Scheffé adjustments are commonly used for multiple comparisons, and their derivation from the F-distribution is pretty straightforward. I noticed that Stata offers a Scheffé adjustment for post-estimation comparisons that rely on maximum likelihood estimation and reported z-tests. For instance:
mixed Y i.landuse || bid: , residual(exc)
pwcompare landuse, mcompare(scheffe)
The Stata manual for pwcompare explains: "For estimation commands that report 𝑧 statistics instead of 𝑡 statistics for the tests on coefficients, a 𝜒2 distribution is used instead of an 𝐹 distribution." I was looking for a reference for using the 𝜒2 instead of the F distribution, but could not find it.
I would much appreciate it if someone could explain the rationale for generalizing the Scheffé adjustment from F to 𝜒2, the actual procedure (I would like to teach this to my students), and a reference. Thank you!
mixed Y i.landuse || bid: , residual(exc)
pwcompare landuse, mcompare(scheffe)
The Stata manual for pwcompare explains: "For estimation commands that report 𝑧 statistics instead of 𝑡 statistics for the tests on coefficients, a 𝜒2 distribution is used instead of an 𝐹 distribution." I was looking for a reference for using the 𝜒2 instead of the F distribution, but could not find it.
I would much appreciate it if someone could explain the rationale for generalizing the Scheffé adjustment from F to 𝜒2, the actual procedure (I would like to teach this to my students), and a reference. Thank you!
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