PROC GLMMOD: A One-Way Design :: SAS/STAT(R) 9.2 User's Guide, Second Edition

The GLMMOD Procedure

A One-Way Design

A one-way analysis of variance considers one treatment factor with two or more treatment levels. This example employs PROC GLMMOD together with PROC REG to perform a one-way analysis of variance to study the effect of bacteria on the nitrogen content of red clover plants. The treatment factor is bacteria strain, and it has six levels. Red clover plants are inoculated with the treatments, and nitrogen content is later measured in milligrams. The data are derived from an experiment by Erdman (1946) and are analyzed in Chapters 7 and 8 of Steel and Torrie (1980). PROC GLMMOD is used to create the design matrix. The following DATA step creates the SAS data set Clover.

      title 'Nitrogen Content of Red Clover Plants';
      data Clover;
         input Strain $ Nitrogen @@;
         datalines;
      3DOK1  19.4 3DOK1  32.6 3DOK1  27.0 3DOK1  32.1 3DOK1  33.0
      3DOK5  17.7 3DOK5  24.8 3DOK5  27.9 3DOK5  25.2 3DOK5  24.3
      3DOK4  17.0 3DOK4  19.4 3DOK4   9.1 3DOK4  11.9 3DOK4  15.8
      3DOK7  20.7 3DOK7  21.0 3DOK7  20.5 3DOK7  18.8 3DOK7  18.6
      3DOK13 14.3 3DOK13 14.4 3DOK13 11.8 3DOK13 11.6 3DOK13 14.2
      COMPOS 17.3 COMPOS 19.4 COMPOS 19.1 COMPOS 16.9 COMPOS 20.8
      ;

The variable Strain contains the treatment levels, and the variable Nitrogen contains the response. The following statements produce the design matrix:

   proc glmmod data=Clover;
      class Strain;
      model Nitrogen = Strain;
   run;

The classification variable, or treatment factor, is specified in the CLASS statement. The MODEL statement defines the response and independent variables. The design matrix produced corresponds to the model

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where $\text{[math]}$ and $\text{[math]}$ .

Figure 40.1 and Figure 40.2 display the output produced by these statements. Figure 40.1 displays information about the data set, which is useful for checking your data.

Figure 40.1 Class Level Information and Parameter Definitions

Nitrogen Content of Red Clover Plants

The GLMMOD Procedure

Class Level Information
Class	Levels	Values
Strain	6	3DOK1 3DOK13 3DOK4 3DOK5 3DOK7 COMPOS

Number of Observations Read	30
Number of Observations Used	30

Parameter Definitions
Column Number	Name of Associated Effect	CLASS Variable Values
Column Number	Name of Associated Effect	Strain
1	Intercept
2	Strain	3DOK1
3	Strain	3DOK13
4	Strain	3DOK4
5	Strain	3DOK5
6	Strain	3DOK7
7	Strain	COMPOS

The design matrix, shown in Figure 40.2, consists of seven columns: one for the mean and six for the treatment levels. The vector of responses, Nitrogen, is also displayed.

Figure 40.2 Design Matrix

Design Points
Observation Number	Nitrogen	Column Number
Observation Number	Nitrogen	1	2	3	4	5	6	7
1	19.4	1	1	0	0	0	0	0
2	32.6	1	1	0	0	0	0	0
3	27.0	1	1	0	0	0	0	0
4	32.1	1	1	0	0	0	0	0
5	33.0	1	1	0	0	0	0	0
6	17.7	1	0	0	0	1	0	0
7	24.8	1	0	0	0	1	0	0
8	27.9	1	0	0	0	1	0	0
9	25.2	1	0	0	0	1	0	0
10	24.3	1	0	0	0	1	0	0
11	17.0	1	0	0	1	0	0	0
12	19.4	1	0	0	1	0	0	0
13	9.1	1	0	0	1	0	0	0
14	11.9	1	0	0	1	0	0	0
15	15.8	1	0	0	1	0	0	0
16	20.7	1	0	0	0	0	1	0
17	21.0	1	0	0	0	0	1	0
18	20.5	1	0	0	0	0	1	0
19	18.8	1	0	0	0	0	1	0
20	18.6	1	0	0	0	0	1	0
21	14.3	1	0	1	0	0	0	0
22	14.4	1	0	1	0	0	0	0
23	11.8	1	0	1	0	0	0	0
24	11.6	1	0	1	0	0	0	0
25	14.2	1	0	1	0	0	0	0
26	17.3	1	0	0	0	0	0	1
27	19.4	1	0	0	0	0	0	1
28	19.1	1	0	0	0	0	0	1
29	16.9	1	0	0	0	0	0	1
30	20.8	1	0	0	0	0	0	1

Usually, you will find PROC GLMMOD most useful for the data sets it can create rather than for its displayed output. For example, the following statements use PROC GLMMOD to save the design matrix for the clover study to the data set CloverDesign instead of displaying it.

   proc glmmod data=Clover outdesign=CloverDesign noprint;
      class Strain;
      model Nitrogen = Strain;
   run;

Now you can use the REG procedure to analyze the data, as the following statements demonstrate:

   proc reg data=CloverDesign;
      model Nitrogen = Col2-Col7;
   run;

The results are shown in Figure 40.3.

Figure 40.3 Regression Analysis Using the REG Procedure

Nitrogen Content of Red Clover Plants

The REG Procedure

Model: MODEL1

Dependent Variable: Nitrogen

Number of Observations Read	30
Number of Observations Used	30

Analysis of Variance
Source	DF	Sum of Squares	Mean Square	F Value	Pr > F
Model	5	847.04667	169.40933	14.37	<.0001
Error	24	282.92800	11.78867
Corrected Total	29	1129.97467

Root MSE	3.43346	R-Square	0.7496
Dependent Mean	19.88667	Adj R-Sq	0.6975
Coeff Var	17.26515

Note:

Model is not full rank. Least-squares solutions for the parameters are not unique. Some statistics will be misleading. A reported DF of 0 or B means that the estimate is biased.

Note:

The following parameters have been set to 0, since the variables are a linear combination of other variables as shown.

Col7 =	Intercept - Col2 - Col3 - Col4 - Col5 - Col6

Parameter Estimates
Variable	Label	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	Intercept	B	18.70000	1.53549	12.18	<.0001
Col2	Strain 3DOK1	B	10.12000	2.17151	4.66	<.0001
Col3	Strain 3DOK13	B	-5.44000	2.17151	-2.51	0.0194
Col4	Strain 3DOK4	B	-4.06000	2.17151	-1.87	0.0738
Col5	Strain 3DOK5	B	5.28000	2.17151	2.43	0.0229
Col6	Strain 3DOK7	B	1.22000	2.17151	0.56	0.5794
Col7	Strain COMPOS	0	0	.	.	.

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