Example 22.2: Mean Score Response Function, r=3 Responses
Four surgical operations for duodenal ulcers are
compared in a clinical trial at four hospitals.
The operations performed are:
Treatment=a, drainage and vagotomy;
Treatment=b, 25%resection and vagotomy;
Treatment=c, 50%resection and vagotomy; and
Treatment=d, 75%resection.
The response is severity of an undesirable complication
called "dumping syndrome." The data are from
Grizzle, Starmer, and Koch (1969, pp. 489 504).
title 'Dumping Syndrome Data';
data operate;
input Hospital Treatment $ Severity $ wt @@;
datalines;
1 a none 23 1 a slight 7 1 a moderate 2
1 b none 23 1 b slight 10 1 b moderate 5
1 c none 20 1 c slight 13 1 c moderate 5
1 d none 24 1 d slight 10 1 d moderate 6
2 a none 18 2 a slight 6 2 a moderate 1
2 b none 18 2 b slight 6 2 b moderate 2
2 c none 13 2 c slight 13 2 c moderate 2
2 d none 9 2 d slight 15 2 d moderate 2
3 a none 8 3 a slight 6 3 a moderate 3
3 b none 12 3 b slight 4 3 b moderate 4
3 c none 11 3 c slight 6 3 c moderate 2
3 d none 7 3 d slight 7 3 d moderate 4
4 a none 12 4 a slight 9 4 a moderate 1
4 b none 15 4 b slight 3 4 b moderate 2
4 c none 14 4 c slight 8 4 c moderate 3
4 d none 13 4 d slight 6 4 d moderate 4
;
The response variable (Severity) is ordinally scaled
with three levels, so assignment of scores is
appropriate (0=none, 0.5=slight, 1=moderate).
For these scores, the response function yields the mean score.
The following statements produce Output 22.2.1 through Output 22.2.6.
proc catmod data=operate order=data ;
weight wt;
response 0 0.5 1;
model Severity=Treatment Hospital / freq oneway;
title2 'MainEffects Model';
quit;
The ORDER= option is specified so that the levels of
the response variable remain in the correct order.
A main effects model is fit. The FREQ option displays the
frequency of each response within each sample (Output 22.2.3), and the
ONEWAY option produces a table of the number of subjects
within each variable level (Output 22.2.1).
Output 22.2.1: Surgical Data: Analysis of Mean Scores
Dumping Syndrome Data 
MainEffects Model 
Response 
Severity 
Response Levels 
3 
Weight Variable 
wt 
Populations 
16 
Data Set 
OPERATE 
Total Frequency 
417 
Frequency Missing 
0 
Observations 
48 
OneWay Frequencies 
Variable 
Value 
Frequency 
Severity 
none 
240 

slight 
129 

moderate 
48 
Treatment 
a 
96 

b 
104 

c 
110 

d 
107 
Hospital 
1 
148 

2 
105 

3 
74 

4 
90 

Output 22.2.2: Population Sizes
Dumping Syndrome Data 
MainEffects Model 
Population Profiles 
Sample 
Treatment 
Hospital 
Sample Size 
1 
a 
1 
32 
2 
a 
2 
25 
3 
a 
3 
17 
4 
a 
4 
22 
5 
b 
1 
38 
6 
b 
2 
26 
7 
b 
3 
20 
8 
b 
4 
20 
9 
c 
1 
38 
10 
c 
2 
28 
11 
c 
3 
19 
12 
c 
4 
25 
13 
d 
1 
40 
14 
d 
2 
26 
15 
d 
3 
18 
16 
d 
4 
23 

Output 22.2.3: Response Frequencies
Dumping Syndrome Data 
MainEffects Model 
Response Profiles 
Response 
Severity 
1 
none 
2 
slight 
3 
moderate 
Response Frequencies 
Sample 
Response Number 
1 
2 
3 
1 
23 
7 
2 
2 
18 
6 
1 
3 
8 
6 
3 
4 
12 
9 
1 
5 
23 
10 
5 
6 
18 
6 
2 
7 
12 
4 
4 
8 
15 
3 
2 
9 
20 
13 
5 
10 
13 
13 
2 
11 
11 
6 
2 
12 
14 
8 
3 
13 
24 
10 
6 
14 
9 
15 
2 
15 
7 
7 
4 
16 
13 
6 
4 

You can use the oneway frequencies (Output 22.2.1) and the response
profiles (Output 22.2.3) to verify that the response levels are
in the desired order (none, slight, moderate) so that the
response scores (0, 0.5, 1.0) are applied appropriately.
If the ORDER=DATA option had not been used,
the levels would have been in a different order.
Output 22.2.4: Design Matrix
Dumping Syndrome Data 
MainEffects Model 
Sample 
Response Function 
Design Matrix 
1 
2 
3 
4 
5 
6 
7 
1 
0.17188 
1 
1 
0 
0 
1 
0 
0 
2 
0.16000 
1 
1 
0 
0 
0 
1 
0 
3 
0.35294 
1 
1 
0 
0 
0 
0 
1 
4 
0.25000 
1 
1 
0 
0 
1 
1 
1 
5 
0.26316 
1 
0 
1 
0 
1 
0 
0 
6 
0.19231 
1 
0 
1 
0 
0 
1 
0 
7 
0.30000 
1 
0 
1 
0 
0 
0 
1 
8 
0.17500 
1 
0 
1 
0 
1 
1 
1 
9 
0.30263 
1 
0 
0 
1 
1 
0 
0 
10 
0.30357 
1 
0 
0 
1 
0 
1 
0 
11 
0.26316 
1 
0 
0 
1 
0 
0 
1 
12 
0.28000 
1 
0 
0 
1 
1 
1 
1 
13 
0.27500 
1 
1 
1 
1 
1 
0 
0 
14 
0.36538 
1 
1 
1 
1 
0 
1 
0 
15 
0.41667 
1 
1 
1 
1 
0 
0 
1 
16 
0.30435 
1 
1 
1 
1 
1 
1 
1 

Output 22.2.5: ANOVA Table
Dumping Syndrome Data 
MainEffects Model 
Analysis of Variance 
Source 
DF 
ChiSquare 
Pr > ChiSq 
Intercept 
1 
248.77 
<.0001 
Treatment 
3 
8.90 
0.0307 
Hospital 
3 
2.33 
0.5065 
Residual 
9 
6.33 
0.7069 

The analysis of variance table (Output 22.2.5) shows that the
additive model fits (since the Residual ChiSquare
is not significant), that the Treatment effect is
significant, and that the Hospital effect is not significant.
Output 22.2.6: Parameter Estimates
Dumping Syndrome Data 
MainEffects Model 
Analysis of Weighted Least Squares Estimates 
Effect 
Parameter 
Estimate 
Standard Error 
Chi Square 
Pr > ChiSq 
Intercept 
1 
0.2724 
0.0173 
248.77 
<.0001 
Treatment 
2 
0.0552 
0.0270 
4.17 
0.0411 

3 
0.0365 
0.0289 
1.59 
0.2073 

4 
0.0248 
0.0280 
0.78 
0.3757 
Hospital 
5 
0.0204 
0.0264 
0.60 
0.4388 

6 
0.0178 
0.0268 
0.44 
0.5055 

7 
0.0531 
0.0352 
2.28 
0.1312 

The coefficients of Treatment in Output 22.2.6 show that the
first two treatments (with negative coefficients) have lower
mean scores than the last two treatments (the fourth coefficient,
not shown, must be positive since the four coefficients must
sum to zero). In other words, the less severe treatments
(the first two) cause significantly less severe dumping
syndrome complications.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.