Rash model is a logistic regression, so we should be able to use SAS PROC LOGISTIC, but I cannot solve two problems (let
me know if you have solutions):
- How can we get rid of perfect data? (This is just a programming issue, so I can solve this one if I have time.)
- How can we center person estimates at their means at each loop of maximum likelihood estimation process? In Moulton's
excel simulaiton (http://www.raschsig.org/EDS_Rasch_Demo.xls), this process is the one that is done at step 5, step 15, ..... I don't know how I can implement this part in SAS
PROC LOGISTICS.
data troy;
input
ID $ 1-8 gender $ 9 item01 11 item02 12 item03
13 item04 14 item05 15
item06 16 item07 17 item08 18 item09 19 item10 20 item11 21 item12 22
item13 23 item14 24 item15
25 item16 26 item17 27 item18 28
;
datalines;
Richard M 111111100000000000
Tracie F 111111111100000000
Walter
M 111111111001000000
Blaise M 111100101000000000
Ron M 111111111100000000
William M
111111111100000000
Susan F 111111111111101000
Linda F 111111111100000000
Kim
F 111111111100000000
Carol F 111111111110000000
Pete M 111011111000000000
Brenda
F 111110101100000000
Mike M 111110011111000000
Zula F 111111111110000000
Frank
M 111111111111100000
Dorothy F 111111111010000000
Rod M 111101111100000000
Britton F 111111111100100000
Janet
F 111111111000000000
David M 111111111100100000
Thomas M 111111111110100000
Betty F
111111111111000000
Bert M 111111111100110000
Rick M 111111111110100110
Don
M 111011000000000000
Barbara F 111111111100000000
Adam M 111111100000000000
Audrey F 111111111010000000
Anne
F 111111001110010000
Lisa F 111111111000000000
James M 111111111100000000
Joe
M 111111111110000000
Martha F 111100100100000000
Elsie F 111111111101010000
Helen F
111000000000000000
;
run;
proc sort;
by ID;
run;
proc transpose data=troy out=troyT(rename = col1 = response);
by ID;
run;
proc logistic data=troyT des;
class _name_ ID;
model response
= _name_ ID /noint;
ods output ParameterEstimates=kaz;
run;
The SAS System
09:58 Monday, August 13, 2007 411
The LOGISTIC Procedure
Model Information
Data Set
WORK.TROYT
Response Variable
response
Number of Response Levels 2
Model
binary logit
Optimization Technique Fisher's scoring
Number of Observations Read
630
Number of Observations Used 630
Response Profile
Ordered
Total
Value response Frequency
1
1 341
2
0 289
Probability modeled is response=1.
The SAS System
09:58 Monday, August 13, 2007 412
The LOGISTIC Procedure
Class Level Information
Class Value
Design Variables
_NAME_ item01 1 0 0
0 0 0 0 0 0 0 0 0
0 0
item02 0 1 0
0 0 0 0 0 0 0 0 0
0 0
item03 0 0 1
0 0 0 0 0 0 0 0 0
0 0
item04 0 0 0
1 0 0 0 0 0 0 0 0
0 0
item05 0 0 0
0 1 0 0 0 0 0 0 0
0 0
item06 0 0 0
0 0 1 0 0 0 0 0 0
0 0
item07 0 0 0
0 0 0 1 0 0 0 0 0
0 0
item08 0 0 0
0 0 0 0 1 0 0 0 0
0 0
item09 0 0 0
0 0 0 0 0 1 0 0 0
0 0
item10 0 0 0
0 0 0 0 0 0 1 0 0
0 0
item11 0 0 0
0 0 0 0 0 0 0 1 0
0 0
item12 0 0 0
0 0 0 0 0 0 0 0 1
0 0
item13 0 0 0
0 0 0 0 0 0 0 0 0
1 0
item14 0 0 0
0 0 0 0 0 0 0 0 0
0 1
item15 0 0 0
0 0 0 0 0 0 0 0 0
0 0
item16 0 0 0
0 0 0 0 0 0 0 0 0
0 0
item17 0 0 0
0 0 0 0 0 0 0 0 0
0 0
item18 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1
ID Adam 1
0 0 0 0 0 0 0 0 0
0 0 0 0
Anne
0 1 0 0 0 0 0 0 0
0 0 0 0 0
Audrey
0 0 1 0 0 0 0 0 0
0 0 0 0 0
The SAS System
09:58 Monday, August 13, 2007 413
The LOGISTIC Procedure
Class Level Information
Design Variables
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
0 0 0
1 0 0
0 1 0
0 0 1
-1 -1 -1
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
The SAS System
09:58 Monday, August 13, 2007 414
The LOGISTIC Procedure
Class Level Information
Design
Variables
0 0
0
0
0 0
The SAS System
09:58 Monday, August 13, 2007 415
The LOGISTIC Procedure
Class Level Information
