Statistics I : Type I SS and Type III SS

[Khokhaz]

Hi , 

What is exactly the definition of Type I SS and Type III SS and how they differ ? How they are related to the total model SS ? 

How to interpret the results as attached for example ? 

Thanks , 

[PaigeMiller]

Please read this documentation

https://documentation.sas.com/?docsetId=statug&docsetTarget=statug_introglmest_sect009.htm&docsetVer...

Usually, the Type III are appropriate for most (but not all) models, but since we don't really know your data, it's impossible to say definitively which one you should use without more of an explanation of the data and the model.

[mkeintz · Accepted solution]

Type I SS is a sort of "sequential" SS.    I.e. for the model
    Y = X1 X2

• The Type I SS for X1   is the same as the total SS for the model Y=X1
• But the type I SS for X2  is the total SS for Y=X1 X2 minus the total SS for Y=X1, i.e. the partial SS for X2, given X1

Consider the case if the variables X1 and X2 were almost perfectly correlated (e.g. X2 is almost always equals k*X1).  Then the Type I SS for X2 in the above would be almost zero, because it would add almost no improvement to X1 in estimating Y.   And if the original model were Y=X2 X1, then it would be X1 with type I SS almost zero.

The type III SS for any variable is the equivalent of its type I SS IF THAT VARIABLE WERE THE LAST ONE ENTERED INTO THE MODEL.  I.e. it is the partial SS for a predictor after controlling for all the other predictors.

This mean that if X1 and X2 were perfectly uncorrelated, then their type I SS values would equal their type III SS values, regardless of their order in the model.