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I wonder if there is a simple way of calculating an achieved power for a mixed-effects model. The fixed effects are the intercept and a slope. The random effect is for the intercept at the two levels ID and User/ID.

Thanks!

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The simplest way is probably estimating the design effect, and then use that to factor the sample size back down to what is usually called "effective sample size." Then you can proceed to use that new number to compute power as if the participants were drawn using simple random sampling.

If you already have the data in hand, you can also record the regression estimates of the fixed effect as well as the variance estimates of the random effects and the residual from your mixed-effect regression model. Afterwards, set up a simulation to recreate the data set and observe the p-values of interest for many times, compile the percent of runs that end up with a rejections of the null hypothesis, and that would be your power.

Some powerful software like PASS 13 should be able to do that but it is pricy. For free software, try MLPowSim, make sure to follow their tutorial in the manual.

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