| gausscop {repeated} | R Documentation |
Multivariate Gaussian Copula with Arbitrary Marginals
Description
gausscop fits multivariate repeated measurements models based
on the Gaussian copula with a choice of marginal distributions.
Dependence among responses is provided by the correlation matrix
containing random effects and/or autoregression.
With two levels of nesting, the first is the individual and the second will consist of clusters within individuals.
For clustered (non-longitudinal) data, where only random effects will be fitted,
times are not necessary.
This function is designed to fit linear and nonlinear models with time-varying covariates observed at arbitrary time points. A continuous-time AR(1) and zero, one, or two levels of nesting can be handled.
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.)
Usage
gausscop(response=NULL, distribution="gamma", mu=NULL, shape=NULL,
autocorr="exponential", pmu=NULL, pshape=NULL, par=NULL,
pre=NULL, delta=NULL, shfn=FALSE, common=FALSE, envir=parent.frame(),
print.level=0, ndigit=10, gradtol=0.00001, steptol=0.00001,
iterlim=100, fscale=1, stepmax=10*sqrt(theta%*%theta),
typsiz=abs(c(theta)))
fitted.gausscop(z)
residuals.gausscop(z)
Arguments
response |
A list of two or three column matrices with response
values, times, and possibly nesting categories, for each individual,
one matrix or dataframe of response values, 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 marginal distribution: exponential, gamma, Weibull, Pareto, inverse Gauss, logistic, Cauchy, Laplace, or Levy. |
mu |
The linear or nonlinear regression model to be fitted for the location parameter. For marginal distributions requiring positive response values, a log link is used. This model can be a function of the parameters or 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 that describes the location, returning a vector the same length as the number of observations. |
shape |
The linear or nonlinear regression model to be fitted for
the log shape parameter. This can be a function of the parameters
or 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 that
describes the location. If it contains unknown parameters, the keyword
mu may be used to specify a function of the location parameter. |
autocorr |
The form of the autocorrelation function:
exponential is the usual rho^|t_i-t_j|;
gaussian is rho^((t_i-t_j)^2);
cauchy is 1/(1+rho(t_i-t_j)^2);
spherical is
((|t_i-t_j|rho)^3-3|t_i-t_j|rho+2)/2
for |t_i-t_j|<=1/rho and zero otherwise. |
pmu |
Initial parameter estimates for the location regression model. |
pshape |
Initial parameter estimate for the shape regression model. |
par |
If supplied, an initial estimate for the autocorrelation parameter. |
pre |
Zero, one or two parameter estimates for the variance components, depending on the number of levels of nesting. |
delta |
Scalar or vector giving the unit of measurement
for each response value, set to unity by default. For example, if a
response is measured to two decimals, delta=0.01. Ignored if
response has class, response or repeated. |
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. |
common |
If TRUE, mu and shape 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; the name of the response variable should be given in
response. If response has class repeated, it is
used as the environment. |
others |
Arguments controlling nlm. |
z |
An object of class, gausscop. |
Value
A list of classgausscop is returned that contains all of the
relevant information calculated, including error codes.Author(s)
J.K. LindseyReferences
Song, P.X.K. (2000) Multivariate dispersion models generated from Gaussian copula. Scandinavian Journal of Statistics 27, 305-320.See Also
carma, elliptic,
finterp, gar,
gettvc, glmm,
gnlmm, gnlr,
iprofile, kalseries,
mprofile, potthoff,
read.list, restovec,
rmna, tcctomat,
tvctomat.
