gnlmix               package:repeated               R Documentation

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

     'gnlmix' fits user-specified nonlinear regression equations to one
     or both parameters of the common one and two parameter
     distributions. One parameter of the location regression is random
     with some specified mixing distribution. 

     It is recommended that initial estimates for 'pmu' and 'pshape' be
     obtained from 'gnlr'.

     These nonlinear regression models must be supplied as formulae
     where parameters are unknowns. (See 'finterp'.)

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

     gnlmix(y=NULL, distribution="normal", mixture="normal",
             random=NULL, nest=NULL, mu=NULL, shape=NULL, linear=NULL,
             pmu=NULL, pshape=NULL, pmix=NULL, delta=1, common=FALSE,
             envir=parent.frame(), print.level=0, typsiz=abs(p),
             ndigit=10, gradtol=0.00001, stepmax=10*sqrt(p%*%p), steptol=0.00001,
             iterlim=100, fscale=1, eps=1.0e-4, points=5, steps=10)

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

       y: A response vector of uncensored data, a two column matrix for
          binomial data, 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 distribution for the response: binomial, beta
          binomial, double binomial, mult(iplicative) binomial,
          Poisson, negative binomial, double Poisson, mult(iplicative)
          Poisson, gamma count, Consul generalized Poisson, logarithmic
          series, geometric, normal, inverse Gauss, logistic,
          exponential, gamma, Weibull, extreme value, Cauchy, Pareto,
          Laplace, Levy, beta, simplex, or two-sided power. (For
          definitions of distributions, see the corresponding
          [dpqr]distribution help.)

 mixture: The mixing distribution for the random parameter: normal,
          Cauchy, logistic, Laplace, inverse Gauss, gamma, inverse
          gamma, Weibull, beta, simplex, or two-sided power. The first
          four have zero location parameter, the next three have unit
          location parameter, and the last two have location parameter
          set to 0.5.

  random: The name of the random parameter in the 'mu' formula.

    nest: The variable classifying observations by the unit upon which
          they were observed. Ignored if 'y' or 'envir' has class,
          'response' or 'repeated'.

      mu: A user-specified formula containing named unknown parameters,
          giving the regression equation for the location parameter.
          This may contain the keyword, 'linear' referring to a linear
          part.

   shape: A user-specified formula containing named unknown parameters,
          giving the regression equation for the shape parameter. This
          may contain the keyword, 'linear' referring to a linear part.
          If nothing is supplied, this parameter is taken to be
          constant. This parameter is the logarithm of the usual one.

  linear: A formula beginning with ~ in W&R notation, specifying the
          linear part of the regression function for the location
          parameter or list of two such expressions for the location
          and/or shape parameters.

     pmu: Vector of initial estimates for the location parameters.
          These must be supplied either in their order of appearance in
          the formula or in a named list.

  pshape: Vector of initial estimates for the shape parameters. These
          must be supplied either in their order of appearance in the
          expression or in a named list.

    pmix: Initial estimate for the logarithm of the dispersion
          parameter of the mixing distribution.

   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'. (The delta values for the
          censored response are ignored.)

  common: If TRUE, the formulae with unknowns for the location and
          shape have names in common. All parameter estimates must be
          supplied in 'pmu'.

   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.

     eps: Precision of the Romberg integration.

   steps: For the Romberg integration, the maximum number of steps, by
          default set to 10.

  points: For the Romberg integration, the number of extrapolation
          points so that 2*points is the order of integration, by
          default set to 5; points=2 is Simpson's rule.

  others: Arguments controlling 'nlm'.

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

     A list of class 'gnlm' 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:

     'carma', 'finterp', 'elliptic', 'glmm', 'gnlmm', 'gnlr', 'hnlmix',
     'kalseries', 'nlr', 'nls'.

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

     library(growth)
     dose <- c(9,12,4,9,11,10,2,11,12,9,9,9,4,9,11,9,14,7,9,8)
     #y <- rgamma(20,shape=2+0.3*dose,scale=2)+rep(rnorm(4,0,4),rep(5,4))
     y <- c(8.674419, 11.506066, 11.386742, 27.414532, 12.135699,  4.359469,
            1.900681, 17.425948,  4.503345,  2.691792,  5.731100, 10.534971,
           11.220260,  6.968932,  4.094357, 16.393806, 14.656584,  8.786133,
           20.972267, 17.178012)
     resp <- restovec(matrix(y, nrow=4, byrow=TRUE), name="y")
     reps <- rmna(resp, tvcov=tvctomat(matrix(dose, nrow=4, byrow=TRUE), name="dose"))

     # same linear normal model with random normal intercept fitted four ways
     elliptic(reps, model=~dose, preg=c(0,0.6), pre=4)
     glmm(y~dose, nest=individuals, data=reps)
     gnlmm(reps, mu=~dose, pmu=c(8.7,0.25), psh=3.5, psd=3)
     gnlmix(reps, mu=~a+b*dose+rand, random="rand", pmu=c(8.7,0.25),
             pshape=3.44, pmix=2.3)

     # gamma model with log link and random normal intercept fitted three ways
     glmm(y~dose, family=Gamma(link=log), nest=individuals, data=reps, points=8)
     gnlmm(reps, distribution="gamma", mu=~exp(a+b*dose), pmu=c(2,0.03),
             psh=1, psd=0.3)
     gnlmix(reps, distribution="gamma", mu=~exp(a+b*dose+rand), random="rand",
             pmu=c(2,0.04), pshape=1, pmix=-2)

     # gamma model with log link and random gamma mixtures
     gnlmix(reps, distribution="gamma", mixture="gamma",
             mu=~exp(a*rand+b*dose), random="rand", pmu=c(2,0.04),
             pshape=1.24, pmix=3.5)
     gnlmix(reps, distribution="gamma", mixture="gamma",
             mu=~exp(a+b*dose)*rand, random="rand", pmu=c(2,0.04),
             pshape=1.24, pmix=2.5)

