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

[Viechtbauer Wolfgang (STAT)]

Maybe I am totally off here, but wouldn't it help if you make what is currently Dose = 0 equal to Dose = -8 and then have what is currently Dose = 8 be equal to Dose = 0? This should help to decrease the correlation between the intercepts and the slopes.

Best,

--
Wolfgang Viechtbauer                        http://www.wvbauer.com/
Department of Methodology and Statistics    Tel: +31 (43) 388-2277
School for Public Health and Primary Care   Office Location:
Maastricht University, P.O. Box 616         Room B2.01 (second floor)
6200 MD Maastricht, The Netherlands         Debyeplein 1 (Randwyck)


----Original Message----
From: r-sig-mixed-models-bounces at r-project.org
[mailto:r-sig-mixed-models-bounces at r-project.org] On Behalf Of Kevin E.
Thorpe Sent: Friday, April 09, 2010 13:04 To:
r-sig-mixed-models at r-project.org Subject: [R-sig-ME] Another case of
-1.0 correlation of random effects

> Hello.
>
> I know this has come up a couple times recently, but I'm still not
> sure
> what to do about it in my data.  Note that my sessionInfo() will be at
> the bottom.
>
> 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 ...
>
>  > xtabs(~Treatment+Dose,data=gluc)
>           Dose
> Treatment  0  2  4  8
>     Barley 12 12 12 12
>     Oat    12 12 12 12
>
> I plot the data (attached as gluc.pdf, if it comes through).
>
>  From the plot, I think I want to fit the model as:
>
> lmer(iAUC~Treatment+Dose+(Treatment|Subject)+(Dose|Subject),data=gluc)
>
> It could possibly be argued that the (Treatment|Subject) part is not
> needed.  When I fit this, I got -1.0 correlation within the Dose
> random
> effects.  To simplify, I will fit a simpler model, since the issue
> persists.
>
>  > lmer(iAUC~Dose+(Dose|Subject),data=gluc,subset=Treatment=="Oat")
> Linear mixed model fit by REML
> Formula: iAUC ~ Dose + (Dose | Subject)
>     Data: gluc
>   Subset: Treatment == "Oat"
>     AIC   BIC logLik deviance REMLdev
>   562.6 573.9 -275.3    563.1   550.6
> Random effects:
>   Groups   Name        Variance Std.Dev. Corr
>   Subject  (Intercept) 8274.324 90.9633
>            Dose          16.214  4.0266  -1.000
>   Residual             4862.319 69.7303
> Number of obs: 48, groups: Subject, 12
>
> Fixed effects:
>              Estimate Std. Error t value
> (Intercept)  309.352     30.539  10.130
> Dose         -14.424      3.596  -4.012
>
> Correlation of Fixed Effects:
>       (Intr)
> Dose -0.647
>
> Now, a plot created by (and attached as lmlist.pdf):
>
> plot(confint(lmList(iAUC~Dose|Subject,data=gluc,subset=Treatment=="Oat"),pooled=TRUE),order=1)
>
> shows (I think) a strong negative correlation between the intercept
> and
> slope random effects for Dose.
>
> So, I would appreciate some advice on how I might specify these random
> effects correctly.
>
> One last thing I tried.  If I treat Dose as a factor (which might be
> reasonable) rather than numeric, I don't get any -1.0 correlations.
>
>  > lmer(iAUC~dose+(dose|Subject),data=gluc,subset=Treatment=="Oat")
> Linear mixed model fit by REML
> Formula: iAUC ~ dose + (dose | Subject)
>     Data: gluc
>   Subset: Treatment == "Oat"
>     AIC   BIC logLik deviance REMLdev
>   545.2 573.3 -257.6      547   515.2
> Random effects:
>   Groups   Name        Variance Std.Dev. Corr
>   Subject  (Intercept)  7509.9   86.660
>            dose2       11993.0  109.513  -0.321
>            dose4        6399.5   79.997   0.043  0.873
>            dose8        6051.7   77.793  -0.743  0.433  0.306
>   Residual              1206.4   34.733
> Number of obs: 48, groups: Subject, 12
>
> Fixed effects:
>              Estimate Std. Error t value
> (Intercept)  293.567     26.951  10.893
> dose2          6.692     34.648   0.193
> dose4        -39.975     27.099  -1.475
> dose8       -105.517     26.558  -3.973
>
> Correlation of Fixed Effects:
>        (Intr) dose2  dose4
> dose2 -0.380
> dose4 -0.103  0.786
> dose8 -0.724  0.443  0.360
>
> Thanks in advance and here is my sessionInfo().
>
>  > sessionInfo()
> R version 2.10.1 Patched (2009-12-29 r50852)
> i686-pc-linux-gnu
>
> locale:
>   [1] LC_CTYPE=en_US       LC_NUMERIC=C         LC_TIME=en_US
>   [4] LC_COLLATE=C         LC_MONETARY=C        LC_MESSAGES=en_US
>   [7] LC_PAPER=en_US       LC_NAME=C            LC_ADDRESS=C
> [10] LC_TELEPHONE=C       LC_MEASUREMENT=en_US LC_IDENTIFICATION=C
>
> attached base packages:
> [1] stats     graphics  grDevices utils     datasets  methods   base
>
> other attached packages:
> [1] lme4_0.999375-32   Matrix_0.999375-33 lattice_0.17-26
>
> loaded via a namespace (and not attached):
> [1] grid_2.10.1
>
>
> --
> 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