nordr {gnlm}

Nonlinear Ordinal Regression Models

Description

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

Usage

nordr(y = NULL, distribution = "proportional", mu = NULL,
  linear = NULL, pmu = NULL, pintercept = NULL, weights = NULL,
  envir = parent.frame(), print.level = 0, ndigit = 10,
  gradtol = 1e-05, steptol = 1e-05, fscale = 1, iterlim = 100,
  typsize = abs(p), stepmax = 10 * sqrt(p %*% p))

Arguments

y

A vector of ordinal responses, integers numbered from zero to one less than the number of categories 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.

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 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 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.

weights

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; 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.

ndigit

Arguments controlling nlm.

gradtol

Arguments controlling nlm.

steptol

Arguments controlling nlm.

fscale

Arguments controlling nlm.

iterlim

Arguments controlling nlm.

typsize

Arguments controlling nlm.

stepmax

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 nordr is returned that contains all of the relevant information calculated, including error codes.

Author(s)

J.K. Lindsey

See Also

finterp, fmr, glm, glmm, gnlmm, gnlr, gnlr3, nlr, ordglm

Examples

# McCullagh (1980) JRSS B42, 109-142
# tonsil size: 2x3 contingency table
y <- c(0:2,0:2)
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, weights=wt, pintercept=1.5)
# using Wilkinson and Rogers notation
nordr(y, dist="prop", mu=~carrierf, pmu=pmu, weights=wt, pintercept=1.5)
# using formula with unknowns
nordr(y, dist="prop", mu=~b0+b1*carrier, pmu=pmu, weights=wt, pintercept=1.5)
# continuation ratio
nordr(y, dist="cont", mu=mu, pmu=pmu, weights=wt, pintercept=1.5)
# adjacent categories
nordr(y, dist="adj", mu=~carrierf, pmu=pmu, weights=wt, pintercept=1.5)
#
# Haberman (1974) Biometrics 30, 589-600
# institutionalized schizophrenics: 3x3 contingency table
y <- rep(0:2,3)
fr <- c(43,6,9,
	16,11,18,
	3,10,16)
length <- gl(3,3)
## Not run: 
# fit continuation ratio model with nordr and as a logistic model
nordr(y, mu=~length, weights=fr, pmu=c(0,-1.4,-2.3), pint=0.13,
	dist="cont")
	
## End(Not run)
# logistic regression with reconstructed table
frcr <- cbind(c(43,16,3,49,27,13),c(6,11,10,9,18,16))
lengthord <- gl(3,1,6)
block <- gl(2,3)
summary(glm(frcr~lengthord+block,fam=binomial))
# note that AICs and deviances are different