Class Value
Design Variables
Barbara 0
0 0 1 0 0 0 0 0 0
0 0 0 0
Bert
0 0 0 0 1 0 0 0 0
0 0 0 0 0
Betty
0 0 0 0 0 1 0 0 0
0 0 0 0 0
Blaise
0 0 0 0 0 0 1 0 0
0 0 0 0 0
Brenda
0 0 0 0 0 0 0 1 0
0 0 0 0 0
Britton
0 0 0 0 0 0 0 0 1
0 0 0 0 0
Carol
0 0 0 0 0 0 0 0 0
1 0 0 0 0
David
0 0 0 0 0 0 0 0 0
0 1 0 0 0
Don
0 0 0 0 0 0 0 0 0
0 0 1 0 0
Dorothy
0 0 0 0 0 0 0 0 0
0 0 0 1 0
Elsie
0 0 0 0 0 0 0 0 0
0 0 0 0 1
Frank
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Helen
0 0 0 0 0 0 0 0 0
0 0 0 0 0
James
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Janet
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Joe
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Kim
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Linda
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Lisa
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Martha
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Mike
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Pete
0 0 0 0 0 0 0 0 0
0 0 0 0 0
The SAS System
09:58 Monday, August 13, 2007 416
The LOGISTIC Procedure
Class Level Information
Design Variables
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
1 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 1 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 1 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 1 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 1
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
1 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 1 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 1 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 1 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 1 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 1 0 0 0
0 0 0 0
The SAS System
09:58 Monday, August 13, 2007 417
The LOGISTIC Procedure
Class Level Information
Design
Variables
0 0
0
0
0 0
0 0
0
0
0 0
0 0
0
0
0 0
0 0
0
0
0 0
0 0
0
0
0 0
0 0
0
0
0 0
0 0
0
0
0 0
0 0
The SAS System
09:58 Monday, August 13, 2007 418
The LOGISTIC Procedure
Class Level Information
Class Value
Design Variables
Richard 0
0 0 0 0 0 0 0 0 0
0 0 0 0
Rick
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Rod
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Ron
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Susan
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Thomas
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Tracie
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Walter
0 0 0 0 0 0 0 0 0
0 0 0 0 0
William
0 0 0 0 0 0 0 0 0
0 0 0 0 0
Zula
-1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1
Class Level Information
Design Variables
0 0 0 0 0
0 0 0 0 0 0 1 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 1 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 1
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
1 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 1 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 1 0
The SAS System
09:58 Monday, August 13, 2007 419
The LOGISTIC Procedure
Class Level Information
Design Variables
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 1
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
0 0 0 0 0
0 0 0 0 0 0 0 0 0
0 0 0 0
-1 -1 -1 -1 -1 -1 -1 -1 -1
-1 -1 -1 -1 -1 -1 -1 -1 -1
Class Level Information
Design
Variables
0 0
0
0
0 0
0 0
0
0
0 0
0 0
1
0
0 1
-1 -1
The SAS System
09:58 Monday, August 13, 2007 420
The LOGISTIC Procedure
Model Convergence Status
Quasi-complete separation of data
points detected.
WARNING: The maximum likelihood estimate may not exist.
WARNING: The
LOGISTIC procedure continues in spite of the above
warning. Results shown
are based on the last maximum
likelihood iteration. Validity of the model
fit is
questionable.
