The TRANSREG Procedure

Main-Effects ANOVA

This example shows how to use PROC TRANSREG to code and fit a main-effects ANOVA model. PROC TRANSREG has very extensive and versatile options for coding or creating so-called dummy variables. PROC TRANSREG is commonly used to code classification variables before they are used for analysis in other procedures. See the sections Using the DESIGN Output Option and Discrete Choice Experiments: DESIGN, NORESTORE, NOZERO. In this example, the input data set contains the dependent variables y, factors x1 and x2, and 12 observations. PROC TRANSREG can be useful for coding even before running procedures with a CLASS statement because of its detailed options that enable you to control how the coded variable names and labels are constructed. The following statements perform a main-effects ANOVA and display the results in Figure 104.12 and Figure 104.13:

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;

* Display TRANSREG output data set;
proc print label;
   format intercept -- x2a 5.2;
run;

The SS2 a-option requests results based on Type II sums of squares. The simple ANOVA model is fit by designating y as an IDENTITY variable, which specifies no transformation. The independent variables are specified with a CLASS expansion, which replaces them with coded variables. There are $(3 - 1) + (2 - 1) = 3$ coded variables created by the CLASS specification, since the two CLASS variables have 3 and 2 different values or levels. In this case, the EFFECTS t-option is specified. This option requests an effects coding (displayed in Figure 104.13), which is also called a deviations from means or 0, 1, –1 coding. The OUTPUT statement requests an output data set with the data and coded variables. The COEFFICIENTS output option, or o-option, adds the parameter estimates and marginal means to the data set. The REPLACE o-option specifies that the transformed variables should replace the original variables in the output data set. The output data set variable names are the same as the original variable name. In an example like this, there are no nonlinear transformations; the transformed variables are the same as the original variables. The REPLACE o-option is used to eliminate unnecessary and redundant transformed variables from the output data set. The results of the PROC TRANSREG step are shown in Figure 104.12.

Figure 104.12: ANOVA Example Output from PROC TRANSREG

Introductory Main-Effects ANOVA Example

The TRANSREG Procedure

Dependent Variable Identity(y)

Class Level Information
Class	Levels	Values
x1	3	a b c
x2	2	a b

Number of Observations Read	12
Number of Observations Used	12

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 104.12 shows the ANOVA results, fit statistics, and regression tables. The output data set, with the coded design, parameter estimates and means, is shown in Figure 104.13. For more information about PROC TRANSREG for ANOVA and other codings, see the section ANOVA Codings.

Figure 104.13: Output Data Set from PROC TRANSREG

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

The output data set has three kinds of observations, identified by values of _TYPE_ as follows:

When _TYPE_=’SCORE’, the observation contains the following information about the dependent and independent variables:
- 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 (parameter estimates).
When _TYPE_=’MEAN’, the observation contains the marginal means.

The observations with _TYPE_=’SCORE’ form the score or data partition of the output data set, and the observations with _TYPE_=’M COEFFI’ and _TYPE_=’MEAN’ form the output statistics partition of the output data set.