gnlr: Generalized Nonlinear Regression Models for One and Two...
In gnlm: Generalized Nonlinear Regression Models
Description
Usage
Arguments
Details
Value
Author(s)
See Also
Examples
Description
gnlr fits user-specified nonlinear regression equations to one or
both parameters of the common one and two parameter distributions. A
user-specified -log likelihood can also be supplied for the distribution.
Most distributions allow data to be left, right, and/or interval censored.
Usage
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gnlr(y = NULL, distribution = "normal", pmu = NULL, pshape = NULL,
mu = NULL, shape = NULL, linear = NULL, exact = FALSE, wt = 1,
delta = 1, shfn = FALSE, common = FALSE, envir = parent.frame(),
print.level = 0, typsize = abs(p), ndigit = 10, gradtol = 1e-05,
stepmax = 10 * sqrt(p %*% p), steptol = 1e-05, iterlim = 100,
fscale = 1)
Arguments
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 left or right
censoring (only interval censoring).
distribution
Either a character string containing the name of the
distribution or a function giving the -log likelihood. (In the latter case,
all initial parameter estimates are supplied in pmu.)
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, Levy, beta, simplex, and two-sided
power. All but the binomial-based distributions and the beta, simplex, and
two-sided power distributions may be right and/or left censored. (For
definitions of distributions, see the corresponding [dpqr]distribution
help.)
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. If distribution is a user-supplied -log likelihood function,
all initial estimates must be supplied here.
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.
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 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.
exact
If TRUE, fits the exact likelihood function for continuous data
by integration over intervals of observation given in delta, 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.)
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 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.
print.level
Arguments controlling nlm.
typsize
Arguments controlling nlm.
ndigit
Arguments controlling nlm.
gradtol
Arguments controlling nlm.
stepmax
Arguments controlling nlm.
steptol
Arguments controlling nlm.
iterlim
Arguments controlling nlm.
fscale
Arguments controlling nlm.
Details
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.
Value
A list of class gnlm is returned that contains all of the
relevant information calculated, including error codes.
Author(s)
J.K. Lindsey
See Also
finterp, fmr,
glm, gnlmix,
glmm, gnlmm,
gnlr3, lm, nlr,
nls.
Examples
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sex <- c(rep(0,10),rep(1,10))
sexf <- gl(2,10)
age <- c(8,10,12,12,8,7,16,7,9,11,8,9,14,12,12,11,7,7,7,12)
y <- cbind(c(9.2, 7.3,13.0, 6.9, 3.9,14.9,17.8, 4.8, 6.4, 3.3,17.2,
14.4,17.0, 5.0,17.3, 3.8,19.4, 5.0, 2.0,19.0),
c(0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1))
# y <- cbind(rweibull(20,2,2+2*sex+age),rbinom(20,1,0.7))
# linear regression with inverse Gauss distribution
mu <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, pmu=c(3,0,0), pshape=1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~sexf+age, pmu=c(3,0,0), pshape=1)
# or
gnlr(y, dist="inverse Gauss", linear=~sexf+age, pmu=c(3,0,0), pshape=1)
# or
gnlr(y, dist="inverse Gauss", mu=~b0+b1*sex+b2*age,
pmu=list(b0=3,b1=0,b2=0), pshape=1)
#
# nonlinear regression with inverse Gauss distribution
mu <- function(p, linear) exp(linear)
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age, pmu=c(3,0,0),
pshape=-1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~exp(b0+b1*sex+b2*age),
pmu=list(b0=3,b1=0,b2=0), pshape=-1)
# or
gnlr(y, dist="inverse Gauss", mu=~exp(linear), linear=~sexf+age,
pmu=c(3,0,0), pshape=-1)
#
# include regression for the shape parameter with same mu function
shape <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age, shape=shape,
pmu=c(3,0,0), pshape=c(3,0,0))
