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. Rats whose body mass has been measured are fed by 3 different diets over time.
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. difference in growth rate between diets). However, my question is could I also look at the p-values of the main effects to say that body mass increased significantly with time for Diet1 (which is the "dummy variable")?
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 Time*Diet2 0.60 0.155 157 3.871 0.0002 Time*Diet3 0.30 0.156 157 1.893 0.0602
As stated by Pinheiro & Bates, the growth rate of diet 2 (
TimeDiet2) differs significantly from diet 1. Although could I state like this for the effect of time on Diet1: 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. And is it more proper to split the data and run the test (
weight ~Time) for each diet separately, when only looking at the effect of time on body mass?