from RRR.

• wgamma: power parameter for constructing adaptive weights.

Similarly, the computational parameters controlling optimization can be specified through argument control. The available elements include

• epsilon: epsilonergence tolerance.

• maxit: maximum number of iterations.

• inner.eps: used in inner loop.

• inner.maxit: used in inner loop.

Value

A list of fitting results

References

Chen, L. and Huang, J.Z. (2012) Sparse reduced-rank regression for simultaneous dimension reduction and variable selection. Journal of the American Statistical Association. 107:500, 1533–1545.

Generalized or mixed-response reduced-rank regression

Description

Peforms either rank constrained maximum likelihood estimation or singular value penalized estimation.

Usage

mrrr(
  Y,
  X,
  is.pca = NULL,
  offset = NULL,
  ctrl.id = c(),
  family = list(gaussian(), binomial()),
  familygroup = NULL,
  maxrank = min(ncol(Y), ncol(X)),
  penstr = list(),
  init = list(),
  control = list()
)

Arguments

Details

The model fitting process can be fine tuned through argument control. The available elements for control include

• epsilon: positive convergence tolerance epsilon; the iterations converge when |new - old | / (old + 0.1) < epsilon. treated as zero.

• sv.tol: tolerance for singular values.

• maxit: integer giving the maximal number of iterations.

• trace:logical indicating if tracing the objective is needed.

• conv.obj:if TRUE, track objective function.

• equal.phi:if TRUE, use a single dispersion parameter for Gaussian responses.

• plot.obj:if TRUE, plot obj values along iterations; for checking only

• plot.cv:if TRUE, plot cross validation error.

• gammaC0:adaptive scaling to speed up computation.

Similarly, the available elements for arguments penstr specifying penalty structure of SVD include

• penaltySVD: penalty for reducing rank

• lambdaSVD: tuning parameter. For penaltySVD = rankCon, this is the specified rank.

Value

S3 mrrr object, a list containing

Examples

library(rrpack)
simdata <- rrr.sim3(n = 100, p = 30, q.mix = c(5, 20, 5),
                    nrank = 2, mis.prop = 0.2)
Y <- simdata$Y
Y_mis <- simdata$Y.mis
X <- simdata$X
X0 <- cbind(1, X)
C <- simdata$C
family <- simdata$family
familygroup <- simdata$familygroup
svdX0d1 <- svd(X0)$d[1]
init1 = list(kappaC0 = svdX0d1 * 5)
offset = NULL
control = list(epsilon = 1e-4, sv.tol = 1e-2, maxit = 2000,
               trace = FALSE, gammaC0 = 1.1, plot.cv = TRUE,
               conv.obj = TRUE)
fit.mrrr <- mrrr(Y_mis, X, family = family, familygroup = familygroup,
                 penstr = list(penaltySVD = "rankCon", lambdaSVD = 2),
                 control = control, init = init1)
summary(fit.mrrr)
coef(fit.mrrr)
par(mfrow = c(1, 2))
plot(fit.mrrr$obj)
plot(C ~ fit.mrrr$coef[- 1 ,])
abline(a = 0, b = 1)

Scatter Plot

Description

S3 methods generating scatter plot for some objects generated by rrpack using ggplot2. An ggplot2 object is returned so that users are allowed to easily further customize the plot.

Usage

## S3 method for class 'rrr'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

## S3 method for class 'sofar'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

## S3 method for class 'cv.sofar'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

## S3 method for class 'srrr'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

## S3 method for class 'cv.srrr'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

## S3 method for class 'rssvd'
plot(
  x,
  y = NULL,
  layer = 1L,
  xlab = paste("latent predictor ", layer, sep = ""),
  ylab = paste("latent response ", layer, sep = ""),
  ...
)

Arguments

Value

ggplot2 object.

Robust reduced-rank regression

Description

Perform robust reduced-rank regression.

Usage

r4(
  Y,
  X,
  maxrank = min(dim(Y), dim(X)),
  method = c("rowl0", "rowl1", "entrywise"),
  Gamma = NULL,
  ic.type = c("AIC", "BIC", "PIC"),
  modstr = list(),
  control = list()
)

Arguments

Details

The model parameters can be controlled through argument modstr. The available elements include

• nlam: parameter in the augmented Lagrangian function.

• adaptive: if TRUE, use leverage values for adaptive penalization. The default value is FALSE.

• weights: user supplied weights for adaptive penalization.

• minlam: maximum proportion of outliers.

• maxlam: maximum proportion of good observations.

• delid: discarded observation indices for initial estimation.

