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

[Dan Wright]

There are also examples on
http://www.ats.ucla.edu/stat/r/examples/alda/ch7.htm (and examples from
their other chapters may also be useful ... Singer and Willet's book is
highly recommended). We go through a similar example using gls in
https://www.researchgate.net/publication/23134911_Multilevel_modeling_Beyond_the_basic_applications

On Wed, Sep 16, 2015 at 8:46 AM, Kevin Wright <kw.stat at gmail.com> wrote:

> This might help:
>
> http://stats.stackexchange.com/questions/6469/simple-linear-model-with-autocorrelated-errors-in-r
>
> Adapting that to your example:
>
> ### autocor with random effects
> set.seed(12345)
> b <- 0.3  # effect of predictor x
> x <- sample(1:20, 1000, TRUE)  # predictor x (time)
> ID <- rep(1:100, each = 10)  # person IDs
> r <- rnorm(100, sd = 1)  # random Intercepts with sd = 1
> e <- arima.sim(model=list(ar=0.5), n=1000, sd=2) # .5 = autocor
> plot(e)
> y <- b*x + r[ID] + e
>
> data <- data.frame(y = y, x = x, ID = ID, time = rep(1:10, 100))
> head(data)
>
> library(lattice)
> xyplot(y~x|ID, data)
>
> ### fit with AR1 effect
> library(nlme)
> fit_lmeA <- lme(y ~ x, data = data, random = ~ 1 | ID, cor = corAR1(form =
> ~1|ID))
> summary(fit_lmeA)
>
> The model recovers phi and b nicely:
>
> Correlation Structure: AR(1)
>  Formula: ~1 | ID
>  Parameter estimate(s):
>       Phi
> 0.5522512
> Fixed effects: y ~ x
>                  Value  Std.Error  DF   t-value p-value
> (Intercept) -0.1189931 0.18745596 899 -0.634779  0.5257
> x            0.3076964 0.01017406 899 30.243235  0.0000
>
>
> Kevin Wright
>
>
> On Wed, Sep 16, 2015 at 3:19 AM, Paul Buerkner <paul.buerkner at gmail.com>
> wrote:
> > 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[1] <- b*x[1] + r[ID[1]] + e[1]
> > 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))
> > head(data)
> > 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]]
> >
> > _______________________________________________
> > R-sig-mixed-models at r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>
>
>
> --
> Kevin Wright
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

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