[R-sig-ME] mixed effects nested repeated measures MANOVA

[Kevin Parsons]

I have what I think is a fairly complex problem that I hope can be
resolved. I've come close but not quite complete using the 'car'
package but now I've turned my attention to lmer. My experiment
involves looking at 6 traits that were measured twice for time, in two
ecomorphs, under two experimental treatments, with four different
families nested within ecomorphs (2 families per ecomorph). There are
363 individuals

I have come up with the following model for use with lmer:
model2 <- lmer(Y3 ~time*ecomorph*diet*family/ecomorph+(1|individual),
data=data1)

I obtain the following:

Linear mixed model fit by REML
Formula: Y3 ~ time * ecomorph * diet * family/ecomorph + (1 | individual)
   Data: data1
   AIC   BIC logLik deviance REMLdev
 -1207 -1124  621.5    -1349   -1243
Random effects:
 Groups   Name        Variance  Std.Dev.
 fish     (Intercept) 0.0012532 0.035401
 Residual             0.0081641 0.090355
Number of obs: 726, groups: individuals, 363

Fixed effects:
                          Estimate Std. Error t value
(Intercept)               -0.67115    0.49360  -1.360
time                       1.06044    0.30750   3.449
ecomorph                   1.18842    0.42141   2.820
diet                       0.63752    0.30018   2.124
family                     0.75811    0.21545   3.519
time:ecomorph             -0.83778    0.26252  -3.191
time:diet                 -0.47492    0.18700  -2.540
ecomorph:diet             -0.60881    0.25211  -2.415
time:family               -0.48472    0.13422  -3.611
ecomorph:family           -0.49755    0.14252  -3.491
diet:family               -0.31653    0.13614  -2.325
time:ecomorph:diet         0.39737    0.15705   2.530
time:ecomorph:family       0.31555    0.08878   3.554
time:diet:family           0.24273    0.08481   2.862
ecomorph:diet:family       0.23655    0.08813   2.684
time:ecomorph:diet:family -0.16362    0.05490  -2.980


While the model runs I'm not feeling comfortable with the results, I
have concerns about the proper F-ratios being used, and as I read more
elsewhere it seems lmer is not taking a wholly multivariate approach?

Someone else has suggested that I calculate coefficients from nested
models that can be found for each response (using either lm, lme,
lmer) . These coefficients can then be concatenated to form a matrix
of coefficients, from which multivariate test statistics can be found.
Could someone please explain how this can be carried out in more
practical terms