## Model Type III Sum of Squares [General Sta­tis­tics]

Hi Obi,

» Now the issue is that I noticed that the Type III Sum of Squares of the Model is not always equal to the sum of the individual Sum of Squares of the various main effects (treatment, period, sequence and subject nested with sequence) for the SAS Outputs I've looked at.

This is true and that is how type III works. It is not because of interactions (these are in your model if you want them or they are out if you don't).
Imagine you have factors A and B and C in your model. You get the type III SS for factor A by looking at the residual SS in a model with A, B and C and comparing it with a model with only B and C. The difference between the two residual SS's is your type III SS for A.
And so forth.

Now, in a design where "subject is nested in sequence" you will see that, technically, the two possible sequence columns (of which some are redundant and removed in the full-rank matrix) are equal to all subject columns. So if you have a model with subject, period and treatment, the type III SS for sequence is in principle nil. But then the software may -as a courtesy extended to good and faithful users- take out subject when trying to figure out the type III SS for sequence, so to get the type III for sequence, you compare the residual from a model with only period and treatment, to the residual from a model with everything.
And so forth. It follows a strict set of logical rules.

Try and look at type I SS and specify subject before sequence, and sequence before subject and see what happens . Play around. Type I SS's will add up (the relative drawback is that the SS's for each factor can depend on which factors specified before others), but type III SS's won't necessarily add up.

I could be wrong, but...

Best regards,
ElMaestro

R's base package has 274 reserved words and operators, along with 1761 functions. I can use 18 of them (about 14 of them properly). I believe this makes me the Donald Trump of programming.

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