nlme(model, data, fixed, random, groups, start, correlation, weights, subset, method, na.action, naPattern, control, verbose)
nlsList
object.
If
data
is given,
all names used in the formula should be defined as parameters
or variables in the data frame.
The method function
nlme.nlsList
is documented
separately.
f1,...,fn
are the names of parameters
included on the right hand side of
model
and the
x1+...+xm
expressions
define linear models for these parameters
(when the left hand side of the formula contains several parameters,
they all are assumed to follow the same linear model,
described by the right hand side expression).
A
1
on the right hand side of the formula(s)
indicates a single fixed effects for the corresponding parameter(s).
model
,
fixed
,
random
,
correlation
,
weights
,
subset
,
and
naPattern
.
By default the variables are taken from the environment from which
nlme
is called.
r1,...,rn
naming parameters
included on the right hand side of
model
,
x1+...+xm
specifying the random-effects model
for these parameters
and
g1/.../gQ
the grouping structure
(
Q
may be equal to 1,
in which case no
/
is required).
The random effects formula will be repeated for all levels of grouping,
in the case of multiple levels of grouping;
(ii) a two-sided formula of the form `r1+...+rn~x1+..+xm',
a list of two-sided formulas of the form `r1~x1+...+xm',
with possibly different random-effects models for different parameters,
a
pdMat
object with a two-sided formula,
or list of two-sided formulas
(i.e. a non-
NULL
value for
formula(random)
),
or a list of pdMat objects with two-sided formulas,
or lists of two-sided formulas.
In this case, the grouping structure formula will be given
in
groups
,
or derived from the data used to fit the nonlinear mixed-effects model,
which should inherit from class
groupedData
,;
(iii) a named list of formulas, lists of formulas,
or
pdMat
objects as in (ii),
with the grouping factors as names.
The order of nesting will be assumed the same as the order of the elements
in the list;
(iv) an
reStruct
object.
See the documentation on
pdClasses
for a description of the available
pdMat
classes.
Defaults to
fixed
,
resulting in all fixed effects having also random effects.
g1,...,gQ
must evaluate to factors
in
data
.
The order of nesting, when multiple levels are present,
is taken from left to right
(i.e.
g1
is the first level,
g2
the second, etc.).
fixed
, given by the vector.
The
fixed
component is required,
unless the model function inherits from class
selfStart
,
in which case initial values will be derived
from a call to
nlsList
.
An optional
random
component is used
to specify initial values for the random effects
and should consist of a matrix,
or a list of matrices with length equal to the number of grouping levels.
Each matrix should have as many rows as the number of groups
at the corresponding level
and as many columns as the number of random effects in that level.
corStruct
object
describing the within-group correlation structure.
See the documentation of
corClasses
for a description of the available
corStruct
classes.
Defaults to
NULL
,
corresponding to no within-group correlations.
varFunc
object
or one-sided formula describing the within-group heteroscedasticity structure.
If given as a formula,
it is used as the argument to
varFixed
,
corresponding to fixed variance weights.
See the documentation on
varClasses
for a description of the available
varFunc
classes.
Defaults to
NULL
,
corresponding to homoscesdatic within-group errors.
data
that should be used in the fit.
This can be a logical vector,
a numeric vector indicating which observation numbers are to be included,
or a character vector of the row names to be included.
All observations are included by default.
"REML"
the model is fit
by maximizing the restricted log-likelihood.
If
"ML"
the log-likelihood is maximized.
Defaults to
"ML"
.
NA
s.
The default action (
na.fail
) causes
nlme
to print an error message
and terminate if there are any incomplete observations.
nlmeControl
.
Defaults to an empty list.
TRUE
information on
the evolution of the iterative algorithm is printed.
Default is
FALSE
.
nlme
representing the nonlinear mixed-effects model fit.
Generic functions such as
print
,
plot
and
summary
have methods
to show the results of the fit.
See
nlmeObject
for the components of the fit.
The functions
resid
,
coef
,
fitted
,
fixed.effects
,
and
random.effects
can be used to extract
some of its components.
Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994). Time Series Analysis: Forecasting and Control (3rd Edition). San Francisco: Holden-Day.
Davidian, M. and Giltinan, D.M. (1995). Nonlinear Mixed Effects Models for Repeated Measurement Data. London: Chapman and Hall.
Laird, N.M. and Ware, J.H. (1982). Random-Effects models for longitudinal data. Biometrics, 38, 963-974.
Lindstrom, M.J. and Bates, D.M. (1990). Nonlinear mixed effects models for repeated measures data. Biometrics, 46, 673-687.
Pinheiro, J.C. and Bates., D.M. (1996). Unconstrained parametrizations for variance-covariance matrices. Statistics and Computing, 6 289-296.
Venables, W.N. and Ripley, B.D. (1997). Modern Applied Statistics with S-PLUS (2nd Edition). New York: Springer-Verlag.
The model formulation and computational methods are described
in Lindstrom and Bates (1990).
The variance-covariance parametrizations are described
in Pinheiro and Bates (1996).
The different correlation structures available for the
correlation
argument are described
in Box, Jenkins, and Reinsel (1994),
Littel, Milliken, Stroup, and Wolfinger (1996), and Venables and Ripley (1997).
The use of variance functions for linear and nonlinear mixed effects models
is presented in detail in Davidian and Giltinan (1995).
## all parameters as fixed and random effects fm1 <- nlme(weight ~ SSlogis(Time, Asym, xmid, scal), data=Soybean, fixed=Asym + xmid + scal ~ 1, start = c(18, 52, 7.5)) ## only Asym and xmid as random, with a diagonal covariance fm2 <- nlme(weight ~ SSlogis(Time, Asym, xmid, scal), data=Soybean, fixed=Asym + xmid + scal ~ 1, random=pdDiag(Asym + xmid ~ 1), start=c(18, 52, 7.5))