# Re: [R] mixed-effects model with two fixed effects: interaction

From: Thomas Stewart <tgstewart_at_gmail.com>
Date: Tue, 29 Jun 2010 09:23:37 -0400

IIona-

I think you may be misinterpreting the t-test.

In model 1, consider the speciesH coefficient. A test that speciesH = 0, essentially asks: Is speciesH the same as speciesB? The test statistic for this hypothesis is the t-value reported in the table. (t-value= -4.2, p-value=0.0001)

In model 2, the corresponding coefficient, t-value, and p-value do not correspond to the same hypothesis test from model 1.

If your goal is to test the overall species effect, then the test you want is:

```model0<-lme(sprouts~moisture,random=~time|ID,method="ML")
model1<-lme(sprouts~species+moisture,random=~time|ID,method="ML")
model2<-lme(sprouts~species*moisture,random=~time|ID,method="ML")

```

anova(model0,model2) #TEST OF SPECIES EFFECT IN MODEL WITH INTERACTION anova(model0,model1) #TEST OF SPECIES EFFECT IN MODEL WITHOUT INTERACTION

And as an added bonus, (which should probably be done before the test of Species Effect)

anova(model1,model2) #TEST OF INTERACTION. That is, do I really need the more complex model?

Hope that helps.
-tgs

On Tue, Jun 29, 2010 at 5:09 AM, Ilona Leyer <ileyer_at_yahoo.de> wrote:

> Dear all,
> In a greenhouse experiment we tested performance of 4 different species
> (B,H,P,R) under 3 different water levels in 10 replications. As response
> variable e.g. the number of emerging sprouts were measured on three dates. A
> simple Anova considering every measurement date separately shows a higly
> significant effect of species and moisture (and partly the interaction of
> both). The mixed-effects model with species and moisture shows a highly
> significant effect of species and moisture as well. However, when I included
> the interaction the t-values of the species dropped strongly and the SE
> increase and the results for the species are not significant anymore. For me
> this does not seem plausible. Has anybody an idea, how this can be
> interpreted and if I have done a mistake in calculating the data?
>
> Thanks in advance for any help!
> Ilona
>
>
> model1<-lme(sprouts~species+moisture,random=~time|ID)
> model2<-lme(sprouts~species*moisture,random=~time|ID)
>
>
> Fixed effects: sprouts ~ species + moisture
> Value Std.Error DF t-value p-value
> (Intercept) 7.971267 1.330500 240 5.991180 0.0000
> speciesH -6.459344 1.536329 114 -4.204400 0.0001
> speciesP -10.063604 1.536329 114 -6.550421 0.0000
> speciesR -5.051894 1.536329 114 -3.288288 0.0013
> moisturemoist 2.228835 1.330500 114 1.675185 0.0966
> moisturewaterlogged 17.111149 1.330500 114 12.860688 0.0000
>
>
> Fixed effects: sprouts ~ species * moisture
> Value Std.Error DF t-value p-value
> (Intercept) 4.831965 1.750970 240 2.759594 0.0062
> speciesH -4.464197 2.476245 108 -1.802809 0.0742
> speciesP -3.986787 2.476245 108 -1.610013 0.1103
> speciesR -0.809376 2.476245 108 -0.326856 0.7444
> moisturemoist 3.505506 2.476245 108 1.415654 0.1598
> moisturewaterlogged 24.766934 2.476245 108 10.001811 0.0000
> speciesH:moisturemoist -0.457291 3.501939 108 -0.130582 0.8963
> speciesP:moisturemoist -2.458125 3.501939 108 -0.701932 0.4842
> speciesR:moisturemoist -2.555356 3.501939 108 -0.729697 0.4672
> speciesH:moisturewaterlogged -5.597498 3.501939 108 -1.598400 0.1129
> speciesP:moisturewaterlogged -15.538272 3.501939 108 -4.437048 0.0000
> speciesR:moisturewaterlogged -10.206874 3.501939 108 -2.914635 0.0043
>
>
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