# or equivalently
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age,
shape=~sexf+age, pmu=c(3,0,0), pshape=c(3,0,0))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=list(~sex+age,~sex+age),
pmu=c(3,0,0),pshape=c(3,0,0))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sex+age,
shape=~c0+c1*sex+c2*age, pmu=c(3,0,0),
pshape=list(c0=3,c1=0,c2=0))
#
# shape as a function of the location
shape <- function(p, mu) p[1]+p[2]*sex+p[3]*mu
gnlr(y, dist="inverse Gauss", mu=~age, shape=shape, pmu=c(3,0),
pshape=c(3,0,0), shfn=TRUE)
# or
gnlr(y, dist="inverse Gauss", mu=~age, shape=~a+b*sex+c*mu, pmu=c(3,0),
pshape=c(3,0,0), shfn=TRUE)
#
# common parameter in location and shape functions for age
mu <- function(p) exp(p[1]+p[2]*age)
shape <- function(p, mu) p[3]+p[4]*sex+p[2]*age
gnlr(y, dist="inverse Gauss", mu=mu, shape=shape, pmu=c(3,0,1,0),
common=TRUE)
# or
gnlr(y, dist="inverse Gauss", mu=~exp(a+b*age), shape=~c+d*sex+b*age,
pmu=c(3,0,1,0), common=TRUE)
#
# user-supplied -log likelihood function
y <- rnorm(20,2+3*sex,2)
dist <- function(p)-sum(dnorm(y,p[1]+p[2]*sex,p[3],log=TRUE))
gnlr(y, dist=dist,pmu=1:3)
dist <- ~-sum(dnorm(y,a+b*sex,v,log=TRUE))
gnlr(y, dist=dist,pmu=1:3)
Example output
Loading required package: rmutil
Attaching package: 'rmutil'
The following object is masked from 'package:stats':
nobs
The following objects are masked from 'package:base':
as.data.frame, units
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, pmu = c(3, 0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
p[1] + p[2] * sex + p[3] * age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
p[1] 2.204 10.432
p[2] -0.193 5.121
p[3] 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~sexf + age, pmu = c(3,
0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
(Intercept) 2.204 10.432
sexf2 -0.193 5.121
age 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", linear = ~sexf + age, pmu = c(3,
0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
(Intercept) 2.204 10.432
sexf2 -0.193 5.121
age 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~b0 + b1 * sex + b2 * age,
pmu = list(b0 = 3, b1 = 0, b2 = 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~b0 + b1 * sex + b2 * age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
b0 2.204 10.432
b1 -0.193 5.121
b2 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
pmu = c(3, 0, 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
(Intercept) 1.63332 0.8649
sexf2 -0.03960 0.4631
age 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(b0 + b1 * sex + b2 *
age), pmu = list(b0 = 3, b1 = 0, b2 = 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(b0 + b1 * sex + b2 * age)
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
b0 1.63332 0.8649
b1 -0.03960 0.4631
b2 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(linear), linear = ~sexf +
age, pmu = c(3, 0, 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
(Intercept) 1.63332 0.8649
sexf2 -0.03960 0.4631
age 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
shape = shape, pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] + p[2] * sex + p[3] * age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sexf2 -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
p[1] -1.01686 1.8218
p[2] 0.07446 0.7231
p[3] -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
shape = ~sexf + age, pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
~sexf + age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sexf2 -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
(Intercept) -1.01686 1.8218
sexf2 0.07446 0.7231
age -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = list(~sex +
age, ~sex + age), pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sex + age
Log shape function:
~sex + age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sex -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
(Intercept) -1.01686 1.8218
sex 0.07446 0.7231
age -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sex + age,
