[R] Main effects and interactions in mixed linear models

[arun]

Hi Ron,

When the interaction is significant, I will not look at the significance of main effects as the main effect significance are irrelevant.  Then the comparisons could be made between the simple effect means.



A.K.  



----- Original Message -----
From: Ron Stone <ronstone1980 at gmail.com>
To: r-help at r-project.org
Cc: 
Sent: Wednesday, June 6, 2012 11:29 AM
Subject: [R] Main effects and interactions in mixed linear models

Dear all,

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 is if the interaction term is significant (i.e. growth rate).
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. Allthoug 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 different places that it people claiming that when the
interaction is significant then it is wrong to interpret p-values for the
main effects. Is it more proper to split the data and run the test (weight
~Time) for each diet seperately, when looking at the simple effect of time
on body mass?

Best regards Ron

    [[alternative HTML version deleted]]

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