[R-sig-ME] interpretation of main effect when interaction term being significant (ex. lme)

[Ron Stone]

Dear all,

I first posted this to the basic R-list, although since the example is
mixed effects model it may be more proper to post it to
r-sig-mixed-models. This question may be too basic quesition for this
list, but if someone has time to answer I will be happy. I have tried
to find out, but haven't found a consice answer.

As an example I use "Pinheiro, J. C. & Bates, D. M. 2000.
Mixed-effects models in S and S-PLUS. Springer, New York." page 225,
where rats are fed by 3 different diets over time, which body mass has
been measured. Response: Body mass, fixed effects Time*Diet, random
effect ~Time|Rat. The main question with this test was if the
interaction term is significant (i.e. growth rate). However, my
question is could I also look at the p-values of the main effects to
say if body mass increase significant with body mass?

>From Pinheiro, J. C. & Bates, D. M. (2000)

Fixed effects: weight ~Time * Diet

                  Value     St.error    DF    t-value   p-value
Intercept    251.60      13.068   157   19.254    <.0001
Time          0.36           0.088      13     4.084    0.0001
Diet2          200.78      22.657     13     8.862   <.0001
Diet3          252.17      22.662    157  11.127   <.0001
TimeDiet2  0.60           0.155     157    3.871      0.0002
TimeDiet3  0.30           0.156     157    1.893      0.0602

As stated by Pinheiro, J. C. & Bates, D. M. (2000), the growth rate of
diet 2 (TimeDiet2) differs significantly from diet 1. Although could I
from this also say that body mass increase significantly with time for
diet 1? Like this: f(x) = 251.60 (+/-13.068) + 0.36 x (+/- 0.088), t =
4.084, p = 0.0001? I have seen that people have claimed that it is
wrong to interpret p-values for the main effects when the interaction
is significant. Is it more proper to split the data and run the test
(weight ~Time) for each diet seperately, when looking at the effect of
time on body mass?

Best regards Ron