

   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, dist="proportional", mu, linear=NULL, pmu,
        pblock, wt=NULL, 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.

       dist: The ordinal distribution: proportional odds, con-
             tinuation ratio, or adjacent categories.

         mu: User-specified function of `pmu', and possibly
             `linear', giving the logistic regression equation.
             This may contain a linear part as the second argu-
             ment to the function. It may also be a language
             expression beginning with ~, specifying a logistic
             regression function for the location parameter. If
             neither is supplied, the location is taken to be
             constant unless the linear argument is given.

     linear: Language expression beginning with ~, specifying
             the linear part of the logistic regression func-
             tion.

        pmu: Vector of initial estimates for the regression
             parameters.

     pblock: Vector of initial estimates for the block parame-
             ters: two less than the number of different ordi-
             nal values.

         wt: Weight vector for use with contingency tables.

     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.

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

        A list of class gnlr 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.

   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 <- 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, pbl=1.5)
        # proportional odds using Wilkinson and Rogers notation
        nordr(y, dist="prop", mu=~carrier, pmu=pmu, wt=wt, pbl=1.5)
        # continuation ratio
        nordr(y, dist="cont", mu=mu, pmu=pmu, wt=wt, pbl=1.5)
        # adjacent categories
        nordr(y, dist="adj", mu=~carrier, pmu=pmu, wt=wt, pbl=1.5)

