Another case of -1.0 correlation of random effects

Shouldn't your preferred model be coded:

(lmer1 <- lmer(iAUC~Treatment+Dose+(Treatment+Dose|Subject),data=gluc))


Linear mixed model fit by REML
Formula: iAUC ~ Treatment + Dose + (Treatment + Dose | Subject)
   Data: gluc
  AIC  BIC logLik deviance REMLdev
 1107 1132 -543.3     1106    1087
Random effects:
 Groups   Name         Variance Std.Dev. Corr         
 Subject  (Intercept)  8402.295 91.6640               
          TreatmentOat 1736.103 41.6666  -0.097       
          Dose           30.774  5.5474  -0.883 -0.335
 Residual              4100.082 64.0319               
Number of obs: 96, groups: Subject, 12

Fixed effects:
             Estimate Std. Error t value
(Intercept)   313.198     29.076  10.772
TreatmentOat   -6.673     17.763  -0.376
Dose          -13.617      2.729  -4.990

Correlation of Fixed Effects:
            (Intr) TrtmnO
TreatmentOt -0.225      
Dose        -0.687 -0.133


Which kind of works but you still have a very high correlation between 2 
random effects.


Your problems stem, i think, from the fact that there's a very high 
correlation between the slope of Dose and the Intercept, i.e. subjects 
with initially higher iAUC respond more strongly to increasing doses of 
the treatment. You can help the estimation by re-coding Dose so that the 
intercept is estimated for the highest dose rather than the smallest.


(lmer1 <- 
lmer(iAUC~Treatment+I(Dose-8)+(Treatment+I(Dose-8)|Subject),data=gluc))

Linear mixed model fit by REML
Formula: iAUC ~ Treatment + I(Dose - 8) + (Treatment + I(Dose - 8) | 
Subject)
   Data: gluc
  AIC  BIC logLik deviance REMLdev
 1107 1132 -543.3     1106    1087
Random effects:
 Groups   Name         Variance Std.Dev. Corr         
 Subject  (Intercept)  3189.270 56.4736               
          TreatmentOat 1736.099 41.6665  -0.421       
          I(Dose - 8)    30.773  5.5474  -0.647 -0.335
 Residual              4100.085 64.0319               
Number of obs: 96, groups: Subject, 12

Fixed effects:
             Estimate Std. Error t value
(Intercept)   204.264     21.214   9.629
TreatmentOat   -6.673     17.763  -0.376
I(Dose - 8)   -13.617      2.729  -4.990

Correlation of Fixed Effects:
            (Intr) TrtmnO
TreatmentOt -0.446      
I(Dose - 8)  0.088 -0.133
 

Andy.