gvcm.cat.flex: Regularized Effects with Flexible Smoothing Parameters

In gvcm.cat: Regularized Categorical Effects/Categorical Effect Modifiers/Continuous/Smooth Effects in GLMs

Description

The function fits the same models with the same approximation as in gvcm.cat but the choice of the tuning parameter lambda for the penalty differs: instead of weighting the penalty terms and choosing on global tuning parmeter based on (generalized) cross-validation methods that again rely on the converged model, gvcm.cat.flex estimates several penalty parameteres lambda_i by linking the local quadratic approximation of gvcm.cat with the fantastic methods implemented in the package mgcv. This is why the arguments of gvcm.cat and gvcm.cat.flex differ. gvcm.cat.flex is not as well-developed as gvcm.cat.

Usage

gvcm.cat.flex(whichCoefs, intercept = TRUE, data, family = gaussian(), method = "REML",
tuning = NULL, indexNrCoefs, indexPenNorm, indexPenA, indexPenWeight, 
control = list(c=1e-05, epsilon=1e-07, gama=35, maxi=1500, nu=.5))

Arguments

whichCoefs	vector with covariates (as characters)
intercept	logical
data	a data frame, with named and coded covariates
family	a family object describing the error distribution and link function to be used in the model; see family for details; everyl family that is compatible with gam is working
method	see gam
tuning	for function gam: argument sp
indexNrCoefs	vector with number of coefficients per covariate
indexPenNorm	vector with norm of the employed penalty (as.character)
indexPenA	list with the penalty matrices A_j for each covariate j
indexPenWeight	list, possible weights for the penalty terms (each entry is a vector)
control	a list of parameters for controlling the fitting process; must be NULL or contain all named elements

Details

The local quadratic approximation are linked to the methods of mgcv by alternating the update of the penalty and the update of the PIRLS algorithm/estimating the tuning parameters lambda_i via mgcv. Therefore, gvcm.cat.flex can be slow (but will be faster than gvcm.cat for the most part).

Value

A gamObject.

See Also

Function gvcm.cat.

Examples

## Not run: 
# compare gvcm.cat.flex and gvcm.cat for Lasso-type penalties:
n <- 100
ncov <- 7
set.seed(123)
X <- matrix(rnorm(n*ncov, sd=5), ncol=ncov)
coefs <- rpois(ncov + 1, 2)
y <- cbind(1, X) 
data <- as.data.frame(cbind(y, X))
names(data) <- c("y", paste("x", 1:ncov, sep=""))

m1 <- gvcm.cat.flex(
whichCoefs = paste("x", 1:ncov, sep=""),
data=data,
indexNrCoefs=rep(1, ncov),
indexPenNorm=rep("L1", ncov),
indexPenA=list(1,1,1,1,1,1,1),
indexPenWeight=list(1,1,1,1,1,1,1)
)

m2 <- gvcm.cat(y ~ 1 + p(x1) + p(x2) + p(x3) + p(x4) + p(x5) + p(x6) + p(x7),
              data=data, tuning=list(lambda=m1$sp, specific=TRUE), start=rep(1, 8))

rbind(m1$coefficients, m2$coefficients)

# Lasso-type fusion penalty with gvcm.cat.flex
n <- 100
ncat <- 8
set.seed(567)
X <- t(rmultinom(n, 1, rep(1/ncat, ncat)))[, -1]
coefs <- c(rpois(1, 2), sort(rpois(ncat-1, 1)))

y <- cbind(1, X) 
data <- as.data.frame(y)
data$x1 <- X
names(data) <- c("y", "x1")

A <- a(1:(ncat-1), ncat-2)

m3 <- gvcm.cat.flex(
whichCoefs = c("x1"),
data = data,
indexNrCoefs = c(ncat-1),
indexPenNorm = c("L1"),
indexPenA = list(A),
indexPenWeight = list(rep(1, ncol(A))),
tuning = 100 # fixed and large - in order to demonstrate the fusion of the coefficients
)
m3$coefficients

## End(Not run)

gvcm.cat documentation built on May 1, 2019, 10:13 p.m.