survPen (version 1.3.0)

NR.beta: Inner Newton-Raphson algorithm for regression parameters estimation

Description

Applies Newton-Raphson algorithm for beta estimation. Two specific modifications aims at guaranteeing convergence : first the hessian is perturbed whenever it is not positive definite and second, at each step, if the penalized log-likelihood is not maximized, the step is halved until it is.

Usage

NR.beta(build, beta.ini, detail.beta, max.it.beta = 200,
  tol.beta = 1e-04)

Arguments

build

list of objects returned by model.cons

beta.ini

vector of initial regression parameters; default is NULL, in which case the first beta will be log(sum(event)/sum(t1)) and the others will be zero (except if there are "by" variables in which case all betas are set to zero)

detail.beta

if TRUE, details concerning the optimization process in the regression parameters are displayed; default is FALSE

max.it.beta

maximum number of iterations to reach convergence in the regression parameters; default is 200

tol.beta

convergence tolerance for regression parameters; default is 1e-04

Value

List of objects:

beta

estimated regression parameters

ll.unpen

log-likelihood at convergence

ll.pen

penalized log-likelihood at convergence

haz.GL

list of all the matrix-vector multiplications X.GL[[i]]%*%beta for Gauss Legendre integration. Useful to avoid repeating operations in survPen.fit

iter.beta

number of iterations needed to converge

Details

If we note ll.pen and beta respectively the current penalized log-likelihood and estimated parameters and ll.pen.old and betaold the previous ones, the algorithm goes on while (abs(ll.pen-ll.pen.old)>tol.beta) or any(abs((beta-betaold)/betaold)>tol.beta)

Examples

# NOT RUN {
library(survPen)

# standard spline of time with 4 knots

data <- data.frame(time=seq(0,5,length=100),event=1,t0=0)

form <- ~ smf(time,knots=c(0,1,3,5))

t1 <- eval(substitute(time), data)
t0 <- eval(substitute(t0), data)
event <- eval(substitute(event), data)
	
# Setting up the model before fitting
model.c <- model.cons(form,lambda=0,data.spec=data,t1=t1,t1.name="time",
t0=rep(0,100),t0.name="t0",event=event,event.name="event",
expected=NULL,expected.name=NULL,type="overall",n.legendre=20,
cl="survPen(form,data,t1=time,event=event)",beta.ini=NULL)
 
# Estimating the regression parameters at given smoothing parameter (here lambda=0)
Newton1 <- NR.beta(model.c,beta.ini=rep(0,4),detail.beta=TRUE)

# }