Examples
Example 33.1. A Two-Way Design
The following program uses the GLMMOD procedure to produce the design matrix for a two-way design. The two classification factors have seven and three levels, respectively, so the design matrix contains 1 + 7 + 3 + 21 = 32 columns in all.
data Plants; input Type $ @; do Block=1 to 3; input StemLength @; output; end; datalines; Clarion 32.7 32.3 31.5 Clinton 32.1 29.7 29.1 Knox 35.7 35.9 33.1 O'Neill 36.0 34.2 31.2 Compost 31.8 28.0 29.2 Wabash 38.2 37.8 31.9 Webster 32.5 31.1 29.7 ; proc glmmod outparm=Parm outdesign=Design; class Type Block; model StemLength = TypeBlock; run; proc print data=Parm; run; proc print data=Design; run;
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The GLMMOD Procedure Class Level Information Class Levels Values Type 7 Clarion Clinton Compost Knox O'Neill Wabash Webster Block 3 1 2 3 Number of Observations Read 21 Number of Observations Used 21
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The GLMMOD Procedure Parameter Definitions Name of Column Associated CLASS Variable Values Number Effect Type Block 1 Intercept 2 Type Clarion 3 Type Clinton 4 Type Compost 5 Type Knox 6 Type O'Neill 7 Type Wabash 8 Type Webster 9 Block 1 10 Block 2 11 Block 3 12 Type*Block Clarion 1 13 Type*Block Clarion 2 14 Type*Block Clarion 3 15 Type*Block Clinton 1 16 Type*Block Clinton 2 17 Type*Block Clinton 3 18 Type*Block Compost 1 19 Type*Block Compost 2 20 Type*Block Compost 3 21 Type*Block Knox 1 22 Type*Block Knox 2 23 Type*Block Knox 3 24 Type*Block O'Neill 1 25 Type*Block O'Neill 2 26 Type*Block O'Neill 3 27 Type*Block Wabash 1 28 Type*Block Wabash 2 29 Type*Block Wabash 3 30 Type*Block Webster 1 31 Type*Block Webster 2 32 Type*Block Webster 3
The GLMMOD Procedure Design Points Observation Stem Column Number Number Length 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 1 32.7 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 2 32.3 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 3 31.5 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 4 32.1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 5 29.7 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 6 29.1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 7 35.7 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 8 35.9 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 9 33.1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 10 36.0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 11 34.2 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 12 31.2 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 13 31.8 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 14 28.0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 15 29.2 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 16 38.2 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 17 37.8 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 18 31.9 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 19 32.5 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 20 31.1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 21 29.7 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0
Design Points Observation Column Number Number 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 8 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 11 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 13 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 17 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 18 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 19 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 20 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 21 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
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Obs _COLNUM_ EFFNAME Type Block 1 1 Intercept 2 2 Type Clarion 3 3 Type Clinton 4 4 Type Compost 5 5 Type Knox 6 6 Type O'Neill 7 7 Type Wabash 8 8 Type Webster 9 9 Block 1 10 10 Block 2 11 11 Block 3 12 12 Type*Block Clarion 1 13 13 Type*Block Clarion 2 14 14 Type*Block Clarion 3 15 15 Type*Block Clinton 1 16 16 Type*Block Clinton 2 17 17 Type*Block Clinton 3 18 18 Type*Block Compost 1 19 19 Type*Block Compost 2 20 20 Type*Block Compost 3 21 21 Type*Block Knox 1 22 22 Type*Block Knox 2 23 23 Type*Block Knox 3 24 24 Type*Block O'Neill 1 25 25 Type*Block O'Neill 2 26 26 Type*Block O'Neill 3 27 27 Type*Block Wabash 1 28 28 Type*Block Wabash 2 29 29 Type*Block Wabash 3 30 30 Type*Block Webster 1 31 31 Type*Block Webster 2 32 32 Type*Block Webster 3
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S t e m L e C C C C C C C C C C C C C C C C C C C C C C C n C C C C C C C C C o o o o o o o o o o o o o o o o o o o o o o o O g o o o o o o o o o l l l l l l l l l l l l l l l l l l l l l l l b t l l l l l l l l l 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 s h 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9 0 1 2 1 32.7 1 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 32.3 1 1 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 31.5 1 1 0 0 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 32.1 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 29.7 1 0 1 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 29.1 1 0 1 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 35.7 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 8 35.9 1 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 9 33.1 1 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 10 36.0 1 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 11 34.2 1 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 12 31.2 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 13 31.8 1 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14 28.0 1 0 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 15 29.2 1 0 0 1 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 16 38.2 1 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 17 37.8 1 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 18 31.9 1 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 19 32.5 1 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 20 31.1 1 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 21 29.7 1 0 0 0 0 0 0 1 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
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Example 33.2. Factorial Screening
Screening experiments are undertaken to select from among the many possible factors that might affect a response the few that actually do, either simply (main effects) or in conjunction with other factors (interactions). One method of selecting significant factors is forward model selection, in which the model is built by successively adding the most statistically significant effects. Forward selection is an option in the REG procedure, but the REG procedure does not allow you to specify interactions directly (as the GLM procedure does, for example). You can use the GLMMOD procedure to create the screening model for a design and then use the REG procedure on the results to perform the screening.
