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Paired t-test evaluates mean change. Mixed models evaluate change in means. How the two can be compatible? For balanced data it works - paired t-test = random intercept model = GLS with compound symmetry. But the power in mixed models is they allow for missing data, say, one subject has 5 measurements, and the other - only 2. So the mean change won't be the same as change in means. So how the two methods can be advised for analysing repeated data?

Paired t-test gives mean change. Regression (also mixed) gives change in means. These usually aren't equal to each other. So the outcomes of these methods won't agree too. So either is wrong for the analysis. Which one?

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Mixed models can be used to test for both between- and within-subjects effects. Both are treated in the same manner as columns of the design matrix for the fixed effects. In the former case, the value of the covariate will be the same for all the measurements of a particular subject (e.g., sex), and in the latter case the covariate will have different values along the repeated measurements (e.g., the time variable indicating when the outcome measurement was recorded).

Mixed models will also indeed account for missing data in your outcome variable that are of the missing at random type.

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  • $\begingroup$ Thank you. I know it can be used, I was rather interested in the outcomes. Paired t-test gives us mean difference. Regression give us change in difference. It's equal in balanced case. But when there are missing data, it is not. Paired t-test requires pairs of data, both at time t0 and t1 must occur. In mixed model t0 may have different length than t1, as it doesn't calculate mean difference, but rather difference in means with appropriate SEs. So, which one is better for analysing repeated observations? $\endgroup$ – Giovanni Mar 10 '20 at 3:52
  • $\begingroup$ @Giovanni the regression model gives you both depending on how you define the design matrix. $\endgroup$ – Dimitris Rizopoulos Mar 10 '20 at 7:42

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