bnlr {gnlm}

Binomial Nonlinear Regression Models

Description

bnlr fits user-specified nonlinear regression equations to binomial data with various link functions (logit, probit, comp log log, log log, Cauchy, Student t, stable, or mixture). The mixture link is a logistic link with extra probability mass for y=0 and y=n.

Usage

bnlr(y = NULL, link = "logit", mu = NULL, linear = NULL,
  pmu = NULL, pshape = NULL, wt = 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

A two column matrix of binomial data or censored data 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.

link

A character string containing the name of the link function. The Student t, stable, and mixture links contain an unknown parameter to be estimated, respectively the logarithm of the degrees of freedom, the tail parameter transformed by log(tail/(2-tail)), and logit of the mixture probability, so that they lie on the whole real line.

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.

linear

A formula beginning with ~ in W&R notation, 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

If the link is Student t, an initial estimate of the degrees of freedom; if it is stable, an estimate of the tail parameter; if it is mixture, an estimate of the mixture probability.

wt

Weight vector.

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.

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.

Value

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

Author(s)

J.K. Lindsey

See Also

finterp, glm, gnlr, gnlr3

Examples

# assay to estimate LD50
y <- c(9,9,10,4,1,0,0)
y <- cbind(y,10-y)
dose <- log10(100/c(2.686,2.020,1.520,1.143,0.860,0.647,0.486))

summary(glm(y~dose, family=binomial))
bnlr(y, mu=~dose, pmu=c(1,1))
summary(glm(y~dose, family=binomial(link=probit)))
bnlr(y, link="probit", mu=~dose, pmu=c(1,1))
## Not run: 
bnlr(y, link="log log", mu=~dose, pmu=c(1,1))
bnlr(y, link="comp log log", mu=~dose, pmu=c(1,1))
bnlr(y, link="Cauchy", mu=~dose, pmu=c(60,-30))
bnlr(y, link="Student", mu=~dose, pmu=c(60,-30), pshape=0.1)
bnlr(y, link="stable", mu=~dose, pmu=c(20,-15), pshape=0, stepmax=1)
bnlr(y, link="mixture", mu=~dose, pmu=c(60,-30), pshape=-2.5)
#
mu <- function(p) -p[1]*(log10(p[2])-dose)
bnlr(y, mu=mu, pmu=c(1,100))
bnlr(y, link="probit", mu=mu, pmu=c(1,100))

## End(Not run)