gnlmm                package:repeated                R Documentation

_G_e_n_e_r_a_l_i_z_e_d _N_o_n_l_i_n_e_a_r _M_i_x_e_d _M_o_d_e_l_s

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

     'gnlmm' fits user-specified nonlinear regression equations to one
     or both parameters of the common one and two parameter
     distributions. The intercept of the location regression has a
     normally-distributed random effect. This normal mixing
     distribution is computed by Gauss-Hermite integration.

     The 'scale' of the random effect is the link function to be
     applied. For example, if it is 'log', the supplied mean function,
     'mu', is transformed as exp(log(mu)+sd), where sd is the random
     effect parameter.

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

     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:

     gnlmm(y=NULL, distribution="normal", mu=NULL, shape=NULL,
             linear=NULL, nest=NULL, pmu=NULL, pshape=NULL, psd=NULL, exact=FALSE,
             wt=1, delta=1, shfn=FALSE, scale=NULL, points=10, common=FALSE,
             envir=parent.frame(), print.level=0, typsiz=abs(p),
             ndigit=10, gradtol=0.00001, stepmax=sqrt(p%*%p)/10, 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') 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.
          The beta, simplex, and two-sided power distributions for
          proportions do not allow censoring.

distribution: Either a character string containing the name of the
          distribution or a function giving the -log likelihood and
          calling the location and shape functions. Distributions are
          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, and Levy, beta, simplex, and
          two-sided power. All but the binomial-based distributions and
          the beta, simplex, and two-sided power may be right and/or
          left censored. (For definitions of distributions, see the
          corresponding [dpqr]distribution help.)

      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 a
          either linear regression function for the location parameter
          in 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.

   shape: A user-specified function of 'pshape', and possibly 'linear'
          and/or 'mu', giving the regression equation for the
          dispersion or shape parameter. This may contain a linear part
          as the second argument to the function and the location
          function as last argument (in which case 'shfn' must be set
          to TRUE). It may also be a formula beginning with ~,
          specifying either a linear regression function for the shape
          parameter in 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 and the keyword 'mu' to specify a
          function of the location parameter. If nothing is supplied,
          this parameter is taken to be constant unless the linear
          argument is given. 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.

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

     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: Vector of initial estimates for the shape parameters. If
          'shape' 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.

     psd: Initial estimate of the standard deviation of the normal
          mixing distribution.

   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. Ignored if y has class, response. 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.)

    shfn: If true, the supplied shape function depends on the location
          (function). The name of this location function must be the
          last argument of the shape function.

   scale: The scale on which the random effect is applied: 'identity',
          'log', 'logit', 'reciprocal', or 'exp'.

  points: The number of points for Gauss-Hermite integration of the
          random effect.

  common: If TRUE, 'mu' and 'shape' must both be either 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 or formulae with unknowns. 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'; 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 '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:

     'finterp', 'fmr', 'glm', 'gnlmix', 'glmm', 'gnlr', 'gnlr3',
     'hnlmix', 'lm', 'nlr', 'nls'.

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

     library(gnlm)
     # data objects
     sex <- c(0,1,1)
     sx <- tcctomat(sex)
     dose <- matrix(rpois(30,10),nrow=3)
     dd <- tvctomat(dose)
     # vectors for functions
     dose <- as.vector(t(dose))
     sex <- c(rep(0,10),rep(1,20))
     nest <- rbind(rep(1,10),rep(2,10),rep(3,10))
     #y <- rgamma(30,2,scale=exp(0.2+0.1*dose+0.1*sex+rep(rnorm(3),rep(10,3)))/2)
     y <- c(0.6490851,0.9313931,0.4765569,0.4188045,2.8339637,2.8158090,
             2.6059975,2.9958184,2.7351583,3.2884980,1.1180961,0.9443986,1.7915571,
             9.0013379,2.3969570,3.4227356,0.5045518,0.7452521,1.8712467,3.6814198,
             0.1489849,1.0327552,0.6102406,1.1536620,2.9145237,9.2847798,5.6454605,
             1.9759672,1.5798008,5.1024496)
     y <- restovec(matrix(y, nrow=3), nest=nest, name="y")
     reps <- rmna(y, ccov=sx, tvcov=dd)
     #
     # log linear regression with gamma distribution
     mu <- function(p) exp(p[1]+p[2]*sex+p[3]*dose)
     print(z <- gnlr(y, dist="gamma", mu=mu, pmu=c(1,0,0), pshape=1))
     gnlmm(y, dist="gamma", mu=mu, nest=nest, pmu=z$coef[1:3],
             pshape=z$coef[4], psd=0.1, points=3)
     # or equivalently
     gnlmm(y, dist="gamma", mu=~exp(b0+b1*sex+b2*dose), nest=nest,
             pmu=z$coef[1:3], pshape=z$coef[4], psd=0.1, points=3, envir=reps)
     # or with identity link
     print(z <- gnlr(y, dist="gamma", mu=~sex+dose, pmu=c(0.1,0,0), pshape=1))
     gnlmm(y, dist="gamma", mu=~sex+dose, nest=nest, pmu=z$coef[1:3],
             pshape=z$coef[4], psd=0.1, points=3)
     # or
     gnlmm(y, dist="gamma", mu=~b0+b1*sex+b2*dose, nest=nest, pmu=z$coef[1:3],
             pshape=z$coef[4], psd=0.1, points=3, envir=reps)
     #
     # nonlinear regression with gamma distribution
     mu <- function(p) p[1]+exp(p[2]+p[3]*sex+p[4]*dose)
     print(z <- gnlr(y, dist="gamma", mu=mu, pmu=c(1,1,0,0), pshape=1))
     gnlmm(y, dist="gamma", mu=mu, nest=nest, pmu=z$coef[1:4],
             pshape=z$coef[5], psd=0.1, points=3)
     # or
     mu2 <- function(p, linear) p[1]+exp(linear)
     gnlmm(y, dist="gamma", mu=mu2, linear=~sex+dose, nest=nest,
             pmu=z$coef[1:4], pshape=1, psd=0.1, points=3)
     # or
     gnlmm(y, dist="gamma", mu=~a+exp(linear), linear=~sex+dose, nest=nest,
             pmu=z$coef[1:4], pshape=1, psd=0.1, points=3)
     # or
     gnlmm(y, dist="gamma", mu=~b4+exp(b0+b1*sex+b2*dose), nest=nest,
             pmu=z$coef[1:4], pshape=z$coef[5], psd=0.1,
             points=3, envir=reps)
     #
     # include regression for the shape parameter with same mu function
     shape <- function(p) p[1]+p[2]*sex
     print(z <- gnlr(y, dist="gamma", mu=mu, shape=shape, pmu=z$coef[1:4],
             pshape=rep(1,2)))
     gnlmm(y, dist="gamma", mu=mu, shape=shape, nest=nest,
             pmu=z$coef[1:4], pshape=z$coef[5:6], psd=0.1, points=3)
     # or
     gnlmm(y, dist="gamma", mu=mu, shape=shape, nest=nest, pmu=z$coef[1:4],
             pshape=z$coef[5:6], psd=0.1, points=3, envir=reps)
     # or
     gnlmm(y, dist="gamma", mu=~b4+exp(b0+b1*sex+b2*dose), shape=~a1+a2*sex,
             nest=nest, pmu=z$coef[1:4], pshape=z$coef[5:6], psd=0.1,
             points=3, envir=reps)

