title 'Multi-Population Repeated Measures';
data group;
input a b c Group wt @@;
datalines;
0 0 0 0 2 0 0 0 1 2
0 0 1 0 1 0 0 1 1 1
0 1 0 0 0 0 1 0 1 0
0 1 1 0 1 0 1 1 1 0
1 0 0 0 0 1 0 0 1 2
1 0 1 0 1 1 0 1 1 2
1 1 0 0 1 1 1 0 1 3
1 1 1 0 24 1 1 1 1 20
; proc catmod data=group;
weight wt;
response marginals;
model a*b*c=Group _response_ Group*_response_
/ freq nodesign;
repeated Trial 3;
title2 'Saturated Model';
run;
title 'Growth Curve Analysis'; data growth;
input Diag $ Treat $ week1 $ week2 $ week4 $ count @@;
datalines; mild std n n n 16 severe std n n n 2
mild std n n a 13 severe std n n a 2
mild std n a n 9 severe std n a n 8
mild std n a a 3 severe std n a a 9
mild std a n n 14 severe std a n n 9
mild std a n a 4 severe std a n a 15
mild std a a n 15 severe std a a n 27
mild std a a a 6 severe std a a a 28
mild new n n n 31 severe new n n n 7
mild new n n a 0 severe new n n a 2
mild new n a n 6 severe new n a n 5
mild new n a a 0 severe new n a a 2
mild new a n n 22 severe new a n n 31
mild new a n a 2 severe new a n a 5
mild new a a n 9 severe new a a n 32
mild new a a a 0 severe new a a a 6
;
proc catmod order=data data=growth;
title2 'Reduced Logistic Model';
weight count;
population Diagnosis Treatment;
response logit;
model week1*week2*week4=
(1 1 1 0 0,/* mild, std */
1 1 1 1 1,
1 1 1 2 2,
1 1 -1 0 0,/* mild, new */
1 1 -1 1 -1,
1 1 -1 2 -2,
1 -1 1 0 0,/* severe, std */
1 -1 1 1 1,
1 -1 1 2 2,
1 -1 -1 0 0,/*severe,new */
1 -1 -1 1 -1,
1 -1 -1 2 -2)
(1='Intercept',
2='Diag',
3='Treat',
4='Time effect',
5='Time*Treat effect')
/ freq;
quit;
run;
Multi-Population Repeated Measures
Saturated Model
The CATMOD Procedure
Data Summary
Response a*b*c Response Levels 7
Weight Variable wt Populations 2
Data Set GROUP Total Frequency 60
Frequency Missing 0 Observations 12
Population Profiles
Sample Group Sample Size
1 0 30
2 1 30
Response Profiles
Response a b c
1 0 0 0
2 0 0 1
3 0 1 1
4 1 0 0
5 1 0 1
6 1 1 0
7 1 1 1
Response Frequencies
Response Number
Sample 1 2 3 4 5 6 7
1 2 1 1 0 1 1 24
2 2 1 0 2 2 3 20
Analysis of Variance
Source DF Chi-Square Pr > ChiSq
Intercept 1 16.92 <.0001
Group 1 0.78 0.3781
Trial 2 3.12 0.2099
Group*Trial 2 4.32 0.1152
Residual 0 . .
Multi-Population Repeated Measures
Saturated Model
The CATMOD Procedure
Analysis of Weighted Least Squares Estimates
Std Chi-
Effect Param. Est. Err Sq. Pr > ChiSq
Intercept 1 .15 .03 16.92 <.0001 Group 2 -.03 .03 0.78 0.3781
Trial 3 -.03 .02 2.60 0.1067
4 .02 .02 1.22 0.2687
Gr*Trial 5 .05 .02 4.30 0.0381
6 -.01 .02 0.44 0.5069
Growth Curve Analysis
Reduced Logistic Model
The CATMOD Procedure
Data Summary
Resp: week1*week2*week4 Resp Levels 8
Weight Variable: count Populations 4
Data Set: growth Total Freq: 340
Freq Missing 0 Observations 29
Population Profiles
Sample Diag Treat Sample Size
1 mild std 80
2 mild new 70
3 severe std 100
4 severe new 90
Response Profiles
Response week1 week2 week4
1 n n n
2 n n a
3 n a n
4 n a a
5 a n n
6 a n a
7 a a n
8 a a a
Response Frequencies
Response Number
Sample 1 2 3 4 5 6 7 8
1 16 13 9 3 14 4 15 6
2 31 0 6 0 22 2 9 0
3 2 2 8 9 9 15 27 28
4 7 2 5 2 31 5 32 6
Growth Curve Analysis
Reduced Logistic Model
The CATMOD Procedure
Response Functions and Design Matrix
Pop. Function Resp Design Matrix
Number Func 1 2 3 4 5
1 1 .05 1 1 1 0 0
2 .35 1 1 1 1 1
3 .73 1 1 1 2 2
2 1 .11 1 1 -1 0 0
2 1.29 1 1 -1 1 -1
3 3.52 1 1 -1 2 -2
3 1 -1.32 1 -1 1 0 0
2 -.94 1 -1 1 1 1
3 -.16 1 -1 1 2 2
4 1 -1.53 1 -1 -1 0 0
2 .00 1 -1 -1 1 -1
3 1.60 1 -1 -1 2 -2
Analysis of Variance
Source DF Chi-Square Pr > ChiSq
Intercept 1 39.31 <.0001
Diag 1 77.07 <.0001
Treat 1 0.05 0.8192
Time effect 1 102.67 <.0001
Time*Treat effect 1 26.93 <.0001
Residual 7 4.15 0.7627
Analysis of Weighted Least Squares Estimates
Std. Chi-
Effect Param. Est. Err. Sq. Pr > ChiSq
Model 1 -0.71 0.11 39.31 <.0001
2 0.64 0.07 77.07 <.0001
3 0.02 0.11 0.05 0.8192
4 0.97 0.09 102.67 <.0001
5 -0.49 0.09 26.93 <.0001