ACF.gls {nlme}

Autocorrelation Function for gls Residuals

Description

This method function calculates the empirical autocorrelation function for the residuals from a gls fit. If a grouping variable is specified in form, the autocorrelation values are calculated using pairs of residuals within the same group; otherwise all possible residual pairs are used. The autocorrelation function is useful for investigating serial correlation models for equally spaced data.

Usage

## S3 method for class 'gls'
ACF(object, maxLag, resType, form, na.action, ...)

Arguments

object

an object inheriting from class "gls", representing a generalized least squares fitted model.

maxLag

an optional integer giving the maximum lag for which the autocorrelation should be calculated. Defaults to maximum lag in the 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".

form

an optional one sided formula of the form ~ t, or ~ t | g, specifying a time covariate t and, optionally, a grouping factor g. The time covariate must be integer valued. When a grouping factor is present in form, the autocorrelations are calculated using residual pairs within the same group. Defaults to ~ 1, which corresponds to using the order of the observations in the data as a covariate, and no groups.

na.action

a function that indicates what should happen when the data contain NAs. The default action (na.fail) causes ACF.gls to print an error message and terminate if there are any incomplete observations.

...

some methods for this generic require additional arguments.

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)

José Pinheiro and Douglas Bates [e-mail]

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.lme, plot.ACF

Examples

fm1 <- gls(follicles ~ sin(2*pi*Time) + cos(2*pi*Time), Ovary)
ACF(fm1, form = ~ 1 | Mare)

# Pinheiro and Bates, p. 255-257
fm1Dial.gls <- gls(rate ~
  (pressure+I(pressure^2)+I(pressure^3)+I(pressure^4))*QB,
                   Dialyzer)

fm2Dial.gls <- update(fm1Dial.gls,
                 weights = varPower(form = ~ pressure))

ACF(fm2Dial.gls, form = ~ 1 | Subject)