Generalized or mixed-response reduced-rank regression
Peforms either rank constrained maximum likelihood estimation or singular value penalized estimation.
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())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 |
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 |
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.
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 |
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 ,])
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