> glucose.mod1 <- aov(glucose ~ conc + day + conc:day + day/run + conc:day/run)
> summary(glucose.mod1)
             Df Sum Sq Mean Sq    F value    Pr(>F)    
conc          2 108264   54132 37693.3290 < 2.2e-16 ***
day           2     25      12     8.6613  0.002317 ** 
conc:day      4    176      44    30.7073 8.057e-08 ***
day:run       3    263      88    61.0689 1.240e-09 ***
conc:day:run  6    180      30    20.9153 3.330e-07 ***
Residuals    18     26       1                         
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
> 
> glucose.mod2 <- aov(glucose ~ conc + day + conc:day + day/run + Error(conc:day/run))
Warning message:
In aov(glucose ~ conc + day + conc:day + day/run + Error(conc:day/run)) :
  Error() model is singular
> summary(glucose.mod2)

Error: conc:day
         Df Sum Sq Mean Sq
conc      2 108264   54132
day       2     25      12
conc:day  4    176      44

Error: conc:day:run
          Df Sum Sq Mean Sq F value Pr(>F)
day:run    3 263.11  87.702  2.9198 0.1223
Residuals  6 180.22  30.037               

Error: Within
          Df Sum Sq Mean Sq F value Pr(>F)
Residuals 18  25.85  1.4361               
> 
> library(nlme)
> 
> glucose.mod3 <- lme(fixed=glucose~conc,random=~1|conc/day/run)
> summary(glucose.mod3)
Linear mixed-effects model fit by REML
 Data: NULL 
       AIC      BIC    logLik
  178.0282 188.5038 -82.01411

Random effects:
 Formula: ~1 | conc
        (Intercept)
StdDev:   0.9224093

 Formula: ~1 | day %in% conc
         (Intercept)
StdDev: 0.0004076642

 Formula: ~1 | run %in% day %in% conc
        (Intercept) Residual
StdDev:    4.557253 1.198379

Fixed effects: glucose ~ conc 
                Value Std.Error DF  t-value p-value
(Intercept)  42.15000  2.105218 18 20.02168       0
conc2        94.40833  2.977227  0 31.71015     NaN
conc3       129.95833  2.977227  0 43.65080     NaN
 Correlation: 
      (Intr) conc2 
conc2 -0.707       
conc3 -0.707  0.500

Standardized Within-Group Residuals:
        Min          Q1         Med          Q3         Max 
-1.95735317 -0.36408898 -0.01036915  0.42462622  1.71427468 

Number of Observations: 36
Number of Groups: 
                  conc          day %in% conc run %in% day %in% conc 
                     3                      9                     18 
Warning message:
In pt(q, df, lower.tail, log.p) : NaNs produced
> anova(glucose.mod3)
            numDF denDF  F-value p-value
(Intercept)     1    18 9256.466  <.0001
conc            2     0 1017.835     NaN
Warning message:
In pf(q, df1, df2, lower.tail, log.p) : NaNs produced
> 
> library(lme4)
Loading required package: Matrix
Loading required package: lattice

Attaching package: 'Matrix'

The following object(s) are masked from 'package:base':

    det


Attaching package: 'lme4'

The following object(s) are masked from 'package:nlme':

    BIC, lmList, VarCorr

The following object(s) are masked from 'package:stats':

    AIC

Warning message:
package 'lme4' was built under R version 2.12.1 
> 
> glucose.mod4 <- lmer(glucose~conc+(1|conc:day)+(1|run:day)+(1|day/conc:run))
> summary(glucose.mod4)
Linear mixed model fit by REML 
Formula: glucose ~ conc + (1 | conc:day) + (1 | run:day) + (1 | day/conc:run) 
   AIC   BIC logLik deviance REMLdev
 179.6 192.3 -81.81    172.8   163.6
Random effects:
 Groups       Name        Variance   Std.Dev.  
 conc:run:day (Intercept) 1.7113e+01 4.1368e+00
 conc:day     (Intercept) 7.2637e-08 2.6951e-04
 run:day      (Intercept) 3.6557e+00 1.9120e+00
 day          (Intercept) 9.6312e-14 3.1034e-07
 Residual                 1.4361e+00 1.1984e+00
Number of obs: 36, groups: conc:run:day, 18; conc:day, 9; run:day, 6; day, 3

Fixed effects:
            Estimate Std. Error t value
(Intercept)   42.150      1.892   22.27
conc2         94.408      2.438   38.72
conc3        129.958      2.438   53.31

Correlation of Fixed Effects:
      (Intr) conc2 
conc2 -0.644       
conc3 -0.644  0.500
> anova(glucose.mod4)
Analysis of Variance Table
     Df Sum Sq Mean Sq F value
conc  2 4359.8  2179.9  1517.9