Dear everyone

I want to test if the correction for first order autocorrelation corAR1() improves significantly my model fit but don't know how to do this.

Accoring to Pinheiro & Bates (2000) p. 242 this should be done using the standard anova function to perform a Likelihood Ration Test. However I was told that from a theoretical point of view this would render inexact results because the chi-square-distribution-assumption is violated. Still I could not get an input on how to consider this in R.

Therefore I wanted to ask if anyone could lend me a hand on which alternatives could be used instead of the anova-LRT? It would be very appreciated.

dataset and if prefered r-script for the two models with and without corAR1() can be retrieved here

```
##reduced model-specific data-set:
datafclr <-read.csv("datafclr.csv", header = TRUE, sep = ",", dec = ".", fill = TRUE)
##without correction for autocorrelation:
tim1 <- lme(fixed=EERTmn ~ male + female +
(male:time7c) + (female:time7c) +
(male:IERT_Cp) + (female:IERT_Cp) +
(male:IERT_Cp_Partner) + (female:IERT_Cp_Partner)-1,
control=list(maxIter=100000), data=datafclr,
random=~male + female -1|dyade, na.action=na.omit)
summary(tim1)
#with correction for autocorrelation of first order:
tim2 <- lme(fixed=EERTmn ~ male + female +
(male:time7c) + (female:time7c) +
(male:IERT_Cp) + (female:IERT_Cp) +
(male:IERT_Cp_Partner) + (female:IERT_Cp_Partner)-1,
control=list(maxIter=100000), data=datafclr,
random=~male + female -1|dyade, correlation=corAR1(), na.action=na.omit)
summary(tim2)
```

Many thanks in advance!

Best, Patrick