Model Fit Statistics
Without With
Criterion Covariates
Covariates
AIC
873.365 323.461
SC
873.365 550.192
-2 Log L 873.365
221.461
The SAS System
09:58 Monday, August 13, 2007 421
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Testing Global Null Hypothesis:
BETA=0
Test Chi-Square
DF Pr > ChiSq
Likelihood Ratio 651.9049
51 <.0001
Score
444.0571 51 <.0001
Wald
111.7812 51 <.0001
Type 3 Analysis of Effects
Wald
Effect DF Chi-Square Pr > ChiSq
_NAME_ 17
107.2071 <.0001
ID 34
66.0526 0.0008
The SAS System
09:58 Monday, August 13, 2007 422
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter
DF Estimate Error Chi-Square Pr > ChiSq
_NAME_ item01 1
25.9555 282.4 0.0085
0.9268
_NAME_ item02 1 25.9555
282.4 0.0085 0.9268
_NAME_ item03
1 25.9555 282.4 0.0085
0.9268
_NAME_ item04 1 3.9159
4.1979 0.8702 0.3509
_NAME_ item05
1 3.3331 4.1758 0.6371
0.4248
_NAME_ item06 1 2.8692
4.1634 0.4749 0.4907
_NAME_ item07
1 3.3331 4.1758 0.6371
0.4248
_NAME_ item08 1 1.8032
4.1441 0.1893 0.6635
_NAME_ item09
1 2.8692 4.1634 0.4749
0.4907
_NAME_ item10 1 0.9926
4.1347 0.0576 0.8103
_NAME_ item11
1 -1.4645 4.1306 0.1257
0.7229
_NAME_ item12 1 -2.9628 4.1473
0.5104 0.4750
_NAME_ item13 1
-2.6644 4.1425 0.4137 0.5201
_NAME_
item14 1 -4.1359 4.1769
0.9805 0.3221
_NAME_ item15 1
-5.5982 4.2679 1.7205 0.1896
_NAME_
item16 1 -5.5982 4.2679
1.7205 0.1896
_NAME_ item17 1
-5.5982 4.2679 1.7205 0.1896
ID
Adam 1 -2.4492 4.1953
0.3408 0.5594
ID Anne
1 0.3602 4.2556 0.0072
0.9325
ID Audrey 1 0.3602
4.2556 0.0072 0.9325
ID
Barbara 1 0.3602 4.2556
0.0072 0.9325
The SAS System
09:58 Monday, August 13, 2007 423
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter
DF Estimate Error Chi-Square Pr > ChiSq
ID Bert
1 2.6821 4.2264 0.4027
0.5257
ID Betty 1 2.6821
4.2264 0.4027 0.5257
ID
Blaise 1 -3.1233 4.1965
0.5539 0.4567
ID Brenda
1 -1.7191 4.2041 0.1672
0.6826
ID Britton 1 1.6247
4.2419 0.1467 0.7017
ID
Carol 1 1.6247 4.2419
0.1467 0.7017
ID David
1 1.6247 4.2419 0.1467
0.7017
ID Don 1 -3.8389
4.2106 0.8312 0.3619
ID
Dorothy 1 0.3602 4.2556
0.0072 0.9325
ID Elsie
1 2.6821 4.2264 0.4027
0.5257
ID Frank 1 3.6239
4.2251 0.7357 0.3910
ID
Helen 1 -14.9490 139.5
0.0115 0.9147
ID James
1 0.3602 4.2556 0.0072
0.9325
ID Janet 1 -0.8258
4.2270 0.0382 0.8451
ID
Joe 1 1.6247 4.2419
0.1467 0.7017
ID Kim
1 0.3602 4.2556 0.0072
0.9325
ID Linda 1 0.3602
4.2556 0.0072 0.9325
ID
Lisa 1 -0.8258 4.2270
0.0382 0.8451
ID Martha
1 -3.1233 4.1965 0.5539
0.4567
ID Mike 1
0.3602 4.2556 0.0072 0.9325
ID
Pete 1 -1.7191 4.2041
0.1672 0.6826
The SAS System
09:58 Monday, August 13, 2007 424
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Analysis of Maximum Likelihood Estimates
Standard Wald
Parameter
DF Estimate Error Chi-Square Pr > ChiSq
ID Richard
1 -2.4492 4.1953 0.3408
0.5594
ID Rick 1
4.5252 4.2330 1.1428 0.2851
ID
Rod 1 -0.8258 4.2270
0.0382 0.8451
ID Ron
1 0.3602 4.2556 0.0072
0.9325
ID Susan 1 4.5252
4.2330 1.1428 0.2851
ID
Thomas 1 2.6821 4.2264
0.4027 0.5257
