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

[David Winsemius]

On Jun 6, 2012, at 11:39 AM, Ron Stone wrote:

> 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.

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:

> 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)
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.

-- 
David.
>
> 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
>
> _______________________________________________
> R-sig-mixed-models at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models

David Winsemius, MD
West Hartford, CT