gnlm (version 1.1.1)

gnlr3: Generalized Nonlinear Regression Models for Three Parameter Distributions

Description

gnlr3 fits user specified nonlinear regression equations to one, two, or all three parameters of three parameter distributions. Continuous data may be left, right, and/or interval censored.

Usage

gnlr3(y = NULL, distribution = "normal", mu = NULL, shape = NULL,
  family = NULL, linear = NULL, pmu = NULL, pshape = NULL,
  pfamily = NULL, exact = FALSE, wt = 1, common = FALSE,
  delta = 1, envir = parent.frame(), print.level = 0,
  typsize = abs(p), ndigit = 10, gradtol = 1e-05, stepmax = 10 *
  sqrt(p %*% p), steptol = 1e-05, iterlim = 100, fscale = 1)

Arguments

y

The response vector for uncensored data, two columns for censored data, with the second being the censoring indicator (1: uncensored, 0: right censored, -1: left censored.), or an object of class, response (created by restovec) or repeated (created by rmna or lvna). If the repeated data object contains more than one response variable, give that object in envir and give the name of the response variable to be used here.

distribution

Either a character string containing the name of the distribution or a function giving the -log likelihood and calling the location, shape, and family functions. Distributions are Box-Cox transformed normal, generalized inverse Gauss, generalized logistic, Hjorth, generalized gamma, Burr, generalized Weibull, power exponential, Student t, generalized extreme value, power variance function Poisson, and skew Laplace. (For definitions of distributions, see the corresponding [dpqr]distribution help.)

mu

A user-specified function of pmu, and possibly linear, giving the regression equation for the location. This may contain a linear part as the second argument to the function. It may also be a formula beginning with ~, specifying either a linear regression function for the location parameter in the Wilkinson and Rogers notation or a general function with named unknown parameters. If it contains unknown parameters, the keyword linear may be used to specify a linear part. If nothing is supplied, the location is taken to be constant unless the linear argument is given.

shape

A user-specified function of pshape, and possibly linear, giving the regression equation for the dispersion or shape parameter. This may contain a linear part as the second argument to the function. It may also be a formula beginning with ~, specifying either a linear regression function for the shape parameter in the Wilkinson and Rogers notation or a general function with named unknown parameters. If it contains unknown parameters, the keyword linear may be used to specify a linear part. If nothing is supplied, this parameter is taken to be constant unless the linear argument is given. This parameter is the logarithm of the usual one.

family

A user-specified function of pfamily, and possibly linear, for the regression equation of the third (family) parameter of the distribution. This may contain a linear part that is the second argument to the function. It may also be a formula beginning with ~, specifying either a linear regression function for the family parameter in the Wilkinson and Rogers notation or a general function with named unknown parameters. If neither is supplied, this parameter is taken to be constant unless the linear argument is given. In most cases, this parameter is the logarithm of the usual one.

linear

A formula beginning with ~ in W&R notation, specifying the linear part of the regression function for the location parameters or list of three such expressions for the location, shape, and/or family parameters.

pmu

Vector of initial estimates for the location parameters. If mu 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.

pshape

Vector of initial estimates for the shape parameters. If shape 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.

pfamily

Vector of initial estimates for the family parameters. If family 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.

exact

If TRUE, fits the exact likelihood function for continuous data by integration over intervals of observation given in delta, i.e. interval censoring.

wt

Weight vector.

common

If TRUE, at least two of mu, shape, and family must both be either functions with, as argument, a vector of parameters having some or all elements in common between them so that indexing is in common between them or formulae with unknowns. All parameter estimates must be supplied in pmu. If FALSE, parameters are distinct between the two functions and indexing starts at one in each function.

delta

Scalar or vector giving the unit of measurement (always one for discrete data) for each response value, set to unity by default - for example, if a response is measured to two decimals, delta=0.01. If the response is transformed, this must be multiplied by the Jacobian. The transformation cannot contain unknown parameters. For example, with a log transformation, delta=1/y. (The delta values for the censored response are ignored.)

envir

Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov; the name of the response variable should be given in y. If y has class repeated, it is used as the environment.

print.level

Arguments controlling nlm.

typsize

Arguments controlling nlm.

ndigit

Arguments controlling nlm.

gradtol

Arguments controlling nlm.

stepmax

Arguments controlling nlm.

steptol

Arguments controlling nlm.

iterlim

Arguments controlling nlm.

fscale

Arguments controlling nlm.

