corCAR1                 package:nlme                 R Documentation

Continuous AR(1) Correlation Structure

Description:

     This function is a constructor for the '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 'Initialize'
     method.

Usage:

     corCAR1(value, form, fixed)

Arguments:

   value: the correlation between two observations one unit of time
          apart. Must be between 0 and 1. Defaults to 0.2.

    form: a one sided formula of the form '~ t', or '~ t | g',
          specifying a time covariate 't' and,  optionally, a grouping
          factor 'g'. Covariates for this correlation structure need
          not be integer valued.  When a grouping factor is present in
          '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 '~ 1', which corresponds to using
          the order of the observations in the data as a covariate, and
          no groups.

   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 'FALSE', in which case
          the coefficients are allowed to vary.

Value:

     an object of class 'corCAR1', representing an autocorrelation
     structure of order 1, with a continuous time covariate.

Author(s):

     Jose Pinheiro Jose.Pinheiro@pharma.novartis.com and Douglas Bates
     bates@stat.wisc.edu

References:

     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.

See Also:

     'corClasses',  'Initialize.corStruct', 'summary.corStruct'

Examples:

     ## 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))

