# ACF.lme

##### Autocorrelation Function for lme Residuals

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.

- Keywords
- models

##### Usage

```
# S3 method for 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`

.

##### 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

##### Examples

```
# NOT RUN {
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)
# }
```

*Documentation reproduced from package nlme, version 3.1-145, License: GPL (>= 2) | file LICENCE*