SAS Type I/III ↔ WinNonlin partial/sequential tests [Software]

posted by Helmut Homepage – Vienna, Austria, 2012-08-28 16:39 (4632 d 20:56 ago) – Posting: # 9118
Views: 8,342

Dear Risherd!

It is not helpful if you give numerical results without stating the data set you used (+ the version of WinNonlin). SAS’ Type III is not given by WinNonlin – only sequential and partial tests. Sequential = SAS Type I, but (quoting WinNonlin’s User’s Guide):

The partial tests in LinMix are not equivalent to the Type III method in SAS though they coincide in most situations.
The Partial Tests worksheet is created by testing each model term given every other model term. Unlike sequential tests, partial tests are invariant under the order in which model terms are listed in the Fixed Effects tab. Partial tests factor out of each model term the contribution attribut­able to the remaining model terms.
This is computed by modifying the basis created by the QR factorization to yield a basis that more closely resembles that found in balanced data.
For fixed effects models, certain properties can be stated for the two types of ANOVA. For the sequential ANOVA, the sums of squares are statistically independent. Also, the sum of the indi­­vi­­dual sums of squares is equal to the model sum of squares; which means the ANOVA represents a partitioning of the model sum of squares. However, some terms in ANOVA may be conta­mi­nat­ed with undesired effects. The partial ANOVA is designed to eliminate the conta­mi­nation problem, but the sums of squares are correlated and do not add up to the model sums of squares. The mixed effects tests have similar properties.

(my emphasis)

Or Phoenix User’s Guide:

Sequential Tests worksheet
   The Sequential Tests worksheet is created by testing each model term sequentially. The first model term is tested to determine whether or not it should enter the model. Then the second model term is tested to determine whether or not it should enter the model, given that the first term is in the model. Then the third model term is tested to determine whether or not it should enter the model, given that the first two terms are in the model. The model term tests continue until all model terms are exhausted.
The tests are computed using a QR factorization of the XY matrix. The QR factorization is seg­ment­ed to match the number of columns that each model term contributes to the X matrix.
Partial Tests worksheet
   The Partial Tests worksheet is created by testing each model term given every other model term. Unlike sequential tests, partial tests are invariant under the order in which model terms are listed in the Fixed Effects tab. Partial tests factor out of each model term the contribution attri­but­able to the remaining model terms.
This is computed by modifying the basis created by the QR factorization to yield a basis that more closely resembles that found in balanced data.
ANOVA
   For fixed effects models, certain properties can be stated for the two types of ANOVA. For the sequential ANOVA, the sums of squares are statistically independent. Also, the sum of the indi­vi­dual sums of squares is equal to the model sum of squares; which means the ANOVA repre­sents a partitioning of the model sum of squares. However, some terms in ANOVA may be contam­inat­ed with undesired effects. The partial ANOVA is designed to eliminate the contami­na­tion problem, but the sums of squares are correlated and do not add up to the model sums of squares. The mixed effects tests have similar properties.


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