shape = ~c0 + c1 * sex + c2 * age, pmu = c(3, 0, 0), pshape = list(c0 = 3,
c1 = 0, c2 = 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sex + age
Log shape function:
~c0 + c1 * sex + c2 * age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sex -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
c0 -1.01686 1.8218
c1 0.07446 0.7231
c2 -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~age, shape = shape, pmu = c(3,
0), pshape = c(3, 0, 0), shfn = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~age
Log shape function:
p[1] + p[2] * sex + p[3] * mu
-Log likelihood 53.46555
Degrees of freedom 15
AIC 58.46555
Iterations 25
Location parameters:
estimate se
(Intercept) 1.656 8.2270
age 1.085 0.8752
Shape parameters:
estimate se
p[1] -0.86983 2.4570
p[2] 0.06949 0.6877
p[3] -0.16672 0.1975
Correlations:
1 2 3 4 5
1 1.00000 -0.953448 0.5797 -0.050577 -0.5864
2 -0.95345 1.000000 -0.5558 0.009936 0.6299
3 0.57967 -0.555784 1.0000 -0.319035 -0.9541
4 -0.05058 0.009936 -0.3190 1.000000 0.1414
5 -0.58641 0.629867 -0.9541 0.141396 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~age, shape = ~a + b * sex +
c * mu, pmu = c(3, 0), pshape = c(3, 0, 0), shfn = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~age
Log shape function:
~a + b * sex + c * mu
-Log likelihood 53.46555
Degrees of freedom 15
AIC 58.46555
Iterations 25
Location parameters:
estimate se
(Intercept) 1.656 8.2270
age 1.085 0.8752
Shape parameters:
estimate se
a -0.86983 2.4570
b 0.06949 0.6877
c -0.16672 0.1975
Correlations:
1 2 3 4 5
1 1.00000 -0.953448 0.5797 -0.050577 -0.5864
2 -0.95345 1.000000 -0.5558 0.009936 0.6299
3 0.57967 -0.555784 1.0000 -0.319035 -0.9541
4 -0.05058 0.009936 -0.3190 1.000000 0.1414
5 -0.58641 0.629867 -0.9541 0.141396 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, shape = shape, pmu = c(3,
0, 1, 0), common = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(p[1] + p[2] * age)
Log shape function:
p[3] + p[4] * sex + p[2] * age
-Log likelihood 54.5085
Degrees of freedom 16
AIC 58.5085
Iterations 39
Common parameters:
estimate se
p[1] 2.05692 0.67920
p[2] 0.04257 0.06443
p[3] -3.35220 0.85535
p[4] 0.28373 0.69463
Correlations:
1 2 3 4
1 1.0000 -0.9443 0.8053 -0.2531
2 -0.9443 1.0000 -0.8004 0.2051
3 0.8053 -0.8004 1.0000 -0.6059
4 -0.2531 0.2051 -0.6059 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(a + b * age), shape = ~c +
d * sex + b * age, pmu = c(3, 0, 1, 0), common = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(a + b * age)
Log shape function:
~c + d * sex + b * age
-Log likelihood 54.5085
Degrees of freedom 16
AIC 58.5085
Iterations 39
Common parameters:
estimate se
a 2.05692 0.67920
b 0.04257 0.06443
c -3.35220 0.85535
d 0.28373 0.69463
Correlations:
1 2 3 4
1 1.0000 -0.9443 0.8053 -0.2531
2 -0.9443 1.0000 -0.8004 0.2051
3 0.8053 -0.8004 1.0000 -0.6059
4 -0.2531 0.2051 -0.6059 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = dist, pmu = 1:3)
own distribution
Response: y
Log likelihood function:
-sum(dnorm(y, p[1] + p[2] * sex, p[3], log = TRUE))
-Log likelihood 43.59446
Degrees of freedom 17
AIC 46.59446
Iterations 12
Model parameters:
estimate se
p[1] 1.752 0.6767
p[2] 4.218 0.9570
p[3] 2.140 0.3389
Correlations:
1 2 3
1 1.000e+00 -0.7071068 -7.279e-05
2 -7.071e-01 1.0000000 3.742e-04
3 -7.279e-05 0.0003742 1.000e+00
Warning messages:
1: In dnorm(y, p[1] + p[2] * sex, p[3], log = TRUE) : NaNs produced
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = dist, pmu = 1:3)
own distribution
Response: y
Log likelihood function:
~-sum(dnorm(y, a + b * sex, v, log = TRUE))
-Log likelihood 43.59446
Degrees of freedom 17
AIC 46.59446
Iterations 12
Model parameters:
estimate se
a 1.752 0.6767
b 4.218 0.9570
v 2.140 0.3389
Correlations:
1 2 3
1 1.000e+00 -0.7071068 -7.279e-05
2 -7.071e-01 1.0000000 3.742e-04
3 -7.279e-05 0.0003742 1.000e+00
Warning messages:
1: In dnorm(y, .p[1] + .p[2] * sex, .p[3], log = TRUE) : NaNs produced
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
gnlm documentation built on May 2, 2019, 7:26 a.m.
