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 _M_o_d_e_l_s

_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 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.

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

     nordr(y, distribution="proportional", mu=NULL, linear=NULL, pmu, 
             pintercept, weights=NULL, envir=parent.frame(),
             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 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.

  others: Arguments controlling 'nlm'.

_V_a_l_u_e:

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

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

     J.K. Lindsey

_S_e_e _A_l_s_o:

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

_E_x_a_m_p_l_e_s:

     # 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)
     # 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")
     # 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

