Fit Linear Model Using Generalized Least Squares

DESCRIPTION:

This function fits a linear model using generalized least squares. The errors are allowed to be correlated and/or have unequal variances. glsD is a slightly enhanced version of the Pinheiro and Bates glsD function in the nlme package to make it easy to use with the Design library and to implement cluster bootstrapping (primarily for nonparametric estimates of the variance-covariance matrix of the parameter estimates and for nonparametric confidence limits of correlation parameters).

USAGE:

glsD(model, data, correlation, weights, subset, method, na.action,
    control, verbose, B=0, dupCluster=FALSE, pr=FALSE,
    opmeth=c('optimize','optim'))

## S3 method for class 'glsD':
print(x, digits=4, ...)

ARGUMENTS:

model
a two-sided linear formula object describing the model, with the response on the left of a ~ operator and the terms, separated by + operators, on the right.
data
an optional data frame containing the variables named in model, correlation, weights, and subset. By default the variables are taken from the environment from which gls is called.
correlation
an optional corStruct object describing the within-group correlation structure. See the documentation of corClasses for a description of the available corStruct classes. If a grouping variable is to be used, it must be specified in the form argument to the corStruct constructor. Defaults to NULL, corresponding to uncorrelated errors.
weights
an optional 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 errors.
subset
an optional expression indicating which subset of the rows of data should be used in the fit. This can be a logical vector, or 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.
method
a character string. If "REML" the model is fit by maximizing the restricted log-likelihood. If "ML" the log-likelihood is maximized. Defaults to "REML".
na.action
a function that indicates what should happen when the data contain NAs. The default action ( na.fail) causes gls to print an error message and terminate if there are any incomplete observations.
control
a list of control values for the estimation algorithm to replace the default values returned by the function glsControl. Defaults to an empty list.
verbose
an optional logical value. If TRUE information on the evolution of the iterative algorithm is printed. Default is FALSE.
B
number of bootstrap resamples to fit and store, default is none
dupCluster
set to TRUE to have glsD when bootstrapping to consider multiply-sampled clusters as if they were one large cluster when fitting using the gls algorithm
pr
set to TRUE to show progress of bootstrap resampling
opmeth
specifies whether the optimize or the optim function is to be used for optimization
x
the result of glsD
digits
number of significant digits to print
...
ignored

VALUE:

an object of classes glsD, Design, and gls representing the linear model fit. Generic functions such as print, plot, and summary have methods to show the results of the fit. See glsObject for the components of the fit. The functions resid , coef, and fitted can be used to extract some of its components. glsD returns the following components not returned by gls: Design, assign, formula , opmeth (see arguments), B (see arguments), bootCoef (matrix of B bootstrapped coefficients), boot.Corr (vector of bootstrapped correlation parameters), Nboot (vector of total sample size used in each bootstrap (may vary if have unbalanced clusters), and var (sample variance-covariance matrix of bootstrapped coefficients).

AUTHOR(S):

Jose Pinheiro mailto:jcp@research.bell-labs.com, Douglas Bates mailto:bates@stat.wisc.edu, Frank Harrell mailto:f.harrell@vanderbilt.edu, Patrick Aboyoun mailto:aboyoun@insightful.com

REFERENCES:

Pinheiro J, Bates D (2000): Mixed effects models in S and S-Plus. New York: Springer-Verlag.

SEE ALSO:

, , , ,

EXAMPLES:

## Not run: 
ns  <- 20  # no. subjects
nt  <- 10  # no. time points/subject
B   <- 10  # no. bootstrap resamples
           # usually do 100 for variances, 1000 for nonparametric CLs
rho <- .5  # AR(1) correlation parameter
V <- matrix(0, nrow=nt, ncol=nt)
V <- rho^abs(row(V)-col(V))   # per-subject correlation/covariance matrix

d <- expand.grid(tim=1:nt, id=1:ns)
d$trt <- factor(ifelse(d$id <= ns/2, 'a', 'b'))
true.beta <- c(Intercept=0,tim=.1,'tim^2'=0,'trt=b'=1)
d$ey  <- true.beta['Intercept'] + true.beta['tim']*d$tim +
  true.beta['tim^2']*(d$tim^2) +  true.beta['trt=b']*(d$trt=='b')
set.seed(13)
library(MASS)   # needed for mvrnorm
d$y <- d$ey + as.vector(t(mvrnorm(n=ns, mu=rep(0,nt), Sigma=V)))

dd <- datadist(d); options(datadist='dd')
# library(nlme)  # S-PLUS: library(nlme3) or later
f <- glsD(y ~ pol(tim,2) + trt, correlation=corCAR1(form= ~tim | id),
          data=d, B=B)
f
f$var      # bootstrap variances
f$varBeta  # original variances
summary(f)
anova(f)
plot(f, tim=NA, trt=NA)
# v <- Variogram(f, form=~tim|id, data=d)
## End(Not run)