# [R-sig-ME] Question about autocorrelation in nlme

Thierry Onkelinx thierry.onkelinx at inbo.be
Wed Sep 16 11:08:30 CEST 2015

```Dear Paul,

The correlation functions in nlme work on the residuals, not on the response.

Best regards,
ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature
and Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

To call in the statistician after the experiment is done may be no
more than asking him to perform a post-mortem examination: he may be
able to say what the experiment died of. ~ Sir Ronald Aylmer Fisher
The plural of anecdote is not data. ~ Roger Brinner
The combination of some data and an aching desire for an answer does
not ensure that a reasonable answer can be extracted from a given body
of data. ~ John Tukey

2015-09-16 10:19 GMT+02:00 Paul Buerkner <paul.buerkner op gmail.com>:
> Dear list,
>
> I have a question concerning autocorrelation models as estimated by nlme.
>
> When I try to recover an autocorrelative (AR1) effect from simulated data,
> I do not get the expected results, that is nlme gives different estimations
> than I would expect based on the parameters used to simulate the data
> (reproducible example below).
>
> ### autocor with random effects
> set.seed(12345)
> phi <- 0.5  # autocorrelation
> b <- 0.3  # effect of predictor x
> x <- sample(1:20, 1000, TRUE)  # predictor x
> ID <- rep(1:100, each = 10)  # person IDs
> r <- rnorm(100, sd = 1)  # random Intercepts with sd = 1
> e <- rnorm(1000, sd = 2)  # residuals with sd = 2
> y <- rep(0,1000)  # initialize y
> y <- b*x + r[ID] + e
> for (i in 2:1000) {
>   if (ID[i] == ID[i-1])
>     y[i] <- phi * y[i-1] + b*x[i] + r[ID[i]] + e[i]  # not the first
> observation for this ID
>   else y[i] <- b*x[i] + r[ID[i]] + e[i]  # first observation for this ID
> }
>
> data <- data.frame(y = y, x = x, ID = ID, time = rep(1:10, 100))
> p <- ggplot(data, aes(x=time, y=y, group=ID))
> p + geom_line()
>
> ### fit with AR1 effect
> library(nlme)
> fit_lmeA <- lme(y ~ x, data = data, random = ~ 1 | ID, cor = corAR1(form =
> ~1|ID))
> summary(fit_lmeA)
>
>
> Accordingly, the model I think of as AR1 does not seem to be the one nlme
> fits to the data. Does someone know what type of model nlme actually
> assumes in this situation?
>
> Thanks for your help!
>
> Best
>  Paul
>
>         [[alternative HTML version deleted]]
>
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```