Value

A list of class gnlm is returned that contains all of the relevant information calculated, including error codes.

Details

Nonlinear regression models can be supplied as formulae where parameters are unknowns in which case factor variables cannot be used and parameters must be scalars. (See finterp.)

The printed output includes the -log likelihood (not the deviance), the corresponding AIC, the maximum likelihood estimates, standard errors, and correlations.

See Also

finterp, fmr, glm, gnlr, lm, nlr, nls.

Examples

# NOT RUN {
sex <- c(rep(0,10),rep(1,10))
sexf <- gl(2,10)
age <- c(8,10,12,12,8,7,16,7,9,11,8,9,14,12,12,11,7,7,7,12)
y <- cbind(c(9.2, 7.3,13.0, 6.9, 3.9,14.9,17.8, 4.8, 6.4, 3.3,17.2,
	14.4,17.0, 5.0,17.3, 3.8,19.4, 5.0, 2.0,19.0),
	c(0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1))
# y <- cbind(rweibull(20,2,2+2*sex+age),rbinom(20,1,0.7))
# log linear regression with the generalized Weibull distribution
mu <- function(p) exp(p[1]+p[2]*sex+p[3]*age)
gnlr3(y, dist="Weibull", mu=mu, pmu=c(3,1,0), pshape=2, pfamily=-2)
# or equivalently
mu1 <- function(p,linear) exp(linear)
gnlr3(y, dist="Weibull", mu=mu1, linear=~sex+age, pmu=c(3,1,0),
	pshape=2, pfamily=-2)
# or
gnlr3(y, dist="Weibull", mu=~exp(b0+b1*sex+b2*age),
	pmu=list(b0=3,b1=1,b2=0), pshape=2, pfamily=-2)
#
# include regression for the shape parameter with same mu function
shape <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr3(y, dist="Weibull", mu=mu, shape=shape,
	pmu=c(3,1,0), pshape=c(2,0,0), pfamily=-2)
# or equivalently
gnlr3(y, dist="Weibull", mu=mu1, linear=list(~sexf+age,~sex+age,NULL),
	pmu=c(3,1,0), pshape=c(2,0,0), pfamily=-2)
# or
gnlr3(y, dist="Weibull", mu=~exp(b0+b1*sex+b2*age),
	shape=~c0+c1*sex+c2*age, pmu=c(3,1,0),
	pshape=list(c0=2,c1=0,c2=0), pfamily=-2)
# include regression for the family parameter with same mu
# and shape functions
family <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr3(y, dist="Weibull", mu=mu1, linear=~sexf+age, shape=shape,
	family=family, pmu=c(2.5,1,0), pshape=c(2,0,0), pfamily=c(-2,0,0))
# or equivalently
gnlr3(y, dist="Weibull", mu=mu1, linear=list(~sex+age,~sex+age,~sex+age),
	pmu=c(2.5,1,0), pshape=c(2,0,0), pfamily=c(-2,0,0))
# or
gnlr3(y, dist="Weibull", mu=~exp(b0+b1*sex+b2*age),
	shape=~c0+c1*sex+c2*age, family=~d0+d1*sex+d2*age,
	pmu=list(b0=2.5,b1=1,b2=0), pshape=list(c0=2,c1=0,c2=0),
	pfamily=list(d0=-2,d1=0,d2=0))
#
# common parameters
mu <- function(p) exp(p[1]+p[2]*sex+p[3]*age)
shape <- function(p) p[4]+p[5]*sex+p[3]*age
family <- function(p) p[6]+p[7]*sex+p[3]*age
gnlr3(y, dist="Weibull", mu=mu, shape=shape, family=family,
	pmu=c(2.5,1,0,1,0,1,0), common=TRUE)
# or
gnlr3(y, dist="Weibull", mu=~exp(a+b*sex+c*age), shape=~d+e*sex+c*age,
	family=~f+g*sex+c*age, pmu=c(2.5,1,0,1,0,1,0), common=TRUE)

# }