[R-sig-ME] Another case of -1.0 correlation of random effects

[Douglas Bates]

On Mon, Apr 12, 2010 at 8:00 AM, Kevin E. Thorpe
<kevin.thorpe at utoronto.ca> wrote:
> Kevin E. Thorpe wrote:
>>
>> Ben Bolker wrote:
>>>
>>> Ken Knoblauch wrote:
>>>>
>>>> Kevin E. Thorpe <kevin.thorpe at ...> writes:
>>>>
>>>>> My data come from a crossover trial and are balanced.
>>>>>
>>>>>  > str(gluc)
>>>>> 'data.frame':    96 obs. of  4 variables:
>>>>>  $ Subject  : int  1 2 3 5 6 7 10 11 12 13 ...
>>>>>  $ Treatment: Factor w/ 2 levels "Barley","Oat": 1 1 1 1 1 1 1 1 1 1
>>>>> ...
>>>>>  $ Dose     : int  8 8 8 8 8 8 8 8 8 8 ...
>>>>>  $ iAUC     : num  110 256 129 207 244 ...
>>>>>
>>>>> clip>
>>>>
>>>> Shouldn't you make Subject into a factor?
>>>>
>>>> Ken
>>>>
>>>
>>>  It would make the plot a little bit prettier but I don't think it
>>> matters in this case because variable that appears as a grouping
>>> variable (i.e. on the right of the | ) is automatically treated as a
>>> factor?  I think?
>>>
>>>  Since it is really a crossover trial, it would seem reasonable in
>>> principle to have the (Treatment|Subject) random effect in there as
>>> well. I'm not sure what to do about the -1 correlation: it seems the
>>> choices (not necessarily in order) are (1) throw up your hands and say
>>> there's not enough data to estimate independently; (2) try WinBUGS,
>>> possibly with slightly informative priors; (3) try using lme4a to create
>>> profiles of the parameters and see if you can figure out what's
>>> happening.
>>
>> Let's see.  I wish (1) was an option.  (2) would be promising if my
>> knowledge of BUGS and Bayesian methods filled more than a thimble. Thanks to
>> Jarrod for his suggestion in response to this.  I'll take a look at that
>> too.  Option (3) is probably worth a go too.
>>
>> Aside from the fact that the Dose variable are the actual doses and not
>> categories, and we all know not to categorize continuous variables, what are
>> your thoughts on treating Dose as a factor (since it seems to behave)?
>>
>> Thanks all for taking the time to provide your suggestions.
>>
>> Kevin
>>
>
> Regarding lme4a: how do I obtain it?  I guess that comes down to, what is
> the repository to give to install.packages()?  Does it require a different
> Matrix package than the one I have, which is, 0.999375-33 and if so, how do
> I not break my current lme4/Matrix combination?

The repository is http://R-forge.R-project.org but be aware that lme4a
is under active development and not guaranteed against breakage.  It
would be inadvisable to rely on functions and classes in that package
to persist.

> By the way, the problems with these data get stranger.  In a different
> outcome from the same trial the following results from a model fitting
> attempt.
>
> lmer(iAUC~Treatment+Dose+(Treatment|Subject)+(Dose|Subject),data=insulin)
> Linear mixed model fit by REML
> Formula: iAUC ~ Treatment + Dose + (Treatment | Subject) + (Dose | Subject)
>   Data: insulin
>  AIC  BIC logLik deviance REMLdev
>  1956 1982   -968     1983    1936
> Random effects:
>  Groups   Name         Variance   Std.Dev.   Corr
>  Subject  (Intercept)  4.2678e-02 2.0659e-01
>          TreatmentOat 1.6115e+07 4.0144e+03 0.000
>  Subject  (Intercept)  3.0430e+08 1.7444e+04
>          Dose         1.5173e+06 1.2318e+03 -1.000

And did you notice that you have an Intercept term by Subject in there
twice?  It is not surprising that the parameter estimates are
unstable.  You will need to rethink the model.

>  Residual              3.1907e+07 5.6486e+03
> Number of obs: 96, groups: Subject, 12
>
> Fixed effects:
>             Estimate Std. Error t value
> (Intercept)   40142.4     5146.7   7.800
> TreatmentOat   1340.3     1634.7   0.820
> Dose          -2675.1      405.5  -6.597
>
> Correlation of Fixed Effects:
>            (Intr) TrtmnO
> TreatmentOt -0.079
> Dose        -0.922  0.000
>
> As you can see, I get a 0 correlation within one set of random effects and
> -1.0 in the other.  Also, the fact the fixed effects estimates are huge
> makes me suspicious.
>
> Note that if I drop the treatment portions and fit the Dose model to only
> one treatment, the correlation is again -1.0 and the fixed effects are
> similar.
>
>
> --
> Kevin E. Thorpe
> Biostatistician/Trialist, Knowledge Translation Program
> Assistant Professor, Dalla Lana School of Public Health
> University of Toronto
> email: kevin.thorpe at utoronto.ca  Tel: 416.864.5776  Fax: 416.864.3016
>
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