SS, Unbalanced 3X3 crossover Design [General Sta­tis­tics]

posted by ElMaestro  – Denmark, 2013-06-06 13:13 (4764 d 03:09 ago) – Posting: # 10738
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Hello im.sagark,

❝ I have 3 periods, 3 treatments and 6 sequences, and 9 subjects. So I don't have exactly 2 subjects in each sequence.

❝ Getting wrong calculations for Sum of squares for sequence,period and treatments.

❝ Can you please provide me the correct formula for the sum of squares??


1. Since you know you that whatever you previously tried gives you the wrong calculation I think you must have access to some sofwtare that gives you the right calculation so why not just use that?
2. It is sometimes a nightmare to derive general non-matrix formulae. Really, truly, honestly, I would rather swim to the South Pole than do it.
Assuming you use a normal linear model and not a mixed model where no SS discussion is particularly relevant, in matrix notation you have logPK=y=Xb+e. So if you construct your design matrices X appropriately then you can analytically estimate the maximum likelihood b (max likelihood is here a minimisation of eTe) using for example
b=(XtX)-1Xty
or some numerically appropriate and stable alternative. That is what the software does also.
From such solutions you can always derive for example type I and type III SS estimates.

Pass or fail!
ElMaestro

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