Chapter 6 : Discrimination example

Obs handicap score
1 NONE 1.90000
2 NONE 2.50000
3 NONE 3.00000
4 NONE 3.60000
5 NONE 4.10000
6 NONE 4.20000
7 NONE 4.90000
8 NONE 5.10000
9 NONE 5.40000
10 NONE 5.90000
11 NONE 6.10000
12 NONE 6.70000
13 NONE 7.40000
14 NONE 7.80000
15 AMPUTEE 1.90000
16 AMPUTEE 2.50000
17 AMPUTEE 2.60000
18 AMPUTEE 3.20000
19 AMPUTEE 3.60000
20 AMPUTEE 3.80000
21 AMPUTEE 4.00000
22 AMPUTEE 4.60000
23 AMPUTEE 5.30000
24 AMPUTEE 5.50000
25 AMPUTEE 5.80000
26 AMPUTEE 5.90000
27 AMPUTEE 6.10000
28 AMPUTEE 7.20000
29 CRUTCHES 3.70000
30 CRUTCHES 4.00000
31 CRUTCHES 4.30000
32 CRUTCHES 4.30000
33 CRUTCHES 5.10000
34 CRUTCHES 5.80000
35 CRUTCHES 6.00000
36 CRUTCHES 6.20000
37 CRUTCHES 6.30000
38 CRUTCHES 6.40000
39 CRUTCHES 7.40000
40 CRUTCHES 7.40000
41 CRUTCHES 7.50000
42 CRUTCHES 8.50000
43 HEARING 1.40000
44 HEARING 2.10000
45 HEARING 2.40000
46 HEARING 2.90000
47 HEARING 3.40000
48 HEARING 3.70000
49 HEARING 3.90000
50 HEARING 4.20000
51 HEARING 4.30000
52 HEARING 4.70000
53 HEARING 5.50000
54 HEARING 5.80000
55 HEARING 5.90000
56 HEARING 6.50000
57 WHEELCHAIR 1.70000
58 WHEELCHAIR 2.80000
59 WHEELCHAIR 3.50000
60 WHEELCHAIR 4.70000
61 WHEELCHAIR 4.80000
62 WHEELCHAIR 5.00000
63 WHEELCHAIR 5.30000
64 WHEELCHAIR 6.10000
65 WHEELCHAIR 6.10000
66 WHEELCHAIR 6.20000
67 WHEELCHAIR 6.40000
68 WHEELCHAIR 7.20000
69 WHEELCHAIR 7.40000
70 WHEELCHAIR 7.60000

Chapter 6 : Discrimination example

The Mixed Procedure

Model Information
Data Set WORK.DISCRIMINATION
Dependent Variable score
Covariance Structure Variance Components
Group Effect handicap
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within

Class Level Information
Class Levels Values
handicap 5 NONE AMPUTEE CRUTCHES HEARING WHEELCHAIR

Dimensions
Covariance Parameters 5
Columns in X 6
Columns in Z 0
Subjects 70
Max Obs Per Subject 1

Number of Observations
Number of Observations Read 70
Number of Observations Used 70
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 261.40673324  
1 1 260.68354737 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Group Estimate
Residual handicap NONE 3.2169
Residual handicap AMPUTEE 2.5145
Residual handicap CRUTCHES 2.1957
Residual handicap HEARING 2.3488
Residual handicap WHEELCHAIR 3.0565

Fit Statistics
-2 Res Log Likelihood 260.7
AIC (smaller is better) 270.7
AICC (smaller is better) 271.7
BIC (smaller is better) 281.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 0.72 0.9484

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
handicap 4 65 3.27 0.0167

Least Squares Means
Effect handicap Estimate Standard Error DF t Value Pr > |t|
handicap NONE 4.9000 0.4794 65 10.22 <.0001
handicap AMPUTEE 4.4286 0.4238 65 10.45 <.0001
handicap CRUTCHES 5.9214 0.3960 65 14.95 <.0001
handicap HEARING 4.0500 0.4096 65 9.89 <.0001
handicap WHEELCHAIR 5.3429 0.4672 65 11.43 <.0001

