Fit a Generalized Nonlinear Regression Model for Three Parameter Distributions

Usage

 gnlr3(y, dist="normal", pmu=NULL, pshape=NULL, pfamily=NULL,
mu=NULL, shape=NULL, family=NULL, linear=NULL, censor=F, exact=F, wt=1,
delta=1, 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 The response vector for uncensored 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.
pfamily Vector of initial estimates for the family parameters.
mu User-specified function of pmu, and possibly linear, giving the regression equation for the location. This may contain a linear part that is 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, giving the regression equation for the dispersion or shape parameter. This may contain a linear part that is the second argument to the function. 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.
family 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 language expression beginning with ~, specifying a linear regression function for the family 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 parameters or list of three such expressions for the location, shape, and/or family 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.)
others Arguments controlling nlm.

Description

gnlr3 fits user specified nonlinear regression equations to one, two, or all three parameters of three parameter distributions (Box-Cox transformed normal, generalized inverse Gauss, generalized logistic, Hjorth, generalized gamma, Burr, generalized Weibull, and generalized extreme value).

Value

A list of class gnlr3 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.

See Also

lm, glm, gnlr, fmr.

Examples

# linear regression with the generalized inverse Gauss distribution
mu <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr3(data, dist="inverse Gauss", pmu=rep(1,3), psh=1, pfam=1, mu=mu)
# or equivalently
gnlr3(data, dist="inverse Gauss", pmu=rep(1,3), psh=1, pfam=1,
	mu=~sex+age)
# or
gnlr3(data, dist="inverse Gauss", pmu=rep(1,3), psh=1, pfam=1,
	linear=~sex+age)
#
# nonlinear regression with generalized inverse Gauss distribution
mu <- function(p, linear) p[4]*exp(linear)
gnlr3(data, dist="inverse Gauss", pmu=rep(1,4), psh=1, pfam=1, mu=mu,
	linear=~sex+age)
#
# include regression for the shape parameter with same mu function
shape <- function(p) p[5]+p[6]*sex+p[7]*age
gnlr3(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3), pfam=1,
	mu=mu, shape=shape)
# or equivalently
gnlr3(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3), pfam=1,
	mu=mu, linear=list(~sex+age,~sex+age))
# include regression for the family parameter with same mu
# and shape functions
family <- function(p) p[8]+p[9]*sex+p[10]*age
gnlr3(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3),
	pfam=rep(1,3), mu=mu, shape=shape, family=shape)
# or equivalently
gnlr3(data, dist="inverse Gauss", pmu=rep(1,4), psh=rep(1,3),
	pfam=rep(1,3), mu=mu, linear=list(~sex+age,~sex+age,~sex+age))


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