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

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

Value

A gamObject.

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).

Examples

Run this code

## 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)