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

[Bilonick, Richard A]

On Tue, 2010-06-29 at 09:09 +0000, Ilona Leyer 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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When there is an interaction effect, the main effects are difficult to
interpret. Your model is not a simple additive one when there is an
interaction. You can't predict the level of one factor without knowing
the level of the other factor. Given there is an interaction between
these factors, you could reparameterize it as a one-way analysis (i.e.,
just create 12 separate treatment groups). When there is an interaction,
you can't get a simple interpretation with just two factors.