Regarding the fact that Stata does not provide Mauchly's (1940!) test
of sphericity, I came across a web page and a book note which suggest
one way out, if you really want a test of the homogeneity of
differences variances in Stata.
This page describes how to modify a factorial anova and pass it to
"oneway" to gain a test of homogeneity of variances using Bartlett's
test.
Maxwell and Delaney (2004, Note 5, p C-21) say the mixed-model ANOVA
produces the same results as would a between subjects ANOVA if the mean
of each subject on the dependent variable is subtracted from each
subject's score (shown by McNemar (1969)). This suggests that the test
in "oneway" could be used in a similar manner for simple repeated
measures ANOVAs.
This does not address multisample sphericity, but you could do one
factor at time.
