fmr                   package:gnlm                   R Documentation

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

     `fmr' fits user specified nonlinear regression equations to the
     location parameter of the common one and two parameter
     distributions (binomial, beta binomial, double binomial,
     multiplicative binomial, Poisson, negative 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 `finterp'.)

_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 column matrix
          for binomial data or censored data, with the second column
          being the censoring indicator (1: uncensored, 0: right
          censored, -1: left censored), or an object of class, response
          (created 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 linear 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
          mixture parameter in the Wilkinson and Rogers notation 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
          expression or in a named list.

  pshape: An initial estimate for the shape parameter.

    pmix: Vector of initial estimates for the mixture parameters. If
          `mix' 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.

  censor: `right', `left', or `both' indicating where the mixing
          distribution is placed. `both' is only possible 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 multiplied 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 function.

   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
     calculated, 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)

