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I am interested in studying the difference between two therapies ('TH') using data obtained from a computational model. Three subjects are modelled and each subject receives both therapies for each level of two factors ('A' with 3 levels and 'B' with 5 levels). The dependent variable ('DV') is the response to the therapy. Unfortunately I cannot model more than three subjects, but I can easily replicate each measurement. So far 30 replicated measurements per condition are available. Here is a glimpse of my data frame:

$ subject <fct> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,...
$ A       <fct> 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 1,...
$ B       <fct> 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5, 5, 5, 1,...
$ TH      <fct> 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,...
$ DV      <dbl> 0.016009750, 0.008925725, 0.005316029, 0.015981987, 0.009186412, 0.004799236, 0.016079657, 0.009259483, 0.005482147, 0.016834199, 0.01158...

From reading various sources, it seems that my analysis question is typically answered using a repeated-measure ANOVA or a linear mixed effect model. However I am facing a couple of issues.

  1. My number of subjects (three) seems to be too low for a mixed effect model as discussed here (five or six subjects appears to be a minimum). Is three subjects also too low for a repeated measure ANOVA? If so, what is the best alternative for my design? To make sure that the dependency of within-subject measures is taken into account, would it be appropriate to simply perform a three-way ANOVA for each subject?
  2. The next issue concerns how my replicated measurements should be dealt with. From reading this, this, this, and this, I understand that I should average these replicated measurements for repeated measures ANOVA. But am I not loosing some information by doing that? Can mixed models avoid this issue?
ongoingActivity
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    Re. point 1, you can use [GPower](https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html) or other (non free) software to determine the sample size required for RM ANOVA with this kind of 3 within-subject design. You'll need to provide an expected effect size as well as the correlation among repeated measures. Statistical power is usually low with a sample size as small as yours. – chl Oct 26 '20 at 12:12
  • Thank you for the suggestion! – ongoingActivity Oct 26 '20 at 17:30
  • Re. point 2, I have since learnt that mixed models do avoid the issue by making use of all of the data. – ongoingActivity Oct 29 '20 at 12:14
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    Yes, and you can take into account different structure of autocorrelation or other forms of within-unit correlation between the observations. The compound symmetry of ANOVA with rempeated measures is also reflected in the variance-covariance matrix of a mixed-effect model. If you're interested in this, I can write a more detailed reply. – chl Oct 29 '20 at 19:00
  • I have asked [in a new question](https://stats.stackexchange.com/questions/494269/which-random-effects-should-be-included-in-my-mixed-effect-model-repeated-measu) how to deal with the dependency of observations in mixed-effect models for this particular design. It would be great if you could shed some light on the issue in the new question! – ongoingActivity Oct 29 '20 at 23:49

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