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.

# 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.

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.

Author

José Pinheiro and Douglas Bates bates@stat.wisc.edu

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)
#>    lag          ACF
#> 1    0  1.000000000
#> 2    1  0.380191824
#> 3    2  0.180089173
#> 4    3  0.036688753
#> 5    4  0.059951162
#> 6    5  0.001916046
#> 7    6  0.063499044
#> 8    7  0.070979841
#> 9    8  0.049660461
#> 10   9  0.029428152
#> 11  10 -0.032162165
#> 12  11 -0.074003608

# 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)) )
#> Error in solve.default(do.call("cbind", Xcols), apply(shifted, 2, fun,     ...)): Lapack routine dgesv: system is exactly singular: U[9,9] = 0
(ACF.fm1Over <- ACF(fm1Over.lme, maxLag=10))
#> Error: object 'fm1Over.lme' not found
plot(ACF.fm1Over, alpha=0.01) 
#> Error: object 'ACF.fm1Over' not found