

   NNoonnlliinneeaarr OOrrddiinnaall RReeggrreessssiioonn

        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))

   AArrgguummeennttss::

          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 con-
             tain 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 esti-
             mates 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'.

   DDeessccrriippttiioonn::

        `nordr' fits arbitrary nonlinear regression functions
        (with logistic link) to ordinal response data by pro-
        portional odds, continuation ratio, or adjacent cate-
        gories.

        Nonlinear regression models can be supplied as formulae
        where parameters are unknowns. Factor variables cannot
        be used and parameters must be scalars. (See `fin-
        terp'.)

   VVaalluuee::

        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 calcu-
        lated, including error codes.

   AAuutthhoorr((ss))::

        J.K. Lindsey

   EExxaammpplleess::

        # 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)