R Package Documentation
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Description Usage Arguments Details Value Author(s) See Also Examples
Description
gnlr fits user-specified nonlinear regression equations to one or
both parameters of the common one and two parameter distributions. A
user-specified -log likelihood can also be supplied for the distribution.
Most distributions allow data to be left, right, and/or interval censored.
Usage
1 2 3 4 5 6 | gnlr(y = NULL, distribution = "normal", pmu = NULL, pshape = NULL,
mu = NULL, shape = NULL, linear = NULL, exact = FALSE, wt = 1,
delta = 1, shfn = FALSE, common = FALSE, envir = parent.frame(),
print.level = 0, typsize = abs(p), ndigit = 10, gradtol = 1e-05,
stepmax = 10 * sqrt(p %*% p), steptol = 1e-05, iterlim = 100,
fscale = 1)
|
Arguments
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, |
distribution |
Either a character string containing the name of the
distribution or a function giving the -log likelihood. (In the latter case,
all initial parameter estimates are supplied in 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, Levy, beta, simplex, and two-sided power. All but the binomial-based distributions and the beta, simplex, and two-sided power distributions may be right and/or left censored. (For definitions of distributions, see the corresponding [dpqr]distribution help.) |
pmu |
Vector of initial estimates for the location parameters. If
|
pshape |
Vector of initial estimates for the shape parameters. If
|
mu |
A user-specified function of |
shape |
A user-specified function of |
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. |
exact |
If TRUE, fits the exact likelihood function for continuous data
by integration over intervals of observation given in |
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, |
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, |
envir |
Environment in which model formulae are to be interpreted or a
data object of class, |
print.level |
Arguments controlling |
typsize |
Arguments controlling |
ndigit |
Arguments controlling |
gradtol |
Arguments controlling |
stepmax |
Arguments controlling |
steptol |
Arguments controlling |
iterlim |
Arguments controlling |
fscale |
Arguments controlling |
Details
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.
Value
A list of class gnlm is returned that contains all of the
relevant information calculated, including error codes.
Author(s)
J.K. Lindsey
See Also
finterp, fmr,
glm, gnlmix,
glmm, gnlmm,
gnlr3, lm, nlr,
nls.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 | sex <- c(rep(0,10),rep(1,10))
sexf <- gl(2,10)
age <- c(8,10,12,12,8,7,16,7,9,11,8,9,14,12,12,11,7,7,7,12)
y <- cbind(c(9.2, 7.3,13.0, 6.9, 3.9,14.9,17.8, 4.8, 6.4, 3.3,17.2,
14.4,17.0, 5.0,17.3, 3.8,19.4, 5.0, 2.0,19.0),
c(0,1,0,1,1,1,0,1,0,1,1,1,1,1,1,1,1,1,1,1))
# y <- cbind(rweibull(20,2,2+2*sex+age),rbinom(20,1,0.7))
# linear regression with inverse Gauss distribution
mu <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, pmu=c(3,0,0), pshape=1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~sexf+age, pmu=c(3,0,0), pshape=1)
# or
gnlr(y, dist="inverse Gauss", linear=~sexf+age, pmu=c(3,0,0), pshape=1)
# or
gnlr(y, dist="inverse Gauss", mu=~b0+b1*sex+b2*age,
pmu=list(b0=3,b1=0,b2=0), pshape=1)
#
# nonlinear regression with inverse Gauss distribution
mu <- function(p, linear) exp(linear)
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age, pmu=c(3,0,0),
