2
$\begingroup$

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?
Improve this question
$\endgroup$
5
  • 1
    $\begingroup$ Re. point 1, you can use GPower 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. $\endgroup$
    – chl
    Oct 26, 2020 at 12:12
  • $\begingroup$ Thank you for the suggestion! $\endgroup$
    – ongoingActivity
    Oct 26, 2020 at 17:30
  • $\begingroup$ Re. point 2, I have since learnt that mixed models do avoid the issue by making use of all of the data. $\endgroup$
    – ongoingActivity
    Oct 29, 2020 at 12:14
  • 1
    $\begingroup$ 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. $\endgroup$
    – chl
    Oct 29, 2020 at 19:00
  • $\begingroup$ I have asked in a new question 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! $\endgroup$
    – ongoingActivity
    Oct 29, 2020 at 23:49

0

Reset to default

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge that you have read and understand our privacy policy and code of conduct.

Browse other questions tagged or ask your own question.