The model fitting can be controlled through argument control. The available elements include

• epsilon: convergence tolerance.

• maxit: maximum number of iterations.

• qr.tol: tolerance for qr decomposition.

• tol: tolerance.

Value

a list consisting of

References

She, Y. and Chen, K. (2017) Robust reduced-rank regression. Biometrika, 104 (3), 633–647.

Examples

## Not run: 
library(rrpack)
n <- 100; p <- 500; q <- 50
xrank <- 10; nrank <- 3; rmax <- min(n, p, q, xrank)
nlam <- 100; gamma <- 2
rho_E <- 0.3
rho_X <- 0.5
nlev <- 0
vlev <- 0
vout <- NULL
vlevsd <- NULL
nout <- 0.1 * n
s2n <- 1
voutsd <- 2
simdata <- rrr.sim5(n, p, q, nrank, rx = xrank, s2n = s2n,
                    rho_X = rho_X, rho_E = rho_E, nout = nout, vout = vout,
                    voutsd = voutsd,nlev = nlev,vlev=vlev,vlevsd=vlevsd)
Y <- simdata$Y
X <- simdata$X
fit <- r4(Y, X, maxrank = rmax,
               method = "rowl0", ic.type= "PIC")
summary(fit)
coef(fit)
which(apply(fit$s,1,function(a)sum(a^2))!=0)

## End(Not run)

Estimated coefficients

Description

S3 methods extracting estimated coefficients for objects generated by rrpack.

Usage

## S3 method for class 'mrrr'
coef(object, ...)

## S3 method for class 'cv.mrrr'
coef(object, ...)

## S3 method for class 'r4'
coef(object, ...)

## S3 method for class 'rrr'
coef(object, ...)

## S3 method for class 'rrr.fit'
coef(object, ...)

## S3 method for class 'cv.rrr'
coef(object, ...)

## S3 method for class 'srrr'
coef(object, ...)

## S3 method for class 'sofar'
coef(object, ...)

## S3 method for class 'rssvd'
coef(object, ...)

Arguments

Value

A numeric matrix.

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

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

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)

Cook's distance in reduced-rank regression for model diagnostics

Description

Compute Cook's distance for model diagnostics in rrr estimation.

Usage

rrr.cookD(Y, X = NULL, nrank = 1, qr.tol = 1e-07)

Arguments

Value

a list containing diagnostics measures

References

Chen, K. Model diagnostics in reduced-rank estimation. Statistics and Its interface, 9, 469–484.

Fitting reduced-rank regression with a specific rank

Description

Given a response matrix and a covariate matrix, this function fits reduced rank regression for a specified rank. It reduces to singular value decomposition if the covariate matrix is the identity matrix.

Usage

rrr.fit(Y, X, nrank = 1, weight = NULL, coefSVD = FALSE)

Arguments

Value

S3 rrr object, a list consisting of

Examples

Y <- matrix(rnorm(400), 100, 4)
X <- matrix(rnorm(800), 100, 8)
rfit <- rrr.fit(Y, X, nrank = 2)
coef(rfit)

Leverage scores and Cook's distance in reduced-rank regression for model diagnostics

Description

Compute leverage scores and Cook's distance for model diagnostics in rrr estimation.

Usage

rrr.leverage(Y, X = NULL, nrank = 1, qr.tol = 1e-07)

Arguments

Value

‘rrr.leverage’ returns a list containing a vector of leverages and a scalar of the degrees of freedom (sum of leverages). ‘rrr.cooks’ returns a list containing

References

Chen, K. Model diagnostics in reduced-rank estimation. Statistics and Its interface, 9, 469–484.

Simulation model 1

Description

Similar to the the RSSVD simulation model in Chen, Chan, Stenseth (2012), JRSSB.

Usage

rrr.sim1(
  n = 50,
  p = 25,
  q = 25,
  nrank = 3,
  s2n = 1,
  sigma = NULL,
  rho_X = 0.5,
  rho_E = 0
)

Arguments

Value

similated model and data

References

Chen, K., Chan, K.-S. and Stenseth, N. C. (2012) Reduced rank stochastic regression with a sparse singular value decomposition. Journal of the Royal Statistical Society: Series B, 74, 203–221.

Simulation model 2

Description

Similar to the the SRRR simulation model in Chen and Huang (2012), JASA

Usage

rrr.sim2(
  n = 100,
  p = 50,
  p0 = 10,
  q = 50,
  q0 = 10,
  nrank = 3,
  s2n = 1,
  sigma = NULL,
  rho_X = 0.5,
  rho_E = 0
)

Arguments

Value

similated model and data

References

Chen, L. and Huang, J.Z. (2012) Sparse reduced-rank regression for simultaneous dimension reduction and variable selection. Journal of the American Statistical Association, 107:500, 1533–1545.

