nordr                  package:gnlm                  R Documentation

_N_o_n_l_i_n_e_a_r _O_r_d_i_n_a_l _R_e_g_r_e_s_s_i_o_n

_D_e_s_c_r_i_p_t_i_o_n:

     `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'.)

_U_s_a_g_e:

     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_r_g_u_m_e_n_t_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 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'.

_V_a_l_u_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
     calculated, including error codes.

_A_u_t_h_o_r(_s):

     J.K. Lindsey

_E_x_a_m_p_l_e_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)

