You should be cautious of trying to incorporate both an random effect for
time and an AR1 structure on the residuals in a mixed-effects model.  The
marginal covariance structures on the responses from those two model
components, while not identical, are quite similar and the modeling will
trade one off against the other, likely resulting in poor precision of the
estimators for the parameters in both.


On Wed, Dec 12, 2012 at 8:51 AM, Viechtbauer Wolfgang (STAT) <
wolfgang.viechtbauer@maastrichtuniversity.nl> wrote:

> Dear All,
>
> I am currently working with some mixed-effects models for longitudinal
> data where I want to test hypotheses about the difference in the strength
> of the autocorrelation between two groups. In particular, let's say I have
> data of the form:
>
> person  time  group  y
> ----------------------------
> 1       0     A      <value>
> 1       1     A      <value>
> 1       2     A      <value>
> ...     ...   ...    ...
> 2       0     A      <value>
> 2       1     A      <value>
> 2       2     A      <value>
> ...     ...   ...    ...
>
> and I want to fit the model:
>
> y_ij = beta_0 + beta_1 time_ij + u_0i + u_1i time + e_ij,
>
> where i is the index for person, j is the index for time, u_0i ~ N(0,
> tau^2_0) is a random effect for the intercepts, u_1i ~ N(0, tau^2_1) is a
> random effect for the slopes, cov(u_0i, u_1i) = tau_01 is the covariance
> between these two random effects, and now I want to fit an AR(1) structure
> for the errors e_ij, where the autocorelation is rho_A for people from
> group A and rho_B for people from group B. In principle, I may also want to
> let the error variance to differ for the two groups (i.e., sigma^2_A and
> sigma^2_B).
>
> In nlme, I can fit models with a common autocorrelation structure for the
> two groups, with:
>
> lme(y ~ time, random = ~ time | person, correlation = corAR1(form = ~ time
> | person))
>
> but as far as I can tell, it is not possible to allow the autocorrelation
> parameter to differ between the two groups.
>
> Does anybody know of a package/function that would allow fitting such a
> model?
>
> Moreover, the groups are actually created by dichotomizing a continuous
> measure. Ideally, I would like to fit a model, where rho depends on the
> continuous measure directly. Or, to avoid issues related to rho having to
> fall between -1 and 1, it would probably make more sense to assume that
> f(rho) depends on that continuous measure, where f() is the arctanh
> (inverse hyperbolic function or Fisher's r-to-z) transformation. Again, any
> ideas on packages/functions that may handle such a model?
>
> Thanks in advance for any suggestions!
>
> Best,
> Wolfgang
>
> --
> Wolfgang Viechtbauer, Ph.D., Statistician
> Department of Psychiatry and Psychology
> School for Mental Health and Neuroscience
> Faculty of Health, Medicine, and Life Sciences
> Maastricht University, P.O. Box 616 (VIJV1)
> 6200 MD Maastricht, The Netherlands
> +31 (43) 388-4170 | http://www.wvbauer.com
>
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> R-sig-mixed-models@r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>

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