I don't know of any specific procedure(s) for testing sphericity when
there are more variables than subjects but I would suggest using the
RELIABILITY procedure to get descriptive statistics on the two
components of sphericity:
(1) What is the ratio of largest variance to the smallest variance.
If this number is large, it provides evidence that sphericity may
not be present (i.e., heterogeneity of variance). I know that
compound symmetry requires all variances to be the same but
sphericity does not (the correlation and variance/SD are involved).
(2) What is the ratio of the largest correlation to the smallest
correlation. Again if the number is large, or there are negative
correlations, this would be evidence for lack of sphericity.
One could do significance testing between the largest and smallest
variances and/or the correlated correlations to determine whether
they are "significantly" different but that will probably depend upon
the number of subjects/cases you have.
If you can get a sorted covariance matrix graphic, it could also
help in seeing whether there are patterns in covariance patterns
(e.g., banding) but SPSS does not provide this though one could
probably write a macro to do it..
I would think that the presence of any negative
covariance would
imply the absence of sphericity.
If others know of more appropriate tests or procedure, I to would
like to know. There may be better general alternatives but the
appropriateness for any actual dataset will depend upon the
characteristics of that dataset.
-Mike Palij
New York University
----- Original Message -----
Sent: Thursday, October 06, 2016 2:20 PM
Subject: Undefined Mauchly's Test
Given the paucity of information online, I was wondering if anyone knows the procedural approach to the evaluation of sphericity when Mauchly's test is undefined, which is the case
when the number of repeated levels is larger than the number of subjects (insufficient df). I am not sure if sphericity can still be assumed based on the reported values of epsilon larger than 0.75, whether based on Greenhouse-Geisser or Huynh-Feldt. In one
particular dataset, epsilon is less than 0.1. Presumably it can be assumed that sphericity is violated when epsilon is that low.
I am aware of using mixed models to overcome the assumptions of sphericity. My concern is with GLM in this case.
Citations would be welcome.
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