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 The TRANSREG Procedure

## Main-Effects ANOVA

This example shows how to use the TRANSREG procedure to code and fit a main-effects ANOVA model. The input data set contains the dependent variables Y, factors X1 and X2, and 11 observations. The following statements perform a main-effects ANOVA:

```   title 'Introductory Main-Effects ANOVA Example';

data A;
input Y X1 \$ X2 \$;
datalines;
8 a a
7 a a
4 a b
3 a b
5 b a
4 b a
2 b b
1 b b
8 c a
7 c a

5 c b
2 c b
;

*---Fit a Main-Effects ANOVA model with 1, 0, -1 coding. ---;
proc transreg ss2;
model identity(Y) = class(X1 X2 / effects);
output coefficients replace;
run;

*---Print TRANSREG output data set---;
proc print label;
format Intercept -- X2a 5.2;
run;
```

 Introductory Main-Effects ANOVA Example

 The TRANSREG Procedure

 TRANSREG Univariate Algorithm Iteration History forIdentity(Y) IterationNumber AverageChange MaximumChange R-Square CriterionChange Note 1 0.00000 0.00000 0.88144 Converged

 Algorithm converged.

 The TRANSREG Procedure Hypothesis Tests for Identity(Y)

 Univariate ANOVA Table Based on the Usual Degrees of Freedom Source DF Sum of Squares Mean Square F Value Pr > F Model 3 57.00000 19.00000 19.83 0.0005 Error 8 7.66667 0.95833 Corrected Total 11 64.66667

 Root MSE 0.97895 R-Square 0.8814 Dependent Mean 4.66667 Adj R-Sq 0.8370 Coeff Var 20.9774

 Univariate Regression Table Based on the Usual Degrees of Freedom Variable DF Coefficient Type IISum ofSquares Mean Square F Value Pr > F Label Intercept 1 4.6666667 261.333 261.333 272.70 <.0001 Intercept Class.X1a 1 0.8333333 4.167 4.167 4.35 0.0705 X1 a Class.X1b 1 -1.6666667 16.667 16.667 17.39 0.0031 X1 b Class.X2a 1 1.8333333 40.333 40.333 42.09 0.0002 X2 a

Figure 65.1: ANOVA Example Output from PROC TRANSREG

The iteration history in Figure 65.1 shows that the final R-Square of 0.88144 is reached on the first iteration.

This is followed by ANOVA, fit statistics, and regression tables. PROC TRANSREG uses an effects (also called deviations from means or 0, 1, -1) coding in this example.

The TRANSREG procedure produces the data set displayed in Figure 65.2.

 Introductory Main-Effects ANOVA Example

 Obs _TYPE_ _NAME_ Y Intercept X1 a X1 b X2 a X1 X2 1 SCORE ROW1 8 1.00 1.00 0.00 1.00 a a 2 SCORE ROW2 7 1.00 1.00 0.00 1.00 a a 3 SCORE ROW3 4 1.00 1.00 0.00 -1.00 a b 4 SCORE ROW4 3 1.00 1.00 0.00 -1.00 a b 5 SCORE ROW5 5 1.00 0.00 1.00 1.00 b a 6 SCORE ROW6 4 1.00 0.00 1.00 1.00 b a 7 SCORE ROW7 2 1.00 0.00 1.00 -1.00 b b 8 SCORE ROW8 1 1.00 0.00 1.00 -1.00 b b 9 SCORE ROW9 8 1.00 -1.00 -1.00 1.00 c a 10 SCORE ROW10 7 1.00 -1.00 -1.00 1.00 c a 11 SCORE ROW11 5 1.00 -1.00 -1.00 -1.00 c b 12 SCORE ROW12 2 1.00 -1.00 -1.00 -1.00 c b 13 M COEFFI Y . 4.67 0.83 -1.67 1.83 14 MEAN Y . . 5.50 3.00 6.50

Figure 65.2: Output Data Set from PROC TRANSREG

The output data set has three kinds of observations, identified by values of _TYPE_.

• When _TYPE_='SCORE', the observation contains information on the dependent and independent variables as follows:
• Y is the original dependent variable.
• X1 and X2 are the independent classification variables, and the Intercept through X2 a columns contain the main effects design matrix that PROC TRANSREG creates. The variable names are Intercept, X1a, X1b, and X2a. Their labels are shown in the listing.
• When _TYPE_='M COEFFI', the observation contains coefficients of the final linear model.
• When _TYPE_='MEAN', the observation contains the marginal means.

The observations with _TYPE_='SCORE' form the score partition of the data set, and the observations with _TYPE_='M COEFFI' and _TYPE_='MEAN' form the coefficient partition of the data set.

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