\HeaderA{corCAR1}{Continuous AR(1) Correlation Structure}{corCAR1}
\keyword{models}{corCAR1}
\begin{Description}\relax
This function is a constructor for the \code{corCAR1} class,
representing an autocorrelation structure of order 1, with a
continuous time covariate. Objects created using this constructor must
be later initialized using the appropriate \code{Initialize}
method.
\end{Description}
\begin{Usage}
\begin{verbatim}
corCAR1(value, form, fixed)
\end{verbatim}
\end{Usage}
\begin{Arguments}
\begin{ldescription}
\item[\code{value}] the correlation between two observations one unit of time
apart. Must be between 0 and 1. Defaults to 0.2.
\item[\code{form}] a one sided formula of the form \code{\textasciitilde{} t}, or \code{\textasciitilde{} t |
     g}, specifying a time covariate \code{t} and,  optionally, a
grouping factor \code{g}. Covariates for this correlation structure
need not be integer valued.  When a grouping factor is present in
\code{form}, the correlation structure is assumed to apply only
to observations within the same grouping level; observations with
different grouping levels are assumed to be uncorrelated. Defaults to
\code{\textasciitilde{} 1}, which corresponds to using the order of the observations
in the data as a covariate, and no groups.
\item[\code{fixed}] an optional logical value indicating whether the
coefficients should be allowed to vary in the optimization, or kept
fixed at their initial value. Defaults to \code{FALSE}, in which case
the coefficients are allowed to vary.
\end{ldescription}
\end{Arguments}
\begin{Value}
an object of class \code{corCAR1}, representing an autocorrelation
structure of order 1, with a continuous time covariate.
\end{Value}
\begin{Author}\relax
Jose Pinheiro \email{Jose.Pinheiro@pharma.novartis.com} and Douglas Bates \email{bates@stat.wisc.edu}
\end{Author}
\begin{References}\relax
Box, G.E.P., Jenkins, G.M., and Reinsel G.C. (1994) "Time Series
Analysis: Forecasting and Control", 3rd Edition, Holden-Day.

Jones, R.H. (1993) "Longitudinal Data with Serial Correlation: A
State-space Approach", Chapman and Hall.

Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models
in S and S-PLUS", Springer, esp. pp. 236, 243.
\end{References}
\begin{SeeAlso}\relax
\code{\LinkA{corClasses}{corClasses}}, 
\code{\LinkA{Initialize.corStruct}{Initialize.corStruct}},
\code{\LinkA{summary.corStruct}{summary.corStruct}}
\end{SeeAlso}
\begin{Examples}
\begin{ExampleCode}
## covariate is Time and grouping factor is Mare
cs1 <- corCAR1(0.2, form = ~ Time | Mare)

# Pinheiro and Bates, pp. 240, 243
fm1Ovar.lme <- lme(follicles ~
           sin(2*pi*Time) + cos(2*pi*Time),
   data = Ovary, random = pdDiag(~sin(2*pi*Time)))
fm4Ovar.lme <- update(fm1Ovar.lme,
          correlation = corCAR1(form = ~Time))

\end{ExampleCode}
\end{Examples}