pshape=-1)
# or equivalently
gnlr(y, dist="inverse Gauss", mu=~exp(b0+b1*sex+b2*age),
pmu=list(b0=3,b1=0,b2=0), pshape=-1)
# or
gnlr(y, dist="inverse Gauss", mu=~exp(linear), linear=~sexf+age,
pmu=c(3,0,0), pshape=-1)
#
# include regression for the shape parameter with same mu function
shape <- function(p) p[1]+p[2]*sex+p[3]*age
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age, shape=shape,
pmu=c(3,0,0), pshape=c(3,0,0))
# or equivalently
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sexf+age,
shape=~sexf+age, pmu=c(3,0,0), pshape=c(3,0,0))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=list(~sex+age,~sex+age),
pmu=c(3,0,0),pshape=c(3,0,0))
# or
gnlr(y, dist="inverse Gauss", mu=mu, linear=~sex+age,
shape=~c0+c1*sex+c2*age, pmu=c(3,0,0),
pshape=list(c0=3,c1=0,c2=0))
#
# shape as a function of the location
shape <- function(p, mu) p[1]+p[2]*sex+p[3]*mu
gnlr(y, dist="inverse Gauss", mu=~age, shape=shape, pmu=c(3,0),
pshape=c(3,0,0), shfn=TRUE)
# or
gnlr(y, dist="inverse Gauss", mu=~age, shape=~a+b*sex+c*mu, pmu=c(3,0),
pshape=c(3,0,0), shfn=TRUE)
#
# common parameter in location and shape functions for age
mu <- function(p) exp(p[1]+p[2]*age)
shape <- function(p, mu) p[3]+p[4]*sex+p[2]*age
gnlr(y, dist="inverse Gauss", mu=mu, shape=shape, pmu=c(3,0,1,0),
common=TRUE)
# or
gnlr(y, dist="inverse Gauss", mu=~exp(a+b*age), shape=~c+d*sex+b*age,
pmu=c(3,0,1,0), common=TRUE)
#
# user-supplied -log likelihood function
y <- rnorm(20,2+3*sex,2)
dist <- function(p)-sum(dnorm(y,p[1]+p[2]*sex,p[3],log=TRUE))
gnlr(y, dist=dist,pmu=1:3)
dist <- ~-sum(dnorm(y,a+b*sex,v,log=TRUE))
gnlr(y, dist=dist,pmu=1:3)
|
Example output
Loading required package: rmutil
Attaching package: 'rmutil'
The following object is masked from 'package:stats':
nobs
The following objects are masked from 'package:base':
as.data.frame, units
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, pmu = c(3, 0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
p[1] + p[2] * sex + p[3] * age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
p[1] 2.204 10.432
p[2] -0.193 5.121
p[3] 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~sexf + age, pmu = c(3,
0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
(Intercept) 2.204 10.432
sexf2 -0.193 5.121
age 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", linear = ~sexf + age, pmu = c(3,
0, 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
(Intercept) 2.204 10.432
sexf2 -0.193 5.121
age 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~b0 + b1 * sex + b2 * age,
pmu = list(b0 = 3, b1 = 0, b2 = 0), pshape = 1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~b0 + b1 * sex + b2 * age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.1341
Degrees of freedom 16
AIC 58.1341
Iterations 34
Location parameters:
estimate se
b0 2.204 10.432
b1 -0.193 5.121
b2 1.072 1.165
Shape parameters:
estimate se
p[1] -2.797 0.341
Correlations:
1 2 3 4
1 1.00000 -0.33276 -0.91821 -0.04008
2 -0.33276 1.00000 0.01445 -0.16563
3 -0.91821 0.01445 1.00000 0.13327
4 -0.04008 -0.16563 0.13327 1.00000
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
pmu = c(3, 0, 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
(Intercept) 1.63332 0.8649
sexf2 -0.03960 0.4631
age 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(b0 + b1 * sex + b2 *
age), pmu = list(b0 = 3, b1 = 0, b2 = 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(b0 + b1 * sex + b2 * age)
