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interpretation of main effect when interaction term being significant (ex. lme)

2 messages · Ron Stone, David Winsemius

Original
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?
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
David Winsemius
#
On Jun 6, 2012, at 11:39 AM, Ron Stone wrote:

            

      
      
      
    

        
I'm copying a comment from one of the replies to which I was halfway  
through a response when I saw this appear. (I'm not an expert in this  
so I'm very prepared to accept critique.)

        
On Jun 6, 2012, at 12:54 PM, arun wrote:

        

            

      
      
      
    

        
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A)
The general rule not to interpret main effects estimates in models  
with interaction terms is certainly valid, but what was asked was  
whether the reported Time estimate could applied to baseline case of  
Diet==1. So, no interaction considerations actually adhere to both the  
estimates and the question at hand.

B)
(I have cracked open my copy of P&B and looked at the graphs and think  
that 0.36 is a sensible result for the slope in Diet group 1. I will  
not that that the df in the table below are not correct. Time should  
have df=157 if it were to agree with P&B (2000) text. )

I see that Ron has now cross-posted to R-SIG-ME, so if you address  
this to that group I will see it.

My check with lmer:

(fm1BW.lmer <- lmer(weight~Time*Diet+(Time|Rat), BodyWeight))
(fm1BW.lmer <- lmer(weight~Time*Diet+(Time|Rat)+(Diet|Rat), BodyWeight))

I'm very open to corrections on the model construction. The Time and  
Diet estimates are the same although the std-errors are different for  
Diet.