Is there a general convention on what variance to expect for a random intercept in a multilevel model? I need to provide an estimate for the power analysis. It is a within-subjects design. Thanks!
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2 Answers
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There are no absolute guidelines, but for instance Arend & Schäfer (2019) suggest, based on their literature review yielding average ICC of .30 that ICC = .30 could be considered a medium-sized ICC. (They also suggest that .05 could be considered a small ICC.)
Thus, if you use 1 for your level 1 residual variance in your power calculations (which is customary because it makes things easier), random intercept variance of ~ 0.43 will get you an ICC of .30.
Reference:
Arend, M. G., & Schäfer, T. (2019). Statistical power in two-level models: A tutorial based on Monte Carlo simulation. Psychological methods, 24(1), 1-19. https://psycnet.apa.org/doi/10.1037/met0000195
Edited because I left it out (thank you Erik Ruzek for pointing this out), the literature review mentioned reviewed psychological studies between 2010-2016 from several different fields of psychology. As Erik says, you should review multilevel studies from your own field to find a suitable number. Then, you can apply the above explained approach to this number.
To edit in some more clarification, random intercept variance is not a standardized parameter, its magnitude is scale-dependent, so you couldn't have e.g. a generally "medium-sized random intercept". ICC is a standardized parameter so you can use it and the fact that ICC is random intercept variance divided by total level 1 variance to get to an appropriate random intercept value.
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To add onto Sointu's excellent response, you should be looking at longitudinal studies on the construct (or related constructs) of interest in your project. This will give you a sense of the size of ICCs found in previous research and will be a better guide than a generic number that comes from looking at studies outside your area. A simple Google search can be immensely helpful. E.g., "icc of construct_name" or "icc of scale_you_will_use".
