[R-sig-ME] help with repeated measures on a split-plot experiment

Mike Dunbar mdu at ceh.ac.uk
Mon Jun 9 10:48:30 CEST 2008

Hi Jamess

Just a couple of comments below



>>> "James Hudson" <jmghudson at gmail.com> 09/06/2008 03:29 >>>
>Dear Mike,

>Thank you very much for the timely, helpful response. My apologies for the
>delay in responding - I have been in the field.

On 5/28/08, Mike Dunbar <mdu at ceh.ac.uk> wrote:
> Dear James
> Some quick initial comments.
> A. You are probably trying to make a much too complex model. I think what
> you want is:
> lmer(response ~ snow*warm*year (1|plot), cass))
> As plot is the only random effect, all the others are fixed.

>I appreciate the simplicity of the model you have suggested. After reviewing
>both Pinheiro & Bates and West, I was initially taking a more rigid approach
>to developing my model following the examples in the texts.

B. Are you sure there is likely to be a measurable autoregressive structure
> to the time series data beyond that which is accounted for by the plot
> random effect. Just looking at the data listing, there are only three years
> (1995, 2000, 2007), or is this a sub-sample? With only three years, and
> these not being sequential years, you may be asking too much of your data.

> This is not a sub-sample - I only have 3 years of data. I assumed that if I
>were to include a repeated measures factor in my model, that I'd need to
>supply a covariance structure.

I don't know if its helpful to consider repeated measures as a special case of a mixed model. The bottom line is if you fit the model with plot as a random effect, can you then see any autocorrelation in the residuals when you plot them? Even if there is truly autocorrelation in the underlying process, you probably can't see it in your data, you'd need to see runs of points through time which were over or under-estimated. Remember that the correlation between times ascribed to them being measured on the same plot is accounted for by the plot random effect: e.g. see the orthodont example in P&B.

C. I might be missing something but are you really interested in year as a
> fixed effect? With this included, are there any degrees of freedom left for
> the residual error, you'll need to get your replication from somewhere. Be
> warned that lmer does seem to give results even when all dfs are used up by
> fixed effects and their interactions (I'm not sure why), but you need to be
> able to judge that you have not fitted a sensible model.

> I am interested in change over time so I need "time" as a fixed factor. I
>can run the model you have suggested as a lme function too but my dfs seem
> ok for this analysis.

If you can make do with time as a linear function then I think that's OK. I've still got a a feeling that if you have time as a factor then you run out of dfs. If you can post a self-contained example with model and data then others can probably comment if this is the case (I received some great help from the list on this topic about a year ago.

> cheers
> Mike

> Using this model in an lme function, I have been unable to identify Type
>III SS rather than Type I. Is there a straightforward way to obtain Type III

In short: have a look at http://www.stats.ox.ac.uk/pub/MASS3/Exegeses.pdf 
Then you might want to look through the main R mailing list where the desirability of Type III sums of squares for aov has been discussed. Others can comment much better on this and why its not such a good idea. It can be done for aov if you really have to, but I don't know for lme: don't forget lme models are not fitted by straightforward least squares.

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