ACF.lme {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)

[Package nlme version 3.1-86 Index]