# [R] Random Effects Model with Interacting Covariates

Dov Stekel d.j.stekel at bham.ac.uk
Mon Jul 31 20:09:01 CEST 2006

```Ooh,

> lme(Measurement~Treatment/When etc)
>

and

lm(Measurement ~ Treat/When + Patient)

give exactly the same results! How interesting!

Dov

> which seems unsatisfactory for independence
> reasons. (I'm not really a statistician - just the most stats-savvy
> person in my department!)
>
> Thanks,
>
> Dov
>
>
> On 31 Jul 2006, at 18:38, Douglas Bates wrote:
>
>> On 7/31/06, Dov Stekel <d.j.stekel at bham.ac.uk> wrote:
>>> Hi
>>>
>>> I have been asked by a colleague to perform a statistical analysis
>>> which uses random effects - but I am struggling to get this to work
>>> with nlme in R. Help would be very much appreciated!
>>>
>>> Essentially, the data consists of:
>>>
>>> 10 patients. Each patient has been given three different treatments
>>> (on
>>> three separate days). 15 measurements (continuous variable) have been
>>> taken from each patient both before and after each of the treatments.
>>> So the data looks like:
>>>
>>> Patient When    Treat   Measurement
>>> a               before  A               10.3
>>> a               before  A               11.2
>>> ...
>>> a               after           A               12.4
>>> ...
>>> a               before  B               11.6
>>> ...
>>> a               after           B               ...
>>>
>>> and the same for treatment C, patients, b,c,d, etc.
>>>
>>> My colleague would like to test to see if the treatments are
>>> different
>>> from each other. i.e., is the change (before to after) due to the
>>> treatments different between the treatments. It would seem to me like
>>> a
>>> random effects model in which we are interested in the significance
>>> of
>>> the interaction terms Treat:When, with repeated measures in the
>>> patients (who are random effects, but crossed with the covariates).
>>> Unfortunately, the groupedData formula only lets me put a single
>>> covariate on the LHS - nothing as complicated as this!
>>
>> I'm not sure I understand what the LHS of a formula for a groupedData
>> object has to do with your question.
>>
>> You will need to specify the model that you wish to fit by lme and,
>> for that, you will need to decide which terms should be fixed effects
>> and which random effects.  Do you think that the patients contribute
>> only an additive shift in the response or do you think that the
>> patients may have different initial values and different levels of
>> change in the Before/After responses?
>>
>> It seems that you could begin by fitting
>>
>> fm1 <- lme(Measurement ~ When*Treat, random = ~ 1 | Patient, data =
>> ...)
>>
>> and
>>
>> fm2 <- lme(Measurement ~ When*Treat, random = ~ 1|Patient/When, data =
>> ...)
>>
>> There are many other variations that you could consider but we can
>> only guess at because we don't know enough of the context of the data.
>> For example, it is possible that it would be appropriate to eliminate
>> a main effect for Treat because the Treatment cannot be expected to
>> influence the measurement before the Treatment is applied.  The
>> fixed-effects term would then be specified as
>>
>> fm3 <- lme(Measurement ~ When + When:Treat, random = ...)
>>
>>>
>>> I could, of course, advise her to simply combine all 30 data points
>>> for
>>> each treatment in each patient into a single number (representing
>>> difference between before and after), but is there a way to use all
>>> the
>>> data in an LME?
>>>
>>> Thanks!
>>>
>>>
>>> Dov
>>>
>>>
>>>
>>> **************************************************************
>>>
>>> Dr Dov Stekel
>>> Lecturer in Bioinformatics
>>> School of Biosciences
>>> University of Birmingham
>>> Birmingham B15 2TT
>>> Tel: +44 121 414 4209
>>> Email: d.j.stekel at bham.ac.uk
>>>
>>> ______________________________________________
>>> R-help at stat.math.ethz.ch mailing list
>>> https://stat.ethz.ch/mailman/listinfo/r-help
>>> http://www.R-project.org/posting-guide.html
>>> and provide commented, minimal, self-contained, reproducible code.
>>>
>>>
>
> **************************************************************
>
> Dr Dov Stekel
> Lecturer in Bioinformatics
> School of Biosciences
> University of Birmingham
> Birmingham B15 2TT
> Tel: +44 121 414 4209
> Email: d.j.stekel at bham.ac.uk
>
> ______________________________________________
> R-help at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
>

**************************************************************

Dr Dov Stekel
Lecturer in Bioinformatics
School of Biosciences
University of Birmingham
Birmingham B15 2TT
Tel: +44 121 414 4209
Email: d.j.stekel at bham.ac.uk

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