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]]
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]] ______________________________________________ R-help at r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
Bert Gunter
2012-Jun-06 17:22 UTC
[R] Main effects and interactions in mixed linear models
Ron: There are some misunderstandings in your message. See inline below. However, this is fundamentally not an R question -- it's about "what to do" not how to do it in R. So I suggest you post on a statistical list like stats.stackexchange.com. But as you have already noted, beware, you are likely to get a range of possibly compet8ing views. I shall add a few of my own in what follows, to which this caution also applies. -- Bert On Wed, Jun 6, 2012 at 8:29 AM, Ron Stone <ronstone1980 at gmail.com> wrote:> 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?Come again? A typo? Do you mean: "Are the main effects of time and diet on body mass significant?" If so, by definition , yes. However, in the presence of imbalance and interactions, your interpetation of this may be wrong.> > >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?This is the R part of your question. You do not understand what contrasts are in linear models and, in particular, R's default choice of contrasts (which actually really aren't contrasts). See ?contrasts and especially ?contr.treatment. The point here is that with 3 diets there are only 2 diet "effects" and their corresponding interactions with time that exist. These can be chosen in any of several different (in theory infinitely many) ways. By default, R chooses Diet 1, time 0 as the "control" (given by the intercept term; note that there can be no "no diet" against which to compare Diet 1) and the Diet 2 and Diet 3 main effects and their corresponding interactions with time represent the differences of these Diets against the Diet 1 control and their differences in growth rate vs Diet 1. So bottom line: Your question is nonsense. 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?I would agree, with the caveat that P values should be ignored. Bottom Line: (keep my caution in mind): 1. Plot your data informatively. lattice or ggplot style trellis plots would be useful here. See also http://addictedtor.free.fr/graphiques/ where you may get some ideas. This is likely to be more useful than formal statistics. 2. Consult a local statistician. Spending an hour or two of time with a local statistician (i.e. anyone with statistical expertise who understands linear models, not necessarily someone with a statistical degree) would be better than any advice that you could obtain here, including, paradoxically, mine. -- Bert> > Best regards Ron > > ? ? ? ?[[alternative HTML version deleted]] > > ______________________________________________ > R-help at r-project.org mailing list > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.-- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm