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

[Kevin E. Thorpe]

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?

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
  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