[R] Repeated measures unbalanced in a split-split design

[Marcelo Laia]

Hi,

I have a experiment with block, plots, sub-plots, and sub-sub-plots
with repeated measures and 3 factors (factorial design) when we have
been observed diameter (mm), high (cm) and leaves number (count).
However, we don't have one treatment in one factor, so, my design is
unbalanced.

On a previous message here, a friend tell me that "It appears to me
that your design is a split-split plot with repeated measures at the
split-split plot level. Because you have multiple sizes of
experimental unit (blocks, plots and sub-plots), you have a different
random error term at each size of unit, so you have to analyze it as a
mixed-effects model. For the diameter and height measurements, you can
probably get away with using normal errors, but for the counts, you
may well have to use a generalized linear mixed model."

So, I am trying to analyze my data with car package.

I have:
time (days after germination) -> 4 levels (38, 53, 73, 85)
Hormone -> 2 levels (SH, CH) on sub-plots
Block -> 4 blocks
Treatment -> 6 levels (1, 2, 3, 4, 5, and 6) on sub-sub-plots
Plant -> subjects

I measured Diameter (mm), Height (cm), HD (height/diameter), and
Number of Leaves (count) at each time point. But, plant can be died
and I got NAs.

However, Treatment 6 (control) is only present on SH sub-plots. It
isn't present on CH sub-plots.

I try this model:

idata.Cana <- data.frame(Time=factor(c(38,53,73,85)))
idata.Cana

mod.Cana <- lm(cbind(Diameter.38, Diameter.53, Diameter.73, Diameter.85)
                ~  Treatment*Hormone, data=marcelo.subset)
mod.Cana

Call:
lm(formula = cbind(Diameter.38, Diameter.53, Diameter.73, Diameter.85)
~     Treatment * Hormone, data = marcelo.subset)

Coefficients:
                      Diameter.38  Diameter.53  Diameter.73  Diameter.85
(Intercept)            1.24000      1.35750      1.99375      2.31000
Treatment2            -0.31625     -0.14250      0.07500     -0.13875
Treatment3            -0.19250     -0.01500     -0.20875     -0.36875
Treatment4            -0.35375     -0.08500     -0.22750     -0.27125
Treatment5            -0.29125      0.04875     -0.14375     -0.26375
Treatment6            -0.00125     -0.25750     -0.81125     -0.77750
HormoneSH             -0.30875     -0.08875      0.31500      0.07000
Treatment2:HormoneSH   0.19875      0.11250     -0.44500     -0.24875
Treatment3:HormoneSH   0.15375      0.01875     -0.12125      0.07000
Treatment4:HormoneSH   0.28000     -0.04250     -0.41750     -0.38750
Treatment5:HormoneSH   0.40875     -0.11125     -0.17750     -0.05125
Treatment6:HormoneSH        NA           NA           NA           NA

av.Cana <- Anova(mod.Cana, idata=idata.Cana, idesign= ~ as.factor(Idade))
Erro em solve.default(crossprod(model.matrix(mod))) :
  rotina Lapack dgesv: sistema é exatamente singular

How I model my data to analyze it with this unbalanced design?

How I could use the block factor on model? Or it is not necessary? And
sub-plots?

Please, here you could find my design
http://www.divshare.com/download/9431636-e0c

and here you could find a subset of my data
http://www.divshare.com/download/9456640-fd7

Thank you very much!

-- 
Marcelo Luiz de Laia
Universidade do Estado de Santa Catarina
UDESC - www.cav.udesc.br
Lages - SC - Brazil
Linux user number 487797