Re: Undefined Mauchly's Test

Posted by Mike on
URL: http://spssx-discussion.165.s1.nabble.com/Undefined-Mauchly-s-Test-tp5733212p5733214.html

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

[hidden email]

 

----- Original Message -----

From: [hidden email]

To: [hidden email]

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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