Differences of Least Squares Means
Effect handicap _handicap Estimate Standard Error DF t Value Pr > |t| Adjustment Adj P
handicap AMPUTEE NONE -0.4714 0.6398 65 -0.74 0.4639 Dunnett 0.8606
handicap CRUTCHES NONE 1.0214 0.6218 65 1.64 0.1053 Dunnett 0.2846
handicap HEARING NONE -0.8500 0.6305 65 -1.35 0.1823 Dunnett 0.4513
handicap WHEELCHAIR NONE 0.4429 0.6694 65 0.66 0.5106 Dunnett 0.8989

Chapter 6 : Discrimination example
Analysis wtih PROC MIXED

The Mixed Procedure

Model Information
Data Set WORK.DISCRIMINATION
Dependent Variable score
Covariance Structure Diagonal
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Residual

Class Level Information
Class Levels Values
handicap 5 NONE AMPUTEE CRUTCHES HEARING WHEELCHAIR

Dimensions
Covariance Parameters 1
Columns in X 6
Columns in Z 0
Subjects 1
Max Obs Per Subject 70

Number of Observations
Number of Observations Read 70
Number of Observations Used 70
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate
Residual 2.6665

Fit Statistics
-2 Res Log Likelihood 261.4
AIC (smaller is better) 263.4
AICC (smaller is better) 263.5
BIC (smaller is better) 265.6

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
handicap 4 65 2.86 0.0301

Least Squares Means
Effect handicap Estimate Standard Error DF t Value Pr > |t|
handicap NONE 4.9000 0.4364 65 11.23 <.0001
handicap AMPUTEE 4.4286 0.4364 65 10.15 <.0001
handicap CRUTCHES 5.9214 0.4364 65 13.57 <.0001
handicap HEARING 4.0500 0.4364 65 9.28 <.0001
handicap WHEELCHAIR 5.3429 0.4364 65 12.24 <.0001
handicap NONE 4.9000 0.4364 65 11.23 <.0001
handicap AMPUTEE 4.4286 0.4364 65 10.15 <.0001
handicap CRUTCHES 5.9214 0.4364 65 13.57 <.0001
handicap HEARING 4.0500 0.4364 65 9.28 <.0001
handicap WHEELCHAIR 5.3429 0.4364 65 12.24 <.0001
handicap NONE 4.9000 0.4364 65 11.23 <.0001
handicap AMPUTEE 4.4286 0.4364 65 10.15 <.0001
handicap CRUTCHES 5.9214 0.4364 65 13.57 <.0001
handicap HEARING 4.0500 0.4364 65 9.28 <.0001
handicap WHEELCHAIR 5.3429 0.4364 65 12.24 <.0001
handicap NONE 4.9000 0.4364 65 11.23 <.0001
handicap AMPUTEE 4.4286 0.4364 65 10.15 <.0001
handicap CRUTCHES 5.9214 0.4364 65 13.57 <.0001
handicap HEARING 4.0500 0.4364 65 9.28 <.0001
handicap WHEELCHAIR 5.3429 0.4364 65 12.24 <.0001

