Assume I test a number of patients repeatedly over time to see how a certain treatment changes their skin conductance in response to a certain colour (cond) after 2 months, 4 months, ... etc. I test the skin conductance on the palm, wrist or arm simultaneously to see whether the place matters.

1. How can I look into the interaction terms? If e.g. place would have been dropped from the model altogether, loking at the folowing post hoc test would take the average over the factor place, right?

    posthoc_test <- glht(model_final, c("condred == 0", "condred + time2:condred == 0", 
                      ..., "condred + time6:condred == 0"))
   

2. How do I report the significant interactions? Is the p-value I get from the model selection precedure (i.e., p=0.003 for time:cond) also the one I can later report for time:cond?

Thank you so much!

Please correct me if I'm wrong and thanks for the effort!

Assume I test a number of patients repeatedly over time to see how a certain treatment changes their skin conductance in response to a certain colour (cond) after 2 months, 4 months, ... etc. I test the skin conductance on the palm, wrist or arm simultaneously to see whether the place matters.

• How can I look into the interaction terms? If e.g. place would have been dropped from the model altogether, looking at the following post hoc test would take the average over the factor place, right?

    posthoc_test <- glht(model_final, c("condred == 0", "condred + time2:condred == 0", 
                      ..., "condred + time6:condred == 0"))
  

• How do I report the significant interactions? Is the p-value I get from the model selection procedure (i.e., p=0.003 for time:cond) also the one I can later report for time:cond?

Please correct me if I'm wrong!

I also retest, whether after removing the non-significant interaction time:place, the other two-way interactions are still significant and they are.

So I end up with the final model being model_4 of the form: sc ~ time + cond + place + time:cond + cond:place + (1|ID), data)

1. How do I report the significant interactions? I know from the model comparison, that e.g. time:cond makes a significant contribution to explain the data, but how do I report it? I found that I get the correct F-values and degrees of freedom for an lmer-model by applying anova(model_final) (see here for example). But what is their p-value? Is the p-value I get from the model comparison (i.e., p=0.003 for time:cond) also the one I can report for time:cond?

2. Because the interaction time:cond is significant, I obviously cannot look at the main effects of time and cond. But I would still like to know at which time point the two conditions (cond) differ significantly.

    posthoc_1 <- glht(model_final, c("condred == 0", "condred + time2:condred == 0", 
                      ..., "condred + time6:condred == 0"))
   

That way, I only get the interaction placeA because this is my reference level for place, right? In this case, it would be placeA. Can I make this post-hoc comparison only for each level of place at a time?

What if I want to see how time and cond interact, regardless of place? glth(..., interaction_average=TRUE) seems to only work for two factors, whereas my model involves three. And interaction_average=TRUE is basically equivalent to treating one of the two factors as a main effect, or did I get that wrong?

In the end I end up with the final model being  sc ~ time + cond + place + time:cond + cond:place + (1|ID), data)

1. How can I look into the interaction terms? If e.g. place would have been dropped from the model altogether, loking at the folowing post hoc test would take the average over the factor place, right?

    posthoc_test <- glht(model_final, c("condred == 0", "condred + time2:condred == 0", 
                      ..., "condred + time6:condred == 0"))
   

Because, however, the factor place is still in the model, the above post hoc test is applied only to the baseline level of place, i.e. placeA

What if I want to see how time and cond interact, regardless of place? Is this even possible given that place is itself "captured" in the interaction cond:place?

2. How do I report the significant interactions? Is the p-value I get from the model selection precedure (i.e., p=0.003 for time:cond) also the one I can later report for time:cond?

Thank you so much!

P.S.
By now I'm almost convinced that the answer to question 2 is, that the values I get from the model comparison are the ones I can report for time:cond in general. In short: it doesn't matter that I got the values from a model comparison instead of getting them from a preformulated ANOVA.

Please correct me if I'm wrong and thanks for the effort!