Main-Effects ANOVA

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 for Identity(Y)
Iteration Number	Average Change	Maximum Change	R-Square	Criterion Change	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	20.97739

Univariate Regression Table Based on the Usual Degrees of Freedom
Variable	DF	Coefficient	Type II Sum of Squares	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.

Chapter Contents
Previous
Next
Top