ID Tracie
1 0.3602 4.2556 0.0072
0.9325
ID Walter 1 0.3602
4.2556 0.0072 0.9325
ID
William 1 0.3602 4.2556
0.0072 0.9325
Odds Ratio Estimates
Point 95% Wald
Effect
Estimate Confidence Limits
_NAME_ item01 vs item18 >999.999
<0.001 >999.999
_NAME_ item02 vs item18 >999.999
<0.001 >999.999
_NAME_ item03 vs item18 >999.999
<0.001 >999.999
_NAME_ item04 vs item18 >999.999
<0.001 >999.999
_NAME_ item05 vs item18 >999.999
<0.001 >999.999
The SAS System
09:58 Monday, August 13, 2007 425
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Odds Ratio Estimates
Point 95% Wald
Effect
Estimate Confidence Limits
_NAME_ item06 vs item18 >999.999
<0.001 >999.999
_NAME_ item07 vs item18 >999.999
<0.001 >999.999
_NAME_ item08 vs item18 >999.999
<0.001 >999.999
_NAME_ item09 vs item18 >999.999
<0.001 >999.999
_NAME_ item10 vs item18 >999.999
<0.001 >999.999
_NAME_ item11 vs item18 >999.999
<0.001 >999.999
_NAME_ item12 vs item18 >999.999
<0.001 >999.999
_NAME_ item13 vs item18 >999.999
<0.001 >999.999
_NAME_ item14 vs item18 >999.999
<0.001 >999.999
_NAME_ item15 vs item18 >999.999
<0.001 >999.999
_NAME_ item16 vs item18 >999.999
<0.001 >999.999
_NAME_ item17 vs item18 >999.999
<0.001 >999.999
ID Adam vs Zula
0.017 0.001 0.287
ID Anne
vs Zula 0.282 0.013
6.311
ID Audrey vs Zula 0.282
0.013 6.311
ID Barbara vs Zula
0.282 0.013 6.311
ID Bert
vs Zula 2.879 0.162
51.143
ID Betty vs Zula 2.879
0.162 51.143
ID Blaise vs Zula
0.009 <0.001 0.148
ID Brenda
vs Zula 0.035 0.002
0.624
ID Britton vs Zula 1.000
0.051 19.751
The SAS System
09:58 Monday, August 13, 2007 426
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Odds Ratio Estimates
Point 95% Wald
Effect
Estimate Confidence Limits
ID Carol vs Zula
1.000 0.051 19.751
ID David
vs Zula 1.000 0.051
19.751
ID Don vs Zula
0.004 <0.001 0.079
ID Dorothy
vs Zula 0.282 0.013
6.311
ID Elsie vs Zula 2.879
0.162 51.143
ID Frank vs Zula
7.383 0.420 129.735
ID Helen
vs Zula <0.001 <0.001
>999.999
ID James vs Zula
0.282 0.013 6.311
ID Janet
vs Zula 0.086 0.004
1.712
ID Joe vs Zula
1.000 0.051 19.751
ID Kim
vs Zula 0.282 0.013
6.311
ID Linda vs Zula 0.282
0.013 6.311
ID Lisa vs Zula
0.086 0.004 1.712
ID Martha
vs Zula 0.009 <0.001
0.148
ID Mike vs Zula 0.282
0.013 6.311
ID Pete vs Zula
0.035 0.002 0.624
ID Richard
vs Zula 0.017 0.001
0.287
ID Rick vs Zula 18.184
0.987 335.106
ID Rod vs Zula
0.086 0.004 1.712
ID Ron
vs Zula 0.282 0.013
6.311
ID Susan vs Zula 18.184
0.987 335.106
The SAS System
09:58 Monday, August 13, 2007 427
The LOGISTIC Procedure
WARNING: The validity of the model fit is questionable.
Odds Ratio Estimates
Point 95% Wald
Effect
Estimate Confidence Limits
ID Thomas vs Zula
2.879 0.162 51.143
ID Tracie
vs Zula 0.282 0.013
6.311
ID Walter vs Zula 0.282
0.013 6.311
ID William vs Zula
0.282 0.013 6.311
Association of Predicted Probabilities and Observed Responses
Percent Concordant 97.9 Somers'
D 0.961
Percent Discordant 1.8 Gamma
0.964
Percent Tied 0.3 Tau-a
0.478
Pairs 98549
c 0.981
