gnlr3(y, dist="normal", mu=NULL, shape=NULL, family=NULL, linear=NULL, pmu=NULL, pshape=NULL, pfamily=NULL, censor=F, exact=F, wt=1, delta=1, 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)
y
|
The response vector for uncensored data, two columns for
censored data, with the second 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 shape 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.
|
shape
|
A user-specified function of pshape , and possibly
linear , giving the regression equation for the dispersion or shape
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 shape 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 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 ~, specifying the linear part of the regression function for the location parameters or list of three such expressions for the location, shape, and/or family 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
|
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.
|
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 . (The delta values for the censored response are
ignored.)
|
envir
| Environment in which model formulae are to be interpreted. |
others
|
Arguments controlling nlm .
|
gnlr3
fits user specified nonlinear regression equations to one,
two, or all three parameters of three parameter distributions
(Box-Cox transformed normal, generalized inverse Gauss, generalized
logistic, Hjorth, generalized gamma, Burr, generalized Weibull,
power exponential, Student t, and generalized extreme value).
Nonlinear regression models can be supplied as formulae where
parameters are unknowns. Factor variables cannot be used and
parameters must be scalars. (See finterp
.)
fmr
, finterp
, glm
,
gnlr
, lm
.y <- rgamma(20,2,1) sex <- c(rep(0,10),rep(1,10)) sexf <- gl(2,10) age <- rpois(20,10) # linear regression with the generalized gamma distribution mu <- function(p) p[1]+p[2]*sex+p[3]*age gnlr3(y, dist="gamma", mu=mu, pmu=rep(1,3), pshape=0, pfamily=0) # or equivalently gnlr3(y, dist="gamma", mu=~sexf+age, pmu=rep(1,3), pshape=0, pfamily=0) # or gnlr3(y, dist="gamma", linear=~sex+age, pmu=rep(1,3), pshape=0, pfamily=0) # or gnlr3(y, dist="gamma", mu=~b0+b1*sex+b2*age, pmu=list(b0=1,b1=1,b2=1), pshape=0, pfamily=0) # # nonlinear regression with generalized gamma distribution mu <- function(p, linear) p[4]+exp(linear) gnlr3(y, dist="gamma", mu=mu, linear=~sex+age, pmu=rep(1,4), pshape=0, pfamily=0) # or equivalently gnlr3(y, dist="gamma", mu=~b4+exp(b0+b1*sex+b2*age), pmu=list(b0=1,b1=1,b2=1,b4=1), pshape=0, pfamily=0) # # include regression for the shape parameter with same mu function shape <- function(p) p[1]+p[2]*sex+p[3]*age gnlr3(y, dist="gamma", mu=mu, linear=~sexf+age, shape=shape, pmu=rep(1,4), pshape=rep(0,3), pfamily=0) # or equivalently gnlr3(y, dist="gamma", mu=mu, linear=list(~sexf+age,~sex+age,NULL), pmu=rep(1,4), pshape=rep(0,3), pfamily=0) # or gnlr3(y, dist="gamma", mu=mu, linear=~sexf+age, shape=~c0+c1*sex+c2*age, pmu=rep(1,4), pshape=list(c0=0,c1=0,c2=0), pfamily=0) # include regression for the family parameter with same mu # and shape functions family <- function(p) p[1]+p[2]*sex+p[3]*age gnlr3(y, dist="gamma", mu=mu, linear=~sexf+age, shape=shape, family=shape, pmu=rep(1,4), pshape=rep(0,3), pfamily=rep(0,3)) # or equivalently gnlr3(y, dist="gamma", mu=mu, linear=list(~sex+age,~sex+age,~sex+age), pmu=rep(1,4), pshape=rep(0,3), pfamily=rep(0,3)) # or gnlr3(y, dist="gamma", mu=~b4+exp(b0+b1*sex+b2*age), shape=~c0+c1*sex+c2*age, family=~d0+d1*sex+d2*age, pmu=list(b0=1,b1=1,b2=1,b4=1), pshape=list(c0=0,c1=0,c2=0), pfamily=list(d0=0,d1=0,d2=0))