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rms (version 4.1-3)

Gls: 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. Gls is a slightly enhanced version of the Pinheiro and Bates Gls function in the nlme package to make it easy to use with the rms package 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

Gls(model, data, correlation, weights, subset, method, na.action=na.omit,
    control, verbose, B=0, dupCluster=FALSE, pr=FALSE, x=FALSE)

## S3 method for class 'Gls': print(x, digits=4, coefs=TRUE, latex=FALSE, title, \dots)

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,
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 do
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
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.omit) results in deletion of observations having any of the variables of interest missing.
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 Gls 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
x
for Gls set to TRUE to store the design matrix in the fit object; otherwise the result of Gls
digits
number of significant digits to print
coefs
specify coefs=FALSE to suppress printing the table of model coefficients, standard errors, etc. Specify coefs=n to print only the first n regression coefficients in the model.
latex
a logical value indicating whether information should be formatted as plain text or as LaTeX markup
title
a character string title to be passed to prModFit
...
ignored

Value

  • an object of classes Gls, rms, 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. Gls returns the following components not returned by gls: Design, assign, formula (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). The $g$-index is also stored in the returned object under the name "g".

Details

The na.delete function will not work with Gls due to some nuance in the model.frame.default function. This probably relates to na.delete storing extra information in the "na.action" attribute of the returned data frame.

References

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

See Also

gls glsControl, glsObject, varFunc, corClasses, varClasses, GiniMd, prModFit

Examples

Run this code
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')
f <- Gls(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(Predict(f, tim, trt))
# v <- Variogram(f, form=~tim|id, data=d)
nlme:::summary.gls(f)$tTable   # print matrix of estimates etc.

options(datadist=NULL)

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