nordr {gnlm}R Documentation

Nonlinear Ordinal Regression

Description

nordr fits arbitrary nonlinear regression functions (with logistic link) to ordinal response data by proportional odds, continuation ratio, or adjacent categories.

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

Usage

nordr(y, distribution="proportional", mu, linear=NULL, pmu, 
        pintercept, wt=NULL, envir=sys.frame(sys.parent()),
        print.level=0, ndigit=10, gradtol=0.00001,
        steptol=0.00001, fscale=1, iterlim=100, typsiz=abs(p),
        stepmax=10*sqrt(p%*%p))

Arguments

y A vector of ordinal responses, integers numbered from one to the maximum value.
distribution The ordinal distribution: proportional odds, continuation ratio, or adjacent categories.
mu User-specified function of pmu, and possibly linear, giving the logistic regression equation. This must contain the first intercept. It may contain a linear part as the second argument to the function. It may also be a formula beginning with ~, specifying a logistic regression function for the location parameter, either a linear one using 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.
linear A formula beginning with ~, specifying the linear part of the logistic regression function.
pmu Vector of initial estimates for the regression parameters, including the first intercept. 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.
pintercept Vector of initial estimates for the contrasts with the first intercept parameter (difference in intercept for successive categories): two less than the number of different ordinal values.
wt Weight vector for use with contingency tables.
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.

Value

A list of class nordr 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

# McCullagh (1980) JRSS B42, 109-142
# Tonsil size: 2x3 contingency table
y <- c(1:3,1:3)
carrier <- c(rep(0,3),rep(1,3))
carrierf <- gl(2,3,6)
wt <- c(19,29,24,497,560,269)
pmu <- c(-1,0.5)
mu <- function(p) c(rep(p[1],3),rep(p[1]+p[2],3))
# proportional odds
# with mean function
nordr(y, dist="prop", mu=mu, pmu=pmu, wt=wt, pintercept=1.5)
# using Wilkinson and Rogers notation
nordr(y, dist="prop", mu=~carrierf, pmu=pmu, wt=wt, pintercept=1.5)
# using formula with unknowns
nordr(y, dist="prop", mu=~b0+b1*carrier, pmu=pmu, wt=wt, pintercept=1.5)
# continuation ratio
nordr(y, dist="cont", mu=mu, pmu=pmu, wt=wt, pintercept=1.5)
# adjacent categories
nordr(y, dist="adj", mu=~carrierf, pmu=pmu, wt=wt, pintercept=1.5)

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