[R-sig-ME] autocorrelation
Douglas Bates
bates at stat.wisc.edu
Mon Mar 31 17:09:44 CEST 2008
On Mon, Mar 31, 2008 at 9:06 AM, Mike Dunbar <mdu at ceh.ac.uk> wrote:
> Am I missing something here? If you need to estimate an autocorrelation parameter at say lag 1, why not make yourself a new column with your response variable lagged by 1 time unit. Then include that as a fixed effect. Clearly there are issues with missing data, but I'm not aware that nlme does anything more than you can do manually. In fact I wonder if this approach is slightly more flexible, as including a random slope for that lagged variable allows it to vary between groups, and I'm not aware that this is allowed using the in-built structures in nlme. Anything more complex, as I'm continually told, there's always Winbugs...
The approach of incorporating a function of the response as a
predictor in a model generally leads you into a quagmire of modeling
the noise term. The approach in nlme is to "pre-whiten" the response
and the model matrices. Given a value of the autocorrelation
parameter, the response is transformed by the inverse of the
corresponding correlation matrix and the model matrices are similarly
transformed. Following that the log-likelihood is evaluated and
optimized with respect to the variance components and the
autocorrelation parameter simultaneously.
> >>> "Douglas Bates" <bates at stat.wisc.edu> 30/03/2008 22:43:32 >>>
>
>
> On Sat, Mar 29, 2008 at 2:52 PM, Alan Cobo-Lewis <alanc at umit.maine.edu> wrote:
> > Doug Bates writes on r-sig-mixed-models at r-project.org on Saturday, March 29, 2008 at 7:00 AM -0500 wrote about his planned book on multilevel modelling in R:
> >
> > >I emphasize graphical displays of the data and aspects
> > >of the fitted models and inferences based on MCMC samples from the
> > >posterior distribution of the model parameters.
> >
> > (n)lme handled correlated error terms, but lme4 does not.
>
> So if you want a model with correlated error terms (in addition to the
> correlation induced by the random effects) then you should use the
> nlme package.
>
> > Leaving aside the superior algorithms in lme4, this appears to be the major impediment to considering lme4 capabilities as a superset of (n)lme capabilities.
>
> I don't recall any statements to the effect that the lme4 capabilities
> would be a superset of the nlme capabilities. It seems that whoever
> made that decision should have informed me of it.
>
> The development of the lme4 package has been generously funded by
> several grants, the most important of which was an STTR contract that
> we had for 3 years. The purpose of that contract was to develop a
> package that could fit generalized linear mixed models using the
> Laplace approximation and allowing for crossed or partially crossed
> grouping factors for the random effects. The development is currently
> funded by another grant specifically to provide for fitting models
> with crossed and partially crossed random effects and with carryover
> of random effects from one time period to another.
>
> Neither generalized linear mixed models nor models with crossed or
> partially crossed random effects can be fit (well without resorting to
> egregious kludges) with the nlme package. Even nonlinear mixed models
> as fit by nlme are sub-optimal compared to the methods in lme4. (lme4
> uses direct optimization of the Laplace approximation to the
> log-likelihood whereas nlme uses an alternating algorithm that Mary
> Lindstrom and I proposed.)
>
> My priorities are to fulfill the tasks that I proposed for these
> grants and to build the best software that I can. The beauty of open
> source software is that if your priorities are different, you have
> full access to the sources and you can modify them to fulfill your
> objectives. So I suggest that you
> - Continue to use the nlme package if you wish to incorporate
> (additional) correlation structures in models
> - Design, code, test and document extensions to the lme4 package to
> do so and then submit these changes as patches
> - Develop your own package so you can have things done the way you
> want them to be done. You already have access to the lme4 sources so
> a lot of the heavy lifting has been done for you.
>
> This developing the software is not as easy as it may seem. There are
> many trade-offs and, at least for me, it takes a lot of effort to
> determine even if it is possible to incorporate various extensions
> harmoniously. It is possible to model the mean and variance of the
> conditional distribution of the response separately when that
> distribution is multivariate normal. It is not as easy to do so when
> that distribution is binomial or Poisson or some other distribution
> for a generalized linear mixed model. Because the first purpose of
> the lme4 package was to allow for generalized linear mixed models I
> did not incorporate (additional) correlation structures and variance
> functions. I'm not even sure it could be done consistently for GLMMs
> but you are welcome to show us how.
>
> > But what do I do if I've got, for example, autocorrelated error terms? Is there a way to "trick" lme4 into handling that (perhaps something analogous to the "random effect variance per treatment group in lmer" thread that David Afshartous and I
> > participated in)? Is there instead a good argument for ignoring it? It seems like something that would arise in practice in a non-negligible amount of problems in real data. Will the upcoming book give some advice on how to address this?
> >
> > I can produce self-contained reproducible code if necessary, but I don't think it is.
> >
> > thanks
> > alan
> >
> > _______________________________________________
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> > https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
> >
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