gnlmm3 {repeated} | R Documentation |

`gnlmm3`

fits user-specified nonlinear regression equations to one
or more parameters of the common three 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`

,
`pshape`

, and `pfamily`

be obtained from `gnlr3`

.

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.

gnlmm3(y=NULL, distribution="normal", mu=NULL, shape=NULL, nest=NULL, family=NULL, linear=NULL, pmu=NULL, pshape=NULL, pfamily=NULL, psd=NULL, exact=FALSE, wt=1, scale=NULL, points=10, common=FALSE, delta=1, envir=parent.frame(), print.level=0, typsiz=abs(p), ndigit=10, gradtol=0.00001, stepmax=10*sqrt(p%*%p),

`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. |

`distribution` |
Either a character string containing the name of the distribution or a function giving the -log likelihood and calling the location, shape, and family functions. Distributions are Box-Cox transformed normal, generalized inverse Gauss, generalized logistic, Hjorth, generalized gamma, Burr, generalized Weibull, power exponential, Student t, generalized extreme value, power variance function Poisson, and skew Laplace. (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. |

`family` |
A user-specified function of `pfamily` , and possibly
`linear` , for the regression equation of the third (family)
parameter of the distribution. This may contain a linear part that is
the second argument to the function. It may also be a formula
beginning with ~, specifying either a linear regression function for
the family parameter in the Wilkinson and Rogers notation or a general
function with named unknown parameters. If neither is supplied, this
parameter is taken to be constant unless the linear argument is
given. In most cases, 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. |

`pfamily` |
Vector of initial estimates for the family parameters.
If `family` 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.) |

`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, at least two of `mu` , `shape` , and
`family` 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` . |

A list of class `gnlm`

is returned that contains all of the
relevant information calculated, including error codes.

J.K. Lindsey

`finterp`

, `fmr`

, `glm`

,
`gnlmix`

, `glmm`

,
`gnlr`

, `gnlr3`

,
`hnlmix`

, `lm`

,
`nlr`

, `nls`

.

library(gnlm) # data objects sex <- c(0,1,1) sx <- tcctomat(sex) #dose <- matrix(rpois(30,10),nrow=3) dose <- matrix(c(8,9,11,9,11,11,7,8,7,12,8,8,9,10,15,10,9,9,20,14,4,7, 4,13,10,13,6,13,11,17),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 <- (rt(30,5)+exp(0.2+0.3*dose+0.5*sex+rep(rnorm(3),rep(10,3))))*3 y <- c(62.39712552,196.94419614,2224.74940087,269.56691601,12.86079662, 14.96743546, 47.45765042,156.51381687,508.68804438,281.11065302, 92.32443655, 81.88000484, 40.26357733, 13.04433670, 15.58490237, 63.62154867, 23.69677549, 53.52885894, 88.02507682, 34.04302506, 44.28232323,116.80732423,106.72564484, 25.09749055, 12.61839145, -0.04060996,153.32670123, 63.25866087, 17.79852591,930.52558064) y <- restovec(matrix(y, nrow=3), nest=nest, name="y") reps <- rmna(y, ccov=sx, tvcov=dd) # # log linear regression with Student t distribution mu <- function(p) exp(p[1]+p[2]*sex+p[3]*dose) print(z <- gnlr3(y, dist="Student", mu=mu, pmu=c(0,0,0), pshape=1, pfamily=1)) gnlmm3(y, dist="Student", mu=mu, nest=nest, pmu=z$coef[1:3], pshape=z$coef[4], pfamily=z$coef[5], psd=50, points=3) # or equivalently gnlmm3(y, dist="Student", mu=~exp(b0+b1*sex+b2*dose), nest=nest, pmu=z$coef[1:3], pshape=z$coef[4], pfamily=z$coef[5], psd=50, points=3, envir=reps) # or with identity link print(z <- gnlr3(y, dist="Student", mu=~sex+dose, pmu=c(0.1,0,0), pshape=1, pfamily=1)) gnlmm3(y, dist="Student", mu=~sex+dose, nest=nest, pmu=z$coef[1:3], pshape=z$coef[4], pfamily=z$coef[5], psd=50, points=3) # or gnlmm3(y, dist="Student", mu=~b0+b1*sex+b2*dose, nest=nest, pmu=z$coef[1:3], pshape=z$coef[4], pfamily=z$coef[5], psd=50, points=3, envir=reps) # # nonlinear regression with Student t distribution mu <- function(p) p[1]+exp(p[2]+p[3]*sex+p[4]*dose) print(z <- gnlr3(y, dist="Student", mu=mu, pmu=c(1,1,0,0), pshape=1, pfamily=1)) gnlmm3(y, dist="Student", mu=mu, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5], pfamily=z$coef[6], psd=50, points=3) # or mu2 <- function(p, linear) p[1]+exp(linear) gnlmm3(y, dist="Student", mu=mu2, linear=~sex+dose, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5], pfamily=z$coef[6], psd=50, points=3) # or gnlmm3(y, dist="Student", mu=~a+exp(linear), linear=~sex+dose, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5], pfamily=z$coef[6], psd=50, points=3) # or gnlmm3(y, dist="Student", mu=~b4+exp(b0+b1*sex+b2*dose), nest=nest, pmu=z$coef[1:4], pshape=z$coef[5], pfamily=z$coef[6], psd=50, points=3, envir=reps) # # include regression for the shape parameter with same mu function shape <- function(p) p[1]+p[2]*sex print(z <- gnlr3(y, dist="Student", mu=mu, shape=shape, pmu=z$coef[1:4], pshape=c(z$coef[5],0), pfamily=z$coef[6])) gnlmm3(y, dist="Student", mu=mu, shape=shape, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5:6], pfamily=z$coef[7], psd=5, points=3) # or gnlmm3(y, dist="Student", mu=mu, shape=shape, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5:6], pfamily=z$coef[7], psd=5, points=3, envir=reps) # or gnlmm3(y, dist="Student", mu=~b4+exp(b0+b1*sex+b2*dose), shape=~a1+a2*sex, nest=nest, pmu=z$coef[1:4], pshape=z$coef[5:6], pfamily=z$coef[7], psd=5, points=3, envir=reps)

[Package *repeated* version 1.0 Index]