Differences of Least Squares Means
Effect handicap _handicap Estimate Standard Error DF t Value Pr > |t| Adjustment Adj P
handicap NONE AMPUTEE 0.4714 0.6172 65 0.76 0.4477   .
handicap NONE CRUTCHES -1.0214 0.6172 65 -1.65 0.1028   .
handicap NONE HEARING 0.8500 0.6172 65 1.38 0.1732   .
handicap NONE WHEELCHAIR -0.4429 0.6172 65 -0.72 0.4756   .
handicap AMPUTEE CRUTCHES -1.4929 0.6172 65 -2.42 0.0184   .
handicap AMPUTEE HEARING 0.3786 0.6172 65 0.61 0.5418   .
handicap AMPUTEE WHEELCHAIR -0.9143 0.6172 65 -1.48 0.1433   .
handicap CRUTCHES HEARING 1.8714 0.6172 65 3.03 0.0035   .
handicap CRUTCHES WHEELCHAIR 0.5786 0.6172 65 0.94 0.3520   .
handicap HEARING WHEELCHAIR -1.2929 0.6172 65 -2.09 0.0401   .
handicap NONE AMPUTEE 0.4714 0.6172 65 0.76 0.4477 Tukey 0.9400
handicap NONE CRUTCHES -1.0214 0.6172 65 -1.65 0.1028 Tukey 0.4686
handicap NONE HEARING 0.8500 0.6172 65 1.38 0.1732 Tukey 0.6443
handicap NONE WHEELCHAIR -0.4429 0.6172 65 -0.72 0.4756 Tukey 0.9517
handicap AMPUTEE CRUTCHES -1.4929 0.6172 65 -2.42 0.0184 Tukey 0.1233
handicap AMPUTEE HEARING 0.3786 0.6172 65 0.61 0.5418 Tukey 0.9725
handicap AMPUTEE WHEELCHAIR -0.9143 0.6172 65 -1.48 0.1433 Tukey 0.5781
handicap CRUTCHES HEARING 1.8714 0.6172 65 3.03 0.0035 Tukey 0.0278
handicap CRUTCHES WHEELCHAIR 0.5786 0.6172 65 0.94 0.3520 Tukey 0.8812
handicap HEARING WHEELCHAIR -1.2929 0.6172 65 -2.09 0.0401 Tukey 0.2348
handicap NONE AMPUTEE 0.4714 0.6172 65 0.76 0.4477 Scheffe 0.9642
handicap NONE CRUTCHES -1.0214 0.6172 65 -1.65 0.1028 Scheffe 0.6051
handicap NONE HEARING 0.8500 0.6172 65 1.38 0.1732 Scheffe 0.7545
handicap NONE WHEELCHAIR -0.4429 0.6172 65 -0.72 0.4756 Scheffe 0.9715
handicap AMPUTEE CRUTCHES -1.4929 0.6172 65 -2.42 0.0184 Scheffe 0.2238
handicap AMPUTEE HEARING 0.3786 0.6172 65 0.61 0.5418 Scheffe 0.9840
handicap AMPUTEE WHEELCHAIR -0.9143 0.6172 65 -1.48 0.1433 Scheffe 0.7007
handicap CRUTCHES HEARING 1.8714 0.6172 65 3.03 0.0035 Scheffe 0.0682
handicap CRUTCHES WHEELCHAIR 0.5786 0.6172 65 0.94 0.3520 Scheffe 0.9265
handicap HEARING WHEELCHAIR -1.2929 0.6172 65 -2.09 0.0401 Scheffe 0.3656
handicap NONE AMPUTEE 0.4714 0.6172 65 0.76 0.4477 Bonferroni 1.0000
handicap NONE CRUTCHES -1.0214 0.6172 65 -1.65 0.1028 Bonferroni 1.0000
handicap NONE HEARING 0.8500 0.6172 65 1.38 0.1732 Bonferroni 1.0000
handicap NONE WHEELCHAIR -0.4429 0.6172 65 -0.72 0.4756 Bonferroni 1.0000
handicap AMPUTEE CRUTCHES -1.4929 0.6172 65 -2.42 0.0184 Bonferroni 0.1838
handicap AMPUTEE HEARING 0.3786 0.6172 65 0.61 0.5418 Bonferroni 1.0000
handicap AMPUTEE WHEELCHAIR -0.9143 0.6172 65 -1.48 0.1433 Bonferroni 1.0000
handicap CRUTCHES HEARING 1.8714 0.6172 65 3.03 0.0035 Bonferroni 0.0349
handicap CRUTCHES WHEELCHAIR 0.5786 0.6172 65 0.94 0.3520 Bonferroni 1.0000
handicap HEARING WHEELCHAIR -1.2929 0.6172 65 -2.09 0.0401 Bonferroni 0.4010