Fit a Generalized Nonlinear Regression Model

Usage

gnlr(y, distribution="normal", mu=NULL, shape=NULL, linear=NULL,
	pmu=NULL, pshape=NULL, exact=F, wt=1, delta=1, shfn=F, common=F,
	envir=sys.frame(sys.parent()), print.level=0, typsiz=abs(p),
	ndigit=10, gradtol=0.00001, stepmax=10*sqrt(p%*%p),
	steptol=0.00001, iterlim=100, fscale=1)

Arguments

y A response vector for uncensored data, a two column matrix for binomial data or censored data, with the second column 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).
distribution Either a character string containing the name of the distribution or a function giving the -log likelihood and calling the location and shape functions.
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 none 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 and/or mu, giving the regression equation for the dispersion or shape parameter. This may contain a linear part as the second argument to the function and the location function as last argument (in which case shfn must be set to TRUE). 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 none is supplied, this parameter is taken to be constant unless the linear argument is given. This parameter is the logarithm of the usual one.
linear A formula beginning with ~, specifying the linear part of the regression function for the location parameter or list of two such expressions for the location and/or shape 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.
exact If TRUE, fits the exact likelihood function for continuous data by integration over intervals of observation, i.e. interval censoring.
wt Weight vector.
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.)
shfn If true, the supplied shape function depends on the location (function). The name of this location function must be the last argument of the shape function.
common If TRUE, mu and shape must both be 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; 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.
envir Environment in which model formulae are to be interpreted or a data object of class, repeated, tccov, or tvcov. If y has class repeated, it is used as the environment.
others Arguments controlling nlm.

Description

gnlr fits user-specified nonlinear regression equations to one or both parameters of the common one and two parameter distributions (binomial, beta binomial, double binomial, mult(iplicative) binomial, Poisson, negative binomial, double Poisson, mult(iplicative) Poisson, gamma count, Consul generalized Poisson, logarithmic series, geometric, normal, inverse Gauss, logistic, exponential, gamma, Weibull, extreme value, Cauchy, Pareto, Laplace, and Levy; all but the binomial-based distributions may be right and/or left censored). A user-specified -log likelihood can also be supplied for the distribution.

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

Value

A list of class gnlr is returned. The printed output includes the -log likelihood (not the deviance), the corresponding AIC, the maximum likelihood estimates, standard errors, and correlations. A list is returned that contains all of the relevant information calculated, including error codes.

Author(s)

J.K. Lindsey

Examples

y <- rgamma(10,2,5)
sex <- c(rep(0,5),rep(1,5))
sexf <- gl(2,5)
age <- rpois(10,10)
# linear regression with inverse Gauss distribution
mu <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, pmu=rep(1,3), pshape=1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~sexf+age, pmu=rep(1,3), pshape=1)
# or
gnlr(y, dist="inverse Gauss", linear=~sex+age, pmu=rep(1,3), pshape=1)
# or
gnlr(y, dist="inverse Gauss", mu=~b0+b1*sex+b2*age,
	pmu=list(b0=1,b1=1,b2=1), pshape=1)
#
# nonlinear regression with inverse Gauss distribution
mu <- function(p, linear) p[1]+exp(linear)
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sex+age, pmu=rep(1,4),
	pshape=1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~b4+exp(b0+b1*sex+b2*age),
	pmu=list(b0=1,b1=1,b2=1,b4=1), pshape=1)
# one explicit parameter in mu, three in linear, one for shape
#
# include regression for the shape parameter with same mu function
shape <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sex+age, shape=shape,
	pmu=rep(1,4), pshape=rep(1,3))
# or equivalently
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age,
	shape=~sexf+age, pmu=rep(1,4), pshape=rep(1,3))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=list(~sex+age,~sex+age),
	pmu=rep(1,4),pshape=rep(1,3))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sex+age,
	shape=~c0+c1*sex+c2*age, pmu=rep(1,4),
	pshape=list(c0=1,c1=1,c2=1))
# shape as a function of the mean
shape <- function(p, mu) p[1]+p[2]*sex+p[3]*mu
gnlr(y, dist="inverse Gauss", mu=~age, shape=shape, pmu=rep(1,2),
	pshape=rep(1,3), shfn=T)


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