My reaction is that you should see whether the
time variable, including all of its interactions, adds anything significant to the model.
Interactions are tricky. The interaction coefficient for
Group2:timet2 represents the difference of the estimated value from what you would predict solely from the individual
timet2 coefficients. (Recall that the
timet2 coefficient itself represents the estimated difference between
timet1 only within
Group1.) Your results show that is the only combination of
time whose effect can be distinguished statistically from those 2 sets of individual coefficients.
What makes me hesitate are the relatively small coefficients for either of
timet3 or for the other interaction coefficients, particularly when compared against the much larger coefficients for
Group. I wonder whether a model without the interaction terms or maybe even without a
time predictor at all might fit the data just as well.
Unless you had a pre-specified hypothesis about this particular interaction, I'd recommend comparing the full set of nested models overall: compare this model to one without the interaction, and compare the model without the interaction against one that just includes
group as a predictor. Those are simple
If the overall test of the models with and without interaction show that the interaction model is significantly better than the one without the interaction, then go ahead and report this result. Otherwise, see whether
time matters at all when added to a model that only contains
Group. It might be that your data support no significant (or at least substantial) effect of
time at all.
Added in response to updated information
As the overall interaction term isn't significant but the
time term adds significantly to the
Group-only model (p = 0.012 in
anova(t0)), you should report the model with just the additive
time terms, no interaction.
Show something like the plot you have now added, which seems to summarize the data pretty well. The differences over time are significant, but they are much less than the difference between
Group1 and the other 2
Group3 don't seem to differ from each other.
You can then discuss whether the "statistically significant" effect of
time is large enough to matter in practice, something that is based on your understanding of the subject matter rather than statistics per se.
As a separate note, consider whether it might be better to use a generalized linear model with a log link rather than to analyze the log-transformed data directly with
lmer(). It's essentially a question of whether you wish to model the mean of the predictions on the log scale (as you are) or the log of the mean estimate from the linear predictor (generalized linear model with log link).