mrrr {rrpack}

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

Y

response matrix

X

covariate matrix

is.pca

If TRUE, mixed principal component analysis with X=I

offset

matrix of the same dimension as Y for offset

ctrl.id

indices of unpenalized predictors

family

a list of family functions as used in glm

familygroup

a list of family indices of the responses

maxrank

integer giving the maximum rank allowed. Usually this can be set to min(n,p,q)

penstr

a list of penalty structure of SVD, contains penstr$penaltySVD is the penalty of SVD, penstr$lambdaSVD is the regularization parameter

init

a list of initial values of kappaC0, kappaS0, C0, and S0

control

a list of controling parameters for the fitting

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

obj

the objective function tracking

converged

TRUE/FALSE for convergence

coef

the estimated coefficient matrix

outlier

the estimated outlier matrix

nrank

the rank of the fitted model

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)