Another paper (Calculating power in analysis of variance. (apa.org)) found on the book Statistical Power Analysis for the Behavioral Sciences | Jacob Cohen | (taylorfrancis.com) also discusses the topic of power calculation in mixed effect models. Of closer revelance to your question is another paper cited in this book: Optimum Sample Size and Number of Levels in a One-Way Random-Effects Analysis of Variance: The Journal of Experimental Education: Vol 41, No 4 (tandfonline.com). A table of optimum sample size or number of levels for the random effects model is included in the latter paper. I hope these information helps.
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