Simulation model 3

Description

Generate data from a mixed-response reduced-rank regression model

Usage

rrr.sim3(
  n = 100,
  p = 30,
  q.mix = c(5, 20, 5),
  nrank = 2,
  intercept = rep(0.5, 30),
  mis.prop = 0.2
)

Arguments

Value

similated model and data

References

Chen, K., Luo, C., and Liang, J. (2017) Leveraging mixed and incomplete outcomes through a mixed-response reduced-rank regression. Technical report.

Simulation model 4

Description

Generate data from a mean-shifted reduced-rank regression model

Usage

rrr.sim4(
  n = 100,
  p = 12,
  q = 8,
  nrank = 3,
  s2n = 1,
  rho_X = 0,
  rho_E = 0,
  nout = 10,
  vout = NULL,
  voutsd = 2,
  nlev = 10,
  vlev = 10,
  vlevsd = NULL,
  SigmaX = "CorrCS",
  SigmaE = "CorrCS"
)

Arguments

Value

similated model and data

References

She, Y. and Chen, K. (2017) Robust reduced-rank regression. Biometrika, 104 (3), 633–647.

Simulation model 5

Description

Generate data from a mean-shifted reduced-rank regression model

Usage

rrr.sim5(
  n = 40,
  p = 100,
  q = 50,
  nrank = 5,
  rx = 10,
  s2n = 1,
  rho_X = 0,
  rho_E = 0,
  nout = 10,
  vout = NULL,
  voutsd = 2,
  nlev = 10,
  vlev = 10,
  vlevsd = NULL,
  SigmaX = "CorrCS",
  SigmaE = "CorrCS"
)

Arguments

Value

similated model and data

References

She, Y. and Chen, K. (2017) Robust reduced-rank regression. Biometrika, 104 (3), 633–647.

Fitting reduced-rank ridge regression with given rank and shrinkage penalty

Description

Fitting reduced-rank ridge regression with given rank and shrinkage penalty

Usage

rrs.fit(Y, X, nrank = min(ncol(Y), ncol(X)), lambda = 1, coefSVD = FALSE)

Arguments

Value

S3 rrr object, a list consisting of

References

Mukherjee, A. and Zhu, J. (2011) Reduced rank ridge regression and its kernal extensions.

Mukherjee, A., Chen, K., Wang, N. and Zhu, J. (2015) On the degrees of freedom of reduced-rank estimators in multivariate regression. Biometrika, 102, 457–477.

Examples

library(rrpack)
Y <- matrix(rnorm(400), 100, 4)
X <- matrix(rnorm(800), 100, 8)
rfit <- rrs.fit(Y, X)

Reduced-rank regression with a sparse singular value decomposition

Description

Reduced-rank regression with a sparse singular value decomposition using the iterative exclusive extraction algorithm.

Usage

rssvd(
  Y,
  X,
  nrank,
  ic.type = c("BIC", "BICP", "AIC"),
  orthX = FALSE,
  control = list(),
  screening = FALSE
)

Arguments

Details

The model fitting can be controled through argument control. The available elements include

• maxit: maximum number of iterations.

• epsilon: convergence tolerance.

• innerMaxit: maximum number of iterations for inner steps.

• innerEpsilon: convergence tolerance for inner steps.

• nlambda: number of tuning parameters.

• adaptive: if Ture, use adaptive penalization.

• gamma0: power parameter for constructing adaptive weights.

• minLambda: multiplicate factor to determine the minimum lambda.

• niter.eea: the number of iterations in the iterative exclusive extraction algorithm.

• df.tol: tolerance.

Value

S3 rssvd.path object, a list consisting of

References

Chen, K., Chan, K.-S. and Stenseth, N. C. (2012) Reduced rank stochastic regression with a sparse singular value decomposition. Journal of the Royal Statistical Society: Series B, 74, 203–221.

Examples

library(rrpack)
## Simulate data from a sparse factor regression model
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)
fit1 <- with(mydata, rssvd(Y, X, nrank = nrank + 1))
summary(fit1)
plot(fit1)

Sparse orthogonal factor regression

Description

Compute solution paths of sparse orthogonal factor regression

Usage

sofar(
  Y,
  X,
  nrank = 1,
  su = NULL,
  sv = NULL,
  ic.type = c("GIC", "BIC", "AIC", "GCV"),
  modstr = list(),
  control = list(),
  screening = FALSE
)

Arguments

Details

The model parameters can be specified through argument modstr. The available elements include

• mu: parameter in the augmented Lagrangian function.