Examples
library(gnlm)
# linear models
y <- matrix(rgamma(40,1,1),ncol=5)+rep(rgamma(8,0.5,1),5)
x1 <- c(rep(0,4),rep(1,4))
reps <- rmna(restovec(y),ccov=tcctomat(x1))
# independence with default gamma marginals
gnlr(y, pmu=1, psh=0, dist="gamma", env=reps)
gausscop(y, pmu=1, pshape=0, env=reps)
gausscop(y, mu=~x1, pmu=c(1,0), pshape=0, env=reps)
# AR(1)
gausscop(y, pmu=1, pshape=0, par=0.1, env=reps)
# random effect
gausscop(y, pmu=1, pshape=0, pre=0.1, env=reps)
# try other marginal distributions
gausscop(y, pmu=1, pshape=0, pre=0.1, env=reps, dist="Weibull")
gausscop(y, pmu=1, pshape=0, pre=0.1, env=reps, dist="inverse Gauss",
stepmax=1)
gausscop(y, pmu=1, pshape=0, pre=0.1, env=reps, dist="Cauchy")
#
# first-order one-compartment model
# create data objects for formulae
dose <- c(2,5)
dd <- tcctomat(dose)
times <- matrix(rep(1:20,2), nrow=2, byrow=TRUE)
tt <- tvctomat(times)
# vector covariates for functions
dose <- c(rep(2,20),rep(5,20))
times <- rep(1:20,2)
# functions
mu <- function(p) exp(p[1]-p[3])*(dose/(exp(p[1])-exp(p[2]))*
(exp(-exp(p[2])*times)-exp(-exp(p[1])*times)))
shape <- function(p) exp(p[1]-p[2])*times*dose*exp(-exp(p[1])*times)
lmu <- function(p) p[1]-p[3]+log(dose/(exp(p[1])-exp(p[2]))*
(exp(-exp(p[2])*times)-exp(-exp(p[1])*times)))
lshape <- function(p) p[1]-p[2]+log(times*dose)-exp(p[1])*times
# response
#conc <- matrix(rgamma(40,shape(log(c(0.1,0.4))),
# scale=mu(log(c(1,0.3,0.2))))/shape(log(c(0.1,0.4))),ncol=20,byrow=TRUE)
#conc[,2:20] <- conc[,2:20]+0.5*(conc[,1:19]-matrix(mu(log(c(1,0.3,0.2))),
# ncol=20,byrow=TRUE)[,1:19])
#conc <- restovec(ifelse(conc>0,conc,0.01),name="conc")
conc <- matrix(c(3.65586845,0.01000000,0.01000000,0.01731192,1.68707608,
0.01000000,4.67338974,4.79679942,1.86429851,1.82886732,1.54708795,
0.57592054,0.08014232,0.09436425,0.26106139,0.11125534,0.22685364,
0.22896015,0.04886441,0.01000000,33.59011263,16.89115866,19.99638316,
16.94021361,9.95440037,7.10473948,2.97769676,1.53785279,2.13059515,
0.72562344,1.27832563,1.33917155,0.99811111,0.23437424,0.42751355,
0.65702300,0.41126684,0.15406463,0.03092312,0.14672610),
ncol=20,byrow=TRUE)
conc <- restovec(conc)
reps <- rmna(conc, ccov=dd, tvcov=tt)
# constant shape parameter
gausscop(conc, mu=lmu, pmu=log(c(1,0.4,0.1)), par=0.5, pshape=0, envir=reps)
# or
gausscop(conc, mu=~absorption-volume+
log(dose/(exp(absorption)-exp(elimination))*
(exp(-exp(elimination)*times)-exp(-exp(absorption)*times))),
pmu=list(absorption=0,elimination=log(0.4),volume=log(0.1)),
par=0.5, pshape=0, envir=reps)
# compare to gar autoregression
gar(conc, dist="gamma", times=1:20, mu=mu,
preg=log(c(1,0.4,0.1)), pdepend=0.5, pshape=1)
#
# time dependent shape parameter
gausscop(conc, mu=lmu, shape=lshape,
pmu=log(c(1,0.4,0.1)), par=0.5, pshape=c(-0.1,-0.1))
# or
gausscop(conc, mu=~absorption-volume+
log(dose/(exp(absorption)-exp(elimination))*
(exp(-exp(elimination)*times)-exp(-exp(absorption)*times))),
shape=~b1-b2+log(times*dose)-exp(b1)*times,
pmu=list(absorption=0,elimination=log(0.4),volume=log(0.1)),
par=0.5, pshape=list(b1=-0.1,b2=-0.1), envir=reps)
#
# shape depends on location
lshape <- function(p, mu) p[1]*log(abs(mu))
gausscop(conc, mu=lmu, shape=lshape, shfn=TRUE, pmu=log(c(1,0.4,0.1)),
par=0.5, pshape=1)
# or
gausscop(conc, mu=~absorption-volume+
log(dose/(exp(absorption)-exp(elimination))*
(exp(-exp(elimination)*times)-exp(-exp(absorption)*times))),
shape=~d*log(abs(mu)), shfn=TRUE,
pmu=list(absorption=0,elimination=log(0.4),volume=log(0.1)),
par=0.5, pshape=list(d=1), envir=reps)
[Package repeated version 1.0 Index]
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