

fmr(gnlm)                                    R Documentation

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

     `fmr' fits user specified nonlinear regression equa-
     tions to the location parameter of the common one and
     two parameter distributions (binomial, beta binomial,
     double binomial, multiplicative binomial, Poisson, neg-
     ative binomial, double Poisson, multiplicative Poisson,
     gamma count, Consul, geometric, normal, inverse Gauss,
     logistic, exponential, gamma, Weibull, extreme value,
     Pareto, Cauchy, Student t, Laplace, and Levy). For the
     Poisson and negative binomial, the mixture involves the
     zero category. For the (beta) binomial, it involves the
     two extreme categories. For all other distributions, it
     involves either left or right censored individuals. A
     user-specified -log likelihood can also be supplied for
     the distribution.

     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'.)

_U_s_a_g_e_:

     fmr(y, distribution="normal", mu=NULL, mix=NULL, linear=NULL, pmu=NULL,
             pshape=NULL, pmix=NULL, censor="right", exact=F, wt=1, delta=1,
             Common=F, envir=sys.frame(sys.parent()), print.level=0,
             typsiz=abs(p), ndigit=10, gradtol=0.00001,
             stepmax=10*sqrt(p%*%p), steptol=0.00001, iterlim=100, fscale=1)

_A_r_g_u_m_e_n_t_s_:

       y: A response vector for uncensored data, a two col-
          umn matrix for binomial data or censored data,
          with the second column being the censoring indica-
          tor (1: uncensored, 0: right censored, -1: left
          censored), or an object of class, response (cre-
          ated by `restovec') or repeated (created by
          `rmna').

distribution: Either a character string containing the name
          of the distribution or a function giving the -log
          likelihood and calling the location and mixture
          functions.

      mu: A user-specified function of `pmu', and possibly
          `linear', giving the regression equation for the
          location. This may contain a linear part as the
          second argument to the function. It may also be a
          formula beginning with ~, specifying either a lin-
          ear regression function for the location parameter
          in 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.

     mix: A user-specified function of `pmix', and possibly
          `linear', giving the regression equation for the
          mixture parameter. This may contain a linear part
          as the second argument to the function. It may
          also be a formula beginning with ~, specifying
          either a linear regression function for the mix-
          ture parameter in the Wilkinson and Rogers nota-
          tion or a general function with named unknown
          parameters. If none is supplied, this parameter is
          taken to be constant. This parameter is the logit
          of the mixture probability.

  linear: A formula beginning with ~, or list of two such
          expressions, specifying the linear part of the
          regression function for the location or location
          and mixture parameters.

     pmu: Vector of initial estimates for the location
          parameters.  If `mu' is a formula with unknown
          parameters, their estimates must be supplied
          either in their order of appearance in the expres-
          sion or in a named list.

  pshape: An initial estimate for the shape parameter.

    pmix: Vector of initial estimates for the mixture param-
          eters.  If `mix' is a formula with unknown parame-
          ters, their estimates must be supplied either in
          their order of appearance in the expression or in
          a named list.

  censor: `right', `left', or `both' indicating where the
          mixing distribution is placed. `both' is only pos-
          sible for binomial data.

   exact: If TRUE, fits the exact likelihood function for
          continuous data by integration over intervals of
          observation, i.e. interval censoring.

      wt: Weight vector.

   delta: Scalar or vector giving the unit of measurement
          (always one for discrete data) for each response
          value, set to unity by default - for example, if a
          response is measured to two decimals, delta=0.01.
          If the response is transformed, this must be mul-
          tiplied by the Jacobian. The transformation cannot
          contain unknown parameters.  For example, with a
          log transformation, `delta=1/y'.

  common: If TRUE, `mu' and `mix' must both be functions
          with, as argument, a vector of parameters having
          some or all elements in common between them so
          that indexing is in common between them; all
          parameter estimates must be supplied in `pmu'.  If
          FALSE, parameters are distinct between the two
          functions and indexing starts at one in each func-
          tion.

   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 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.

_A_u_t_h_o_r_(_s_)_:

     J.K. Lindsey

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

     `finterp', `glm', `gnlr', `gnlr3', `lm'.

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

     y <- cbind(rweibull(20,2,5),rbinom(20,1,0.7))
     sex <- c(rep(0,10),rep(1,10))
     sexf <- gl(2,10)
     age <- rpois(20,10)
     # linear regression with Weibull distribution with a point mass
     # for right censored individuals
     mu <- function(p) p[1]+p[2]*sex+p[3]*age
     fmr(y, dist="Weibull", mu=mu, pmu=rep(1,3), pmix=1, pshape=1)
     # or equivalently
     fmr(y, dist="Weibull", mu=~sexf+age, pmu=rep(1,3), pmix=1, pshape=1)
     # or
     fmr(y, dist="Weibull", linear=~sex+age, pmu=rep(1,3), pmix=1, pshape=1)
     # or
     fmr(y, dist="Weibull", mu=~b0+b1*sex+b2*age, pmu=list(b0=1,b1=1,b2=1),
             pmix=1, pshape=1)
     #
     # nonlinear regression with Weibull distribution
     mu <- function(p, linear) p[1]*exp(linear)
     fmr(y, dist="Weibull", mu=mu, linear=~sex+age, pmu=rep(1,4),
             pmix=1, pshape=1)
     # or equivalently
     fmr(y, dist="Weibull", mu=~b4*exp(b0+b1*sex+b2*age),
             pmu=list(b0=1,b1=1,b2=1,b4=1), pmix=1, pshape=1)
     #
     # include logistic regression for the mixture parameter
     mix <- function(p) p[1]+p[2]*sex
     fmr(y, dist="Weibull", mu=~age, mix=mix, pmu=rep(1,2),
             pmix=rep(1,2), pshape=1)
     # or equivalently
     fmr(y, dist="Weibull", linear=list(~age,~sex), pmu=rep(1,2),
             pmix=rep(1,2), pshape=1)
     # or
     fmr(y, dist="Weibull", mu=~b0+b1*age, mix=~c0+c1*sex,
             pmu=list(b0=1,b1=1), pmix=list(c0=1,c1=1), pshape=1)

