I have an experiment with two fixed factors (repeated 2 x 2 design)
- Between-factor: Treatment Group vs. Control Group (TREAT)
- Repeated-factor: Pre-Treatment vs. Post-Treatment (TIME)
The dependent variable in the Scenario is depressiveness (questionnaire score 0-45). We are interested in the interaction, in such that only patients in the Treatment Group should improve, resulting in less Depression at Post-Treatment.
Now I add one additional factor resulting in a slightly different / extended scenario. Usually every patient fills out one questionnaire before Treatment (Pre-) and after Treatment (Post-). In this new Scenario, however, we assess Depression 5 times at Pre- as well as 5 times at Post- Measurement. We do this in order to increase measurment precission / reduce error within each subject. (This method is called ecological momentary assessment (EMA), usually assessed automatically by the mobile phone).
Here is my question: How can I use this new Information optimally? Are both strategies (A and B) applicable?
A) Different slopes for each Patient? Here, we would calculate the average of the 5 Pre-Measurements as well as the average of the 5 Post-Measurements. This reduces the error within each subject. Next we can specify a model which accounts for the interaction plus one random effect for different slopes for each participant:
lmer(Depression ~ TREAT*TIME + (TIME|Patient), dataset)
B) Nesting the 5 Pre- and the 5 Post-Measurements within the repeated factor (TIME)? Instead of taking the average of 5 measurements (as in Option A), we would like to construct 5 different slopes within each Patient (connect Pre1 with Post1, Pre2 with Post2, Pre3 with Post3 and so on). Is this possible by Lmer? Do we violate something, if we do this? How would the command look like?
lmer(Depression ~ TREAT*TIME + (5 Measurements[?] | TIME [?]), dataset)
"Bonus" question: Is it even possible to combine both perspectives? Maybe in a scheme close to this?
lmer(Depression ~ TREAT*TIME + (TIME|Patient) + (5 Measurements[?]|TIME [?]), dataset)
I'm now posting here, as I changed computers and stack doesnt recognize me any more. Yes thats true, we increased power as expectable by definition. And thats a good point, that more sophisticated models come at the price of complexity. However, can you think of any other method except averaging the 5M's that could lead to increases in power?
@ your comment from below: I think thats the problem. There is no predictive value it seems (horizontal line in the drawing) but only a reduction of the error term.