Optimal Sample Size/Power Analysis for Panel Data

Question

I'm running a economic experiment. From a previous pilot I already know which size of treatment-effect I can expect. Each participant plays 20 rounds, so it't a repeated measures approach. I want to know the minimum number of participants i will need to get the same results (same effect size at 5% significance level) as in the pilot.

I already tried to use this formula to determine the sample size, based on $\alpha=0.05$, $\beta=0.20$ and an effect magnitude of $\frac{1}{10}$ of a sd :

$$n_o=2(1,96+0,84)^2(10)^2=1568$$

However this treats each observation as independent, which they are not due to the panel structure. I do multiple regressions, using both fixed-effects and tobit models. Is there an easy way to get the optimal sample size? I'm thinking about simulating the data, but getting the within subject correlation right might be tricky.

Answer 1

Unfortunately, the power of a mixed model analysis reduces as the level of intracluster correlation increases. I asked a relevant question here and was pointed to this useful article regarding what's called design effect: a descriptive statistic relating the ICC (intraclass correlation) to the sample size/design as it pertains to the power of the comparison.

To perform a power or sample size calculation, use the design effect to magnify the standard deviation and calculate what the power would be under an independent analysis. You must take account of this value. If you don't know it, you'll have to speculate over a range of possible values, or collect some preliminary data, or do literature review to find it.