New answers tagged lme
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If there is interaction in the model, the interpretations for main effects would change. For example, in your model, if there is no interaction between Time and Diet, Diet2 means the difference between Diet2 and Diet1 regardless the value of Time; however, if you add the interaction Time*Diet, Diet2 means the difference between Diet2 and Diet1 when Time ...
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@GaelLaurans makes a good point that you are thinking of this as a repeated-measures analysis, but you are actually fitting a regular ANOVA. Thus, this isn't the problem of how to correctly determine the denominator's degrees of freedom (which is what I had linked to in my comment above).
I think the issue here is simpler. You have four data points, ...
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If you include the intercept/constant term in the model (which is included implicitly by default), then what you are essentially doing here is trying to fit 4 group means with 5 parameters: 4 contrasts plus the intercept. Obviously this isn't going to work, because there are more "unknowns" (parameters) than there are "equations" (group means).
To get the ...
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