Nonlinear Mixed-Effects Models
This generic function fits a nonlinear mixed-effects model in the formulation described in Lindstrom and Bates (1990) but allowing for nested random effects. The within-group errors are allowed to be correlated and/or have unequal variances.
nlme(model, data, fixed, random, groups, start, correlation, weights,
subset, method, na.action, naPattern, control, verbose)model |
a nonlinear model formula, with the response on the left
of a |
data |
an optional data frame containing the variables named in
|
fixed |
a two-sided linear formula of the form
|
random |
optionally, any of the following: (i) a two-sided formula
of the form |
groups |
an optional one-sided formula of the form |
start |
an optional numeric vector, or list of initial estimates
for the fixed effects and random effects. If declared as a numeric
vector, it is converted internally to a list with a single component
|
correlation |
an optional |
weights |
an optional |
subset |
an optional expression indicating the subset of the rows of
|
method |
a character string. If |
na.action |
a function that indicates what should happen when the
data contain |
naPattern |
an expression or formula object, specifying which returned values are to be regarded as missing. |
control |
a list of control values for the estimation algorithm to
replace the default values returned by the function |
verbose |
an optional logical value. If |
an object of class 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.
The function does not do any scaling internally: the optimization will work best when the response is scaled so its variance is of the order of one.
José Pinheiro and Douglas Bates bates@stat.wisc.edu
The model formulation and computational methods are described in
Lindstrom, M.J. and Bates, D.M. (1990). The variance-covariance
parametrizations are described in Pinheiro, J.C. and Bates., D.M.
(1996). The different correlation structures available for the
correlation argument are described in Box, G.E.P., Jenkins,
G.M., and Reinsel G.C. (1994), Littel, R.C., Milliken, G.A., Stroup,
W.W., and Wolfinger, R.D. (1996), and Venables, W.N. and Ripley,
B.D. (2002). The use of variance functions for linear and nonlinear
mixed effects models is presented in detail in Davidian, M. and
Giltinan, D.M. (1995).
Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series Analysis: Forecasting and Control", 3rd Edition, Holden-Day.
Davidian, M. and Giltinan, D.M. (1995) "Nonlinear Mixed Effects Models for Repeated Measurement Data", Chapman and Hall.
Laird, N.M. and Ware, J.H. (1982) "Random-Effects Models for Longitudinal Data", Biometrics, 38, 963-974.
Littel, R.C., Milliken, G.A., Stroup, W.W., and Wolfinger, R.D. (1996) "SAS Systems for Mixed Models", SAS Institute.
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.
Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S and S-PLUS", Springer.
Venables, W.N. and Ripley, B.D. (2002) "Modern Applied Statistics with S", 4th Edition, Springer-Verlag.
fm1 <- nlme(height ~ SSasymp(age, Asym, R0, lrc),
data = Loblolly,
fixed = Asym + R0 + lrc ~ 1,
random = Asym ~ 1,
start = c(Asym = 103, R0 = -8.5, lrc = -3.3))
summary(fm1)
fm2 <- update(fm1, random = pdDiag(Asym + lrc ~ 1))
summary(fm2)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.