Ryan,
What you wrote suggests that using the covariances only
increases the power, and that we always want more power.
In that case, one might conclude that it is always "safe" to ignore
the extra power by using the unstructured alternative, since it
only sacrifices power.
This bothers me, because I doubt that it is true. It reminds me
of the assertion I have heard, that it is always "safe" to use
the grouped t-test instead of a paired test, because "you only lose
power." And for the t-test, *that* is not true. When the correlation
is negative, the error term is larger for the paired -test, and so the
paired t-test is *necessarily* the right one, by virtue of the fact that
it has less power than the grouped test.
I don't know how well the simple t-test generalizes to the structure
in question, but a negative intra-class correlation is not impossible,
when you use the proper definition of ICC. (I have seen a lousy
definition in one popular description of hierarchical analysis, which
defines its so-called ICC by an inadequate analogy. And it can't be
negative, so it is a flawed analogy.) Negative ICCs are not the most
common ones, but I did see a lecturer on HA who unwittingly stated
an example that featured it.
--
Rich Ulrich
Date: Sun, 17 Mar 2013 09:22:19 -0400
From:
[hidden email]Subject: Re: Missing values in MIXED
To:
[hidden email]Dear SPSS-L,
Diana made a bold statement that under all circumstances one should employ a residual unstructured variance-covariance structure. Let me dispel that myth immediately. Run the code BELOW, and note that by employing a likelihood ratio test we observe that the first-order autoregressive structure is fitting the data equally well to the unstructured residual matrix. If the objective in science is to obtain the most parsimonious model that best explains the phenomenon, why would we not apply the same rule when building statistical models?
Second, by using the more parsimonious model (first-order autoregressive residaul structure), for the illustration below, take note that one obtains a statistically more powerful test of the fixed effect of time. In fact, by employing an unstructured residual matrix the fixed effect of time is not significant at alpha=.05, whereas the fixed effect for time is significant at alpha=.05 for the first-order autoregressive matrix.
This is one of many examples I could have simulated where using the general recommendation that Diana made to only use an unstructured matrix will result in not only poor science, but differential conclusions.
Ryan
--
... snip, lengthy example.