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Suppose you have data that is grouped in one way or another and therefore the assumption of independence is suspect. But you look at the intraclass correlation (or autocorrelation) and it is very close to 0 - indicating independence (or, at least, no strong dependence).

In this situation, is there any harm in using a multilevel model anyway (instead of OLS regression)? (e.g. does it lose power?)

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    $\begingroup$ A low sample autocorrelation or intraclass correlation would indicate that those population correlations were small, rather than indicating independence and there are potential costs either way. (The question itself is a great question however) $\endgroup$ – Glen_b Mar 21 at 2:36
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    $\begingroup$ Yes. (Sorry, having computer issues for a few days; I missed the reply) $\endgroup$ – Glen_b Mar 23 at 23:52
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    $\begingroup$ Would a more specific example be like doing a mixed effects regression (and giving up degrees of freedom for including the computation of the correlation structure for the errors, even when it is absent) instead of a fixed effects regression? $\endgroup$ – Martijn Weterings Mar 25 at 9:00
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    $\begingroup$ @PeterFlom but isn't it a bit trivial that power is lost when one is adding useless parameters to determine a (non-existing) more complex (correlated) structure of the errors? Or are you looking for some less simple answers? For instance ideas about the point when the independence is low enough that one can consider adding multiple levels becomes useless? Or the degree in which the power is lost? $\endgroup$ – Martijn Weterings Mar 25 at 16:26
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    $\begingroup$ I'm really casting a general question here. E.g. yes, it's pretty clear that power is lost by adding useless terms, but the term is almost never completely useless. $\endgroup$ – Peter Flom Mar 25 at 17:48

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