The following statements create the SAS data set Screening , which contains the results of a screening experiment:
title 'PROC GLMMOD and PROC REG for Forward Selection Screening'; data Screening; input a b c d e y; datalines; 1 1 1 1 1 6.688 1 1 1 1 1 10.664 1 1 1 1 1 1.459 1 1 1 1 1 2.042 1 1 1 1 1 8.561 1 1 1 1 1 7.095 1 1 1 1 1 0.553 1 1 1 1 1 2.352 1 1 1 1 1 4.802 1 1 1 1 1 5.705 1 1 1 1 1 14.639 1 1 1 1 1 2.151 1 1 1 1 1 5.884 1 1 1 1 1 3.317 1 1 1 1 1 4.048 1 1 1 1 1 15.248 ; run;
The data set contains a single dependent variable ( y )and five independent factors ( a , b , c , d , and e ). The design is a half-fraction of the full 2 5 factorial, the precise half-fraction having been chosen to provide uncorrelated estimates of all main effects and two-factor interactions.
The following statements use the GLMMOD procedure to create a design matrix data set containing all the main effects and two factor interactions for the preceding screening design.
ods output DesignPoints = DesignMatrix; proc glmmod data=Screening; model y = abcde@2; run;
Notice that the preceding statements use ODS to create the design matrix data set, instead of the OUTDESIGN= option in the PROC GLMMOD statement. The results are equivalent, but the columns of the data set produced by ODS have names that are directly related to the names of their corresponding effects.
Finally, the following statements use the REG procedure to perform forward model selection for the screening design. Two MODEL statements are used, one without the selection options (which produces the regression analysis for the full model) and one with the selection options.
proc reg data=DesignMatrix; model y = a--d_e; model y = a--d_e / selection = forward details = summary slentry = 0.05; run;
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PROC GLMMOD and PROC REG for Forward Selection Screening The REG Procedure Model: MODEL1 Dependent Variable: y Analysis of Variance Sum of Mean Source DF Squares Square F Value Pr > F Model 15 861.48436 57.43229 . . Error 0 0 . Corrected Total 15 861.48436 Root MSE . R-Square 1.0000 Dependent Mean 0.33325 Adj R-Sq . Coeff Var . Parameter Estimates Parameter Standard Variable Label DF Estimate Error t Value Pr > t Intercept Intercept 1 0.33325 . . . a 1 4.61125 . . . b 1 0.21775 . . . a_b a*b 1 0.30350 . . . c 1 4.02550 . . . a_c a*c 1 0.05150 . . . b_c b*c 1 0.20225 . . . d 1 0.11850 . . . a_d a*d 1 0.12075 . . . b_d b*d 1 0.18850 . . . c_d c*d 1 0.03200 . . . e 1 3.45275 . . . a_e a*e 1 1.97175 . . . b_e b*e 1 0.35625 . . . c_e c*e 1 0.30900 . . . d_e d*e 1 0.30750 . . .
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PROC GLMMOD and PROC REG for Forward Selection Screening The REG Procedure Model: MODEL2 Dependent Variable: y Summary of Forward Selection Variable Number Partial Model Step Entered Label Vars In R-Square R-Square C(p) F Value Pr > F 1 a 1 0.3949 0.3949 . 9.14 0.0091 2 c 2 0.3010 0.6959 . 12.87 0.0033 3 e 3 0.2214 0.9173 . 32.13 0.0001 4 a_e a*e 4 0.0722 0.9895 . 75.66 <.0001
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Output 33.2.1 and Output 33.2.2 contain the results of the REG analysis. The full model has 16 parameters (the intercept + 5 main effects + 10 interactions). These are all estimable , but since there are only 16 observations in the design, there are no degrees of freedom left to estimate error; consequently, there is no way to use the full model to test for the statistical significance of effects. However, the forward selection method chooses only four effects for the model: the main effects of factors a , c ,and e , and the interaction between a and e . Using this reduced model enables you to estimate the underlying level of noise, although note that the selection method biases this estimate somewhat.
EAN: N/A
Pages: 105
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