[R-sig-ME] Mixed-Effects Models with Group or Covariate-Dependent Autocorrelation

[Viechtbauer Wolfgang (STAT)]

Thank you for the feedback. Indeed, that is a concern. Fortunately, I have highly repeated measurements (40-60 obs per person) and quite a large n, so I think I have enough information to fit such a model.

Best,
Wolfgang

> -----Original Message-----
> From: dmbates at gmail.com [mailto:dmbates at gmail.com] On Behalf Of Douglas
> Bates
> Sent: Wednesday, December 26, 2012 21:18
> To: Viechtbauer Wolfgang (STAT)
> Cc: r-sig-mixed-models at r-project.org
> Subject: Re: [R-sig-ME] Mixed-Effects Models with Group or Covariate-
> Dependent Autocorrelation
> 
> 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 at 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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