Modeling and Multivariate Methods - SAS

68 Fitting Standard Least Squares Models Chapter 3
Estimates
However, you probably do not want to hand calculate the estimate for the last level. The Expanded
Estimates option in the Estimates menu calculates these missing estimates and shows them in a text
report. You can verify that the mean (or sum) of the estimates across a classification is zero.
Keep in mind that the Expanded Estimates option with high-degree interactions of two-level factors
produces a lengthy report. For example, a five-way interaction of two-level factors produces only one
parameter but has 2 5 = 32 expanded coefficients, which are all the same except for sign changes.
Indicator Parameterization Estimates
This option displays the estimates using the Indicator Variable parameterization. To re-create the report in
Figure 3.7, follow the steps in “Show Prediction Expression” on page 65 with one exception: instead of
selecting Estimates > Show Prediction Expression, select Estimates > Indicator Parameterization
Estimates.
Figure 3.7 Indicator Parameterization Estimates
This parameterization is inspired by the PROC GLM parameterization. Some models match, but others,
such as no-intercept models, models with missing cells, and mixture models, will most likely show
differences.
Sequential Tests
Sequential Tests show the reduction in the residual sum of squares as each effect is entered into the fit. The
sequential tests are also called Type I sums of squares (Type I SS). One benefit of the Type I SS is that they are
independent and sum to the regression SS. One disadvantage is that they depend on the order of terms in
the model; each effect is adjusted only for the preceding effects in the model.
The following models are considered appropriate for the Type I hypotheses:
• balanced analysis of variance models specified in proper sequence (that is, interactions do not precede
main effects in the effects list, and so on)
• purely nested models specified in the proper sequence
• polynomial regression models specified in the proper sequence.
Custom Test
If you want to test a custom hypothesis, select Custom Test from the Estimates menu. To jointly test
several linear functions, click on Add Column. This displays the window shown to the left in Figure 3.8 for
constructing the test in terms of all the parameters. After filling in the test, click Done. The dialog then
changes to a report of the results, as shown on the right in Figure 3.8.