Fit a Generalized Nonlinear Regression Model

Usage

gnlr(y, dist="normal", pmu=NULL, pshape=NULL, mu=NULL, shape=NULL,
linear=NULL, exact=F, wt=1, delta=1, shfn=F,
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 or a two column matrix for binomial data. For censored data, two columns with the second being the censoring indicator (1: uncensored, 0: right censored, -1: left censored.) It may also be an object of class, response.
dist Either a character string containing the name of the distribution or a function giving the -log likelihood and calling the location and shape functions.
pmu Vector of initial estimates for the location parameters.
pshape Vector of initial estimates for the shape parameters.
mu 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 language expression beginning with ~, specifying a linear regression function for the location parameter. If neither is supplied, the location is taken to be constant unless the linear argument is given.
shape 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 as last argument (in which case shfn must be set to TRUE). It may also be a language expression beginning with ~, specifying a linear regression function for the shape parameter. If neither 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 Language expression 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.
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.
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, Poisson, negative binomial, double Poisson, Consul generalized Poisson, logarithmic series, geometric, normal, inverse Gauss, logistic, exponential, gamma, Weibull, extreme value, Cauchy, Student t, and Laplace; all but the binomial and beta binomial may be right and/or left censored). A user-specified -log likelihood can also be supplied for the distribution.

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.

Examples

# linear regression with inverse Gauss distribution
mu <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(data, dist="inverse Gauss", pmu=rep(1,3), psh=1, mu=mu)
# or equivalently
gnlr(data, dist="inverse Gauss", pmu=rep(1,3), psh=1, mu=~sex+age)
# or
gnlr(data, dist="inverse Gauss", pmu=rep(1,3), psh=1,
	linear=~sex+age)
#
# nonlinear regression with inverse Gauss distribution
mu <- function(p, linear) p[4]+exp(linear)
gnlr(data, dist="inverse Gauss", pmu=rep(1,4), psh=1, mu=mu,
	linear=~sex+age)
# 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(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3), mu=mu,
	shape=shape)
# or equivalently
gnlr(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3), mu=mu,
	linear=~sex+age, shape=~sex+age)
# or
gnlr(data, dist="inverse Gauss", p=rep(1,7), mu=mu,
	linear=list(~sex+age,~sex+age))
# shape as a function of the mean
shape <- function(p, mu) p[1]+p[2]*sex+p[3]*mu
gnlr(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3), mu=mu,
	shape=shape, linear=~sex+age, shfn=T)


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