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The TRANSREG Procedure

Using the DESIGN Output Option

This example uses PROC TRANSREG and the DESIGN o-option to prepare an input data set with classification variables for the LOGISTIC procedure. The DESIGN o-option specifies that the goal is design matrix creation, not analysis. When you specify DESIGN, dependent variables are not required. The DEVIATIONS (or EFFECTS) t-option requests a deviations-from-means (1, 0, -1) coding of the classification variables, which is the same coding the CATMOD procedure uses. See Figure 65.29. PROC TRANSREG automatically creates a macro variable &_trgind that contains the list of independent variables created. This macro is used in the PROC LOGISTIC MODEL statement. See Figure 65.30. For comparison, the same analysis is also performed with PROC CATMOD. See Figure 65.31.

   title 'Using PROC TRANSREG to Create a Design Matrix';

   data a;
      do y = 1, 2;
         do a = 1 to 4;
            do b = 1 to 3;
               w = ceil(uniform(1) * 10 + 10);
               output;
            end;
         end;
      end;
   run;

   proc transreg data=a design;
      model class(a b / deviations);
      id y w;
      output;
   run;

   proc print;
      title2 'PROC TRANSREG Output Data Set';
   run;

   proc logistic;
      title2 'PROC LOGISTIC with Classification Variables';
      freq w;
      model y = &_trgind;
   run;

   proc catmod data=a;
      title2 'PROC CATMOD Should Produce the Same Results';
      model y = a b;
      weight w;
   run;

Using PROC TRANSREG to Create a Design Matrix
PROC TRANSREG Output Data Set

Obs _TYPE_ _NAME_ Intercept a1 a2 a3 b1 b2 a b y w
1 SCORE 1 1 1 0 0 1 0 1 1 1 12
2 SCORE 1 1 1 0 0 0 1 1 2 1 20
3 SCORE 1 1 1 0 0 -1 -1 1 3 1 14
4 SCORE 1 1 0 1 0 1 0 2 1 1 13
5 SCORE 1 1 0 1 0 0 1 2 2 1 20
6 SCORE 1 1 0 1 0 -1 -1 2 3 1 20
7 SCORE 1 1 0 0 1 1 0 3 1 1 16
8 SCORE 1 1 0 0 1 0 1 3 2 1 16
9 SCORE 1 1 0 0 1 -1 -1 3 3 1 11
10 SCORE 1 1 -1 -1 -1 1 0 4 1 1 11
11 SCORE 1 1 -1 -1 -1 0 1 4 2 1 19
12 SCORE 1 1 -1 -1 -1 -1 -1 4 3 1 16
13 SCORE 2 1 1 0 0 1 0 1 1 2 19
14 SCORE 2 1 1 0 0 0 1 1 2 2 11
15 SCORE 2 1 1 0 0 -1 -1 1 3 2 20
16 SCORE 2 1 0 1 0 1 0 2 1 2 13
17 SCORE 2 1 0 1 0 0 1 2 2 2 13
18 SCORE 2 1 0 1 0 -1 -1 2 3 2 17
19 SCORE 2 1 0 0 1 1 0 3 1 2 20
20 SCORE 2 1 0 0 1 0 1 3 2 2 13
21 SCORE 2 1 0 0 1 -1 -1 3 3 2 17
22 SCORE 2 1 -1 -1 -1 1 0 4 1 2 15
23 SCORE 2 1 -1 -1 -1 0 1 4 2 2 16
24 SCORE 2 1 -1 -1 -1 -1 -1 4 3 2 13

Figure 65.29: The PROC TRANSREG Design Matrix

Using PROC TRANSREG to Create a Design Matrix
PROC LOGISTIC with Classification Variables

The LOGISTIC Procedure

Model Information
Data Set WORK.DATA8
Response Variable y
Number of Response Levels 2
Number of Observations 24
Frequency Variable w
Sum of Frequencies 375
Link Function Logit
Optimization Technique Fisher's scoring

Response Profile
Ordered
Value
y Total
Frequency
1 1 188
2 2 187

Model Convergence Status
Convergence criterion (GCONV=1E-8) satisfied.

Model Fit Statistics
Criterion Intercept
Only
Intercept
and
Covariates
AIC 521.858 524.378
SC 525.785 547.939
-2 Log L 519.858 512.378

Testing Global Null Hypothesis: BETA=0
Test Chi-Square DF Pr > ChiSq
Likelihood Ratio 7.4799 5 0.1873
Score 7.4312 5 0.1905
Wald 7.3356 5 0.1969

Figure 65.30: PROC LOGISTIC Output

Using PROC TRANSREG to Create a Design Matrix
PROC LOGISTIC with Classification Variables

The LOGISTIC Procedure

Analysis of Maximum Likelihood Estimates
Parameter DF Estimate Standard
Error
Chi-Square Pr > ChiSq
Intercept 1 -0.00040 0.1044 0.0000 0.9969
a1 1 -0.0802 0.1791 0.2007 0.6542
a2 1 0.2001 0.1800 1.2363 0.2662
a3 1 -0.1350 0.1819 0.5514 0.4578
b1 1 -0.2392 0.1500 2.5436 0.1107
b2 1 0.3433 0.1474 5.4223 0.0199

Association of Predicted Probabilities and
Observed Responses
Percent Concordant 54.0 Somers' D 0.163
Percent Discordant 37.8 Gamma 0.177
Percent Tied 8.2 Tau-a 0.082
Pairs 35156 c 0.581

Using PROC TRANSREG to Create a Design Matrix
PROC CATMOD Should Produce the Same Results

The CATMOD Procedure

Response y Response Levels 2
Weight Variable w Populations 12
Data Set A Total Frequency 375
Frequency Missing 0 Observations 24

Population Profiles
Sample a b Sample Size
1 1 1 31
2 1 2 31
3 1 3 34
4 2 1 26
5 2 2 33
6 2 3 37
7 3 1 36
8 3 2 29
9 3 3 28
10 4 1 26
11 4 2 35
12 4 3 29

Response Profiles
Response y
1 1
2 2

Figure 65.31: PROC CATMOD Output

Using PROC TRANSREG to Create a Design Matrix
PROC CATMOD Should Produce the Same Results

The CATMOD Procedure

Maximum Likelihood Analysis
Iteration Sub Iteration -2 Log
Likelihood
Convergence Criterion Parameter Estimates
1 2 3 4 5 6
0 0 519.86039 1.0000 0 0 0 0 0 0
1 0 512.3792 0.0144 -0.001162 -0.0790 0.1965 -0.1327 -0.2365 0.3393
2 0 512.37786 2.608E-6 -0.000404 -0.0802 0.2001 -0.1350 -0.2392 0.3433
3 0 512.37786 9.929E-13 -0.000403 -0.0802 0.2001 -0.1350 -0.2392 0.3434

Maximum likelihood computations converged.

Maximum Likelihood Analysis of Variance
Source DF Chi-Square Pr > ChiSq
Intercept 1 0.00 0.9969
a 3 1.50 0.6823
b 2 5.64 0.0597
Likelihood Ratio 6 2.81 0.8329

Analysis of Maximum Likelihood Estimates
Effect Parameter Estimate Standard
Error
Chi-
Square
Pr > ChiSq
Intercept 1 -0.00040 0.1044 0.00 0.9969
a 2 -0.0802 0.1791 0.20 0.6542
  3 0.2001 0.1800 1.24 0.2662
  4 -0.1350 0.1819 0.55 0.4578
b 5 -0.2392 0.1500 2.54 0.1107
  6 0.3434 0.1474 5.42 0.0199

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