• mugamma: increament of mu along iterations to speed up computation.

• WA: weight matrix for A.

• WB: weight matrix for B.

• Wd: weight matrix for d.

• wgamma: power parameter in constructing adaptive weights.

The model fitting can be controled through argument control. The avilable elements include

• nlam: number of lambda triplets to be used.

• lam.min.factor: set the smallest lambda triplets as a fraction of the estimation lambda.max triplets.

• lam.max.factor: set the largest lambda triplets as a multiple of the estimation lambda.max triplets.

• lam.AB.factor: set the relative penalty level between A/B and D.

• penA,penB,penD: if TRUE, penalty is applied.

• lamA: sequence of tuning parameters for A.

• lamB: sequence of tuning parameters for B.

• lamD: sequence of tuning parameters for d.

• methodA: penalty for penalizing A.

• methodB: penalty for penalizing B.

• epsilon: convergence tolerance.

• maxit: maximum number of iterations.

• innerEpsilon: convergence tolerance for inner subroutines.

• innerMaxit: maximum number of iterations for inner subroutines.

• sv.tol: tolerance for singular values.

Value

A sofar object containing

References

Uematsu, Y., Fan, Y., Chen, K., Lv, J., & Lin, W. (2019). SOFAR: large-scale association network learning. IEEE Transactions on Information Theory, 65(8), 4924–4939.

Examples

## Not run: 
library(rrpack)
## Simulate data from a sparse factor regression model
p <- 100; 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)
Y <- mydata$Y
X <- mydata$X

fit1 <- sofar(Y, X, ic.type = "GIC", nrank = nrank + 2,
              control = list(methodA = "adlasso", methodB = "adlasso"))
summary(fit1)
plot(fit1)

fit1$U
crossprod(fit1$U) #check orthogonality
fit1$V
crossprod(fit1$V) #check orthogonality

## End(Not run)

Row-sparse reduced-eank regresssion

Description

Row-sparse reduced-rank regresssion for a prespecified rank; produce a solution path for selecting predictors

Usage

srrr(
  Y,
  X,
  nrank = 2,
  method = c("glasso", "adglasso"),
  ic.type = c("BIC", "BICP", "AIC", "GCV", "GIC"),
  A0 = NULL,
  V0 = NULL,
  modstr = list(),
  control = list(),
  screening = FALSE
)

Arguments

Details

Model parameters controlling the model fitting can be specified through argument modstr. The available elements include

• lamA: tuning parameter sequence.

• nlam: number of tuning parameters; no effect if lamA is specified.

• minLambda: minimum lambda value, no effect if lamA is specified.

• maxLambda: maxmum lambda value, no effect if lamA is specified.

• WA: adaptive weights. If NULL, the weights are constructed from RRR.

• wgamma: power parameter for constructing adaptive weights.

Similarly, the computational parameters controlling optimization can be specified through argument control. The available elements include

• epsilon: epsilonergence tolerance.

• maxit: maximum number of iterations.

• inner.eps: used in inner loop.

• inner.maxit: used in inner loop.

Value

A list of fitting results

References

Chen, L. and Huang, J. Z. (2012) Sparse reduced-rank regression for simultaneous dimension reduction and variable selection. Journal of the American Statistical Association. 107:500, 1533–1545.

Examples

library(rrpack)
p <- 100; n <- 100; nrank <- 3
mydata <- rrr.sim2(n, p, p0 = 10,q = 50, q0 = 10, nrank = 3,
                   s2n = 1, sigma = NULL, rho_X = 0.5, rho_E = 0)
fit1 <- with(mydata, srrr(Y, X, nrank = 3))
summary(fit1)
coef(fit1)
plot(fit1)

Summarize rrpack Objects

Description

S3 methods summarizing objects generated by rrpack.

Usage

## S3 method for class 'mrrr'
summary(object, ...)

## S3 method for class 'cv.mrrr'
summary(object, ...)

## S3 method for class 'r4'
summary(object, ...)

## S3 method for class 'rrr'
summary(object, ...)

## S3 method for class 'cv.rrr'
summary(object, ...)

## S3 method for class 'sofar'
summary(object, ...)

## S3 method for class 'cv.sofar'
summary(object, ...)

## S3 method for class 'srrr'
summary(object, ...)

## S3 method for class 'cv.srrr'
summary(object, ...)

## S3 method for class 'rssvd'
summary(object, ...)

Arguments