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

[arun]

HI Dave,

My comment was based  on:
"

>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?"

Here, the result shown were from the summary of the linear model.   We report the p-values of the main effects and intenraction from the anova table:
anova(fm1BW.lmer).  Of course, it is possible to interpret the main effects and interaction from summary table as ANOVA is only a special case of regression.  Time estimates at individual levels of factor Diet (in this case, baseline Diet0) is okay for interpretation.  

A.K.




----- Original Message -----
From: David Winsemius <dwinsemius at comcast.net>
To: Ron Stone <ronstone1980 at gmail.com>; arun <smartpink111 at yahoo.com>
Cc: r-sig-mixed-models at r-project.org
Sent: Wednesday, June 6, 2012 4:44 PM
Subject: Re: [R-sig-ME] interpretation of main effect when interaction term being significant (ex. lme)


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
> 
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David Winsemius, MD
West Hartford, CT