Sample size calculation for mixed models I am wondering if there are any methods for calculating sample size in mixed models? I'm using lmer in R to fit the models (I have random slopes and intercepts).
 A: The simr package uses simulation to estimate power fairly flexibly in linear and generalised linear mixed models.
A: The longpower package implements the sample size calculations in Liu and Liang (1997) and Diggle et al (2002). The documentation has example code. Here's one, using the lmmpower() function:
> require(longpower)
> require(lme4)
> fm1 <- lmer(Reaction ~ Days + (Days|Subject), sleepstudy) 
> lmmpower(fm1, pct.change = 0.30, t = seq(0,9,1), power = 0.80)

     Power for longitudinal linear model with random slope (Edland, 2009) 

              n = 68.46972
          delta = 3.140186
         sig2.s = 35.07153
         sig2.e = 654.941
      sig.level = 0.05
              t = 0, 1, 2, 3, 4, 5, 6, 7, 8, 9
          power = 0.8
    alternative = two.sided
       delta.CI = 2.231288, 4.049084
           Days = 10.46729
        Days CI = 7.437625, 13.496947
           n.CI = 41.18089, 135.61202

Also check the liu.liang.linear.power() which "performs the sample size calculation for a linear mixed model"
Liu, G., & Liang, K. Y. (1997). Sample size calculations for studies with correlated observations. Biometrics, 53(3), 937-47.
Diggle PJ, Heagerty PJ, Liang K, Zeger SL. Analysis of longitudinal data. Second Edition. Oxford. Statistical Science Serires. 2002
Edit: Another way is to "correct" for the effect of clustering. In an ordinary linear model each observation is independent, but in the presence of clustering observations are not independent which can be thought of as having fewer independent observations - the effective sample size is smaller. This loss of effectiveness is known as the design effect :
$$ DE = 1 +(m-1)\rho$$
where $m$ is the average cluster size and $\rho$ is the intraclass correlation coefficient (variance partition coefficient). So the sample size obtained through a calculation that ignores clustering is inflated by $DE$ to obtain a sample size that allows for clustering.
A: For anything beyond the simple 2 sample tests I prefer to use simulation for sample size or power studies.  With prepackaged routines you can sometimes see large differences between the results from the programs based on the assumptions that they are making (and you may not be able to find out what those assumptions are, let alone if they are reasonble for your study).  With simulation you control all the assumptions.
Here is a link to an example:
https://stat.ethz.ch/pipermail/r-sig-mixed-models/2009q1/001790.html