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
b0 1.63332 0.8649
b1 -0.03960 0.4631
b2 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(linear), linear = ~sexf +
age, pmu = c(3, 0, 0), pshape = -1)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] * rep(1, n)
-Log likelihood 54.04785
Degrees of freedom 16
AIC 58.04785
Iterations 12
Location parameters:
estimate se
(Intercept) 1.63332 0.8649
sexf2 -0.03960 0.4631
age 0.09204 0.0858
Shape parameters:
estimate se
p[1] -2.799 0.3426
Correlations:
1 2 3 4
1 1.000000 -0.38964 -0.90026 0.005675
2 -0.389637 1.00000 0.04022 -0.194441
3 -0.900263 0.04022 1.00000 0.112301
4 0.005675 -0.19444 0.11230 1.000000
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
shape = shape, pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
p[1] + p[2] * sex + p[3] * age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sexf2 -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
p[1] -1.01686 1.8218
p[2] 0.07446 0.7231
p[3] -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sexf + age,
shape = ~sexf + age, pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sexf + age
Log shape function:
~sexf + age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sexf2 -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
(Intercept) -1.01686 1.8218
sexf2 0.07446 0.7231
age -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = list(~sex +
age, ~sex + age), pmu = c(3, 0, 0), pshape = c(3, 0, 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sex + age
Log shape function:
~sex + age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sex -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
(Intercept) -1.01686 1.8218
sex 0.07446 0.7231
age -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, linear = ~sex + age,
shape = ~c0 + c1 * sex + c2 * age, pmu = c(3, 0, 0), pshape = list(c0 = 3,
c1 = 0, c2 = 0))
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(linear)
Linear part:
~sex + age
Log shape function:
~c0 + c1 * sex + c2 * age
-Log likelihood 53.29904
Degrees of freedom 14
AIC 59.29904
Iterations 29
Location parameters:
estimate se
(Intercept) 1.56432 0.83173
sex -0.05123 0.45930
age 0.09534 0.06906
Shape parameters:
estimate se
c0 -1.01686 1.8218
c1 0.07446 0.7231
c2 -0.19480 0.1704
Correlations:
1 2 3 4 5 6
1 1.00000 -0.4748 -0.89143 0.02607 -0.2404 0.04569
2 -0.47478 1.0000 0.11558 -0.19937 0.2960 0.09680
3 -0.89143 0.1156 1.00000 0.04066 0.1043 -0.05590
4 0.02607 -0.1994 0.04066 1.00000 -0.3955 -0.95355
5 -0.24036 0.2960 0.10432 -0.39549 1.0000 0.17413
6 0.04569 0.0968 -0.05590 -0.95355 0.1741 1.00000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~age, shape = shape, pmu = c(3,
0), pshape = c(3, 0, 0), shfn = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~age
Log shape function:
p[1] + p[2] * sex + p[3] * mu
-Log likelihood 53.46555
Degrees of freedom 15
AIC 58.46555
Iterations 25
Location parameters:
estimate se
(Intercept) 1.656 8.2270
age 1.085 0.8752
Shape parameters:
estimate se
p[1] -0.86983 2.4570
p[2] 0.06949 0.6877
p[3] -0.16672 0.1975
Correlations:
1 2 3 4 5
1 1.00000 -0.953448 0.5797 -0.050577 -0.5864
2 -0.95345 1.000000 -0.5558 0.009936 0.6299
3 0.57967 -0.555784 1.0000 -0.319035 -0.9541
4 -0.05058 0.009936 -0.3190 1.000000 0.1414
5 -0.58641 0.629867 -0.9541 0.141396 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~age, shape = ~a + b * sex +
c * mu, pmu = c(3, 0), pshape = c(3, 0, 0), shfn = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~age
