R: Autocorrelation Function for gls Residuals

ACF.gls {nlme} | R Documentation

## 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 `NA`s. 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 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.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)

[Package nlme version 3.1-118 Index]