Another case of -1.0 correlation of random effects
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