[R-sig-ME] lme: several slopes, same variance, no correlation

[Douglas Bates]

I wouldn't recommend using lme to fit models with multiple crossed
random-effects terms.  The example in Pinheiro and Bates (2000) has only a
few levels in one of the two grouping factors, which is necessary for the
method used there to work.

The methods used in lme4 are much more effective for crossed grouping
factors. (And, I might add,  the methods used in the MixedModels package
for Julia are even more effective).  As Thierry has pointed out in this
group many times, starting with a very complex model for your data is
usually not a good approach.

On Fri, Jul 15, 2016 at 4:45 AM Thierry Onkelinx <thierry.onkelinx at inbo.be>
wrote:

> Dear Ben,
>
> Crossed random effects are doable but not easy in nlme. It is described
> somewhere in Pinheiro and Bates (2000).
>
> However, correlation structures in nlme work only on the residuals within
> the same level of the random effects. In case of nested random effects the
> most detailed level is used. The residuals of observations from different
> random effect levels are assumed to be independent! I'm not sure how it
> works with crossed random effects but it won't surprise me if it would use
> the levels of id1:id2:id3:id4. That is something you may, or may not, want.
>
> I'd suggest that you think on how the correlation structure should work
> before you try the crossed random effects in nlme. If the correlation
> structure doesn't make sense, then you don't have to bother the switch from
> lme4 to nlme.
>
> Another option would be to switch to INLA (www.rinla.org) which allows for
> correlated random effects.
>
> 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
>
> 2016-07-15 11:16 GMT+02:00 Ben Pelzer <b.pelzer at maw.ru.nl>:
>
> > Dear list,
> >
> > I am trying to fit a model with 4 crossed (no hierarchy) random effects
> > which all four are considered to be independent draws from one and the
> same
> > normal distribution. So, all four have the same variance and the
> > correlations are zero. In lmer I could specify something like:
> >
> > lmer(y ~ 1+ (x1|id1) + (x2|id2) + (x3|id3) + (id4|id4))
> >
> > but then four different variances would be estimated and also all the
> > covariances.
> >
> > Would it be possible to estimate such a model in lme, where one can have
> > all kinds of correlation structures? Thanks for any help!
> >
> > Ben.
> >
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