Log shape function:
~a + b * sex + c * mu
-Log likelihood 53.46555
Degrees of freedom 15
AIC 58.46555
Iterations 25
Location parameters:
estimate se
(Intercept) 1.656 8.2270
age 1.085 0.8752
Shape parameters:
estimate se
a -0.86983 2.4570
b 0.06949 0.6877
c -0.16672 0.1975
Correlations:
1 2 3 4 5
1 1.00000 -0.953448 0.5797 -0.050577 -0.5864
2 -0.95345 1.000000 -0.5558 0.009936 0.6299
3 0.57967 -0.555784 1.0000 -0.319035 -0.9541
4 -0.05058 0.009936 -0.3190 1.000000 0.1414
5 -0.58641 0.629867 -0.9541 0.141396 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = mu, shape = shape, pmu = c(3,
0, 1, 0), common = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
exp(p[1] + p[2] * age)
Log shape function:
p[3] + p[4] * sex + p[2] * age
-Log likelihood 54.5085
Degrees of freedom 16
AIC 58.5085
Iterations 39
Common parameters:
estimate se
p[1] 2.05692 0.67920
p[2] 0.04257 0.06443
p[3] -3.35220 0.85535
p[4] 0.28373 0.69463
Correlations:
1 2 3 4
1 1.0000 -0.9443 0.8053 -0.2531
2 -0.9443 1.0000 -0.8004 0.2051
3 0.8053 -0.8004 1.0000 -0.6059
4 -0.2531 0.2051 -0.6059 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = "inverse Gauss", mu = ~exp(a + b * age), shape = ~c +
d * sex + b * age, pmu = c(3, 0, 1, 0), common = TRUE)
censored inverse Gauss distribution
Response: y
Log likelihood function:
{
m <- mu1(p)
t <- sh1(p)
s <- exp(t)
-sum(wt * (cc * (-(t + (y[, 1] - m)^2/(y[, 1] * s * m^2))/2) +
log(lc - rc * pinvgauss(y[, 1], m, s))))
}
Location function:
~exp(a + b * age)
Log shape function:
~c + d * sex + b * age
-Log likelihood 54.5085
Degrees of freedom 16
AIC 58.5085
Iterations 39
Common parameters:
estimate se
a 2.05692 0.67920
b 0.04257 0.06443
c -3.35220 0.85535
d 0.28373 0.69463
Correlations:
1 2 3 4
1 1.0000 -0.9443 0.8053 -0.2531
2 -0.9443 1.0000 -0.8004 0.2051
3 0.8053 -0.8004 1.0000 -0.6059
4 -0.2531 0.2051 -0.6059 1.0000
Warning messages:
1: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
3: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
4: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
5: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
6: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
7: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = dist, pmu = 1:3)
own distribution
Response: y
Log likelihood function:
-sum(dnorm(y, p[1] + p[2] * sex, p[3], log = TRUE))
-Log likelihood 43.59446
Degrees of freedom 17
AIC 46.59446
Iterations 12
Model parameters:
estimate se
p[1] 1.752 0.6767
p[2] 4.218 0.9570
p[3] 2.140 0.3389
Correlations:
1 2 3
1 1.000e+00 -0.7071068 -7.279e-05
2 -7.071e-01 1.0000000 3.742e-04
3 -7.279e-05 0.0003742 1.000e+00
Warning messages:
1: In dnorm(y, p[1] + p[2] * sex, p[3], log = TRUE) : NaNs produced
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
Call:
gnlr(y, dist = dist, pmu = 1:3)
own distribution
Response: y
Log likelihood function:
~-sum(dnorm(y, a + b * sex, v, log = TRUE))
-Log likelihood 43.59446
Degrees of freedom 17
AIC 46.59446
Iterations 12
Model parameters:
estimate se
a 1.752 0.6767
b 4.218 0.9570
v 2.140 0.3389
Correlations:
1 2 3
1 1.000e+00 -0.7071068 -7.279e-05
2 -7.071e-01 1.0000000 3.742e-04
3 -7.279e-05 0.0003742 1.000e+00
Warning messages:
1: In dnorm(y, .p[1] + .p[2] * sex, .p[3], log = TRUE) : NaNs produced
2: In nlm(fcn, p = p, hessian = TRUE, print.level = print.level, typsize = typsize, :
NA/Inf replaced by maximum positive value
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