ACF.lme                 package:nlme                 R Documentation

Autocorrelation Function for lme Residuals

Description:

     This method function calculates the empirical autocorrelation
     function for the within-group residuals from an 'lme' fit. The
     autocorrelation values are calculated using pairs of residuals
     within the innermost group level. The autocorrelation function is 
     useful for investigating serial correlation models for equally
     spaced data.

Usage:

     ## S3 method for class 'lme':
     ACF(object, maxLag, resType, ...)

Arguments:

  object: an object inheriting from class 'lme', representing a fitted
          linear mixed-effects model.

  maxLag: an optional integer giving the maximum lag for which the
          autocorrelation should be calculated. Defaults to maximum lag
          in the within-group residuals.

 resType: an optional character string specifying the type of residuals
          to be used. If '"response"', the "raw" residuals (observed -
          fitted) are used; else, if '"pearson"', the standardized
          residuals (raw residuals divided by the corresponding
          standard errors) are used; else, if '"normalized"', the
          normalized residuals (standardized residuals pre-multiplied
          by the inverse square-root factor of the estimated error
          correlation matrix) are used. Partial matching of arguments
          is used, so only the first character needs to be provided.
          Defaults to '"pearson"'.

     ...: some methods for this generic require additional arguments -
          not used.

Value:

     a data frame with columns 'lag' and 'ACF' representing,
     respectively, the lag between residuals within a pair and the
     corresponding empirical autocorrelation. The returned value
     inherits from class 'ACF'.

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. 

     Pinheiro, J.C., and Bates, D.M. (2000) "Mixed-Effects Models in S
     and S-PLUS", Springer.

See Also:

     'ACF.gls', 'plot.ACF'

Examples:

     fm1 <- lme(follicles ~ sin(2*pi*Time) + cos(2*pi*Time),
                Ovary, random = ~ sin(2*pi*Time) | Mare)
     ACF(fm1, maxLag = 11)

     # Pinheiro and Bates, p240-241
     fm1Over.lme <- lme(follicles  ~ sin(2*pi*Time) +
                cos(2*pi*Time), data=Ovary,
          random=pdDiag(~sin(2*pi*Time)) )
     (ACF.fm1Over <- ACF(fm1Over.lme, maxLag=10))
     plot(ACF.fm1Over, alpha=0.01) 

