ehr {event}

Regression Models for Event History Intensity Functions

Description

ehr fits an intensity function to event histories, where point is produced by point <- pp(y) and lambda is the user-defined log intensity function.

Nonlinear regression models for lambda can be supplied as formulae where parameters are unknowns. Factor variables cannot be used and parameters must be scalars. (See finterp.)

Usage

ehr(point, lambda=NULL, linear=NULL, plambda=NULL, delta=1,
	envir=parent.frame(), print.level=0, typsize=rep(1,length(plambda)),
	ndigit=10, gradtol=0.00001, iterlim=100, fscale=1,
	stepmax=max(10*sqrt(plambda%*%plambda),10), steptol=0.0004)

Arguments

point

A point process vector produced by pp.

lambda

User-specified function of p, and possibly linear, giving the regression equation for the intensity or a formula beginning with ~, specifying either a linear regression function in the Wilkinson and Rogers notation or a general function with named unknown parameters. The function may contain a linear part that must simply be given the name, linear, in the function. If no function is supplied, the intensity is taken to be constant (a homogeneous Poisson process).

linear

A formula beginning with ~ specifying the linear part of the regression function.

plambda

Vector of initial parameter estimates. If lambda is a formula with unknown parameters, their estimates must be supplied either in their order of appearance in the expression or in a named list.

delta

If any time intervals are different from unity, a vector of time intervals.

envir

Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov. If point has class repeated, it is used as the environment.

print.level

nlm control options.

ndigit

nlm control options.

gradtol

nlm control options.

steptol

nlm control options.

iterlim

nlm control options.

fscale

nlm control options.

typsize

nlm control options.

stepmax

nlm control options.

Author(s)

J.K. Lindsey

References

Lindsey, J.K. (1995) Fitting parametric counting processes by using log linear models. Journal of the Royal Statistical Society C44, 201-212.

See Also

bp, finterp, ident, pp, tccov, tpast, ttime, tvcov.

Examples

y <- c(5,3,2,4)
# event indicator
py <- pp(y)
# time since previous event
ptime <- tpast(y)
# individual ID
i <- c(1,1,2,2)
id <- ident(y, i)
# times and corresponding covariate values
tx <- c(2,3,1,2,2,2,2)
x <- c(1,2,2,1,2,2,1)
zcov <- tvcov(y, x, tx)
# Poisson process
ehr(py, plambda=1)
# Weibull process
lambda1 <- function(p) p[1]+p[2]*log(ptime)
ehr(py, lambda=lambda1, plambda=c(1,1))
# or
ehr(py, lambda=~log(ptime), plambda=c(1,1))
# or
ehr(py, lambda=~b0+b1*log(ptime), plambda=list(b0=1,b1=1))
# Poisson process with time-varying covariate
lambda2 <- function(p) p[1]+p[2]*zcov
ehr(py, lambda=lambda2, plambda=c(1,1))
# or
ehr(py, lambda=~zcov, plambda=c(1,1))
# or
ehr(py, lambda=~c0+c1*zcov, plambda=list(c0=1,c1=1))
# Weibull process with time-varying covariate
lambda3 <- function(p) p[1]+p[2]*log(ptime)+p[3]*zcov
ehr(py, lambda=lambda3, plambda=c(1,1,1))
# or
ehr(py, lambda=~log(ptime)+zcov, plambda=c(1,1,1))
# or
ehr(py, lambda=~c0+b1*log(ptime)+c1*zcov, plambda=list(c0=1,c1=1,b1=1))
# gamma process with time-varying covariate
lambda4 <- function(p) hgamma(ptime, p[1], exp(p[2]+p[3]*zcov))
ehr(py, lambda=lambda4, plambda=c(1,1,1))
# or
ehr(py, lambda=~hgamma(ptime, b1, exp(c0+c1*zcov)),
	plambda=list(c0=1,c1=1,b1=1))
# or
lambda5 <- function(p, linear) hgamma(ptime, p[1], exp(linear))
ehr(py, lambda=lambda5, linear=~zcov, plambda=c(1,1,1))