Chapter 11b: Descriptive Statistics for Student and Year-Specific Class Variables

The FREQ Procedure

girl: Student is Boy=0 or Girl=1
girl Frequency Percent Cumulative
Frequency		 Cumulative
Percent
0 263 54.12 263 54.12
1 223 45.88 486 100.00

Frequency
Percent
Row Pct
Col Pct
Table of ClassID_year0 by grade_year0
ClassID_year0(ClassID_year0:
Class ID Variable
at Year 0)		 grade_year0(grade_year0: Class is Grade
3, 4, or 5 at Year 0)
3 4 5 Total
1
24
5.85
100.00
17.02
0
0.00
0.00
0.00
0
0.00
0.00
0.00
24
5.85
 
 
3
24
5.85
100.00
17.02
0
0.00
0.00
0.00
0
0.00
0.00
0.00
24
5.85
 
 
4
25
6.10
100.00
17.73
0
0.00
0.00
0.00
0
0.00
0.00
0.00
25
6.10
 
 
5
21
5.12
100.00
14.89
0
0.00
0.00
0.00
0
0.00
0.00
0.00
21
5.12
 
 
6
25
6.10
100.00
17.73
0
0.00
0.00
0.00
0
0.00
0.00
0.00
25
6.10
 
 
7
22
5.37
100.00
15.60
0
0.00
0.00
0.00
0
0.00
0.00
0.00
22
5.37
 
 
8
0
0.00
0.00
0.00
24
5.85
100.00
17.39
0
0.00
0.00
0.00
24
5.85
 
 
10
0
0.00
0.00
0.00
24
5.85
100.00
17.39
0
0.00
0.00
0.00
24
5.85
 
 
11
0
0.00
0.00
0.00
22
5.37
100.00
15.94
0
0.00
0.00
0.00
22
5.37
 
 
12
0
0.00
0.00
0.00
21
5.12
100.00
15.22
0
0.00
0.00
0.00
21
5.12
 
 
13
0
0.00
0.00
0.00
25
6.10
100.00
18.12
0
0.00
0.00
0.00
25
6.10
 
 
14
0
0.00
0.00
0.00
22
5.37
100.00
15.94
0
0.00
0.00
0.00
22
5.37
 
 
15
0
0.00
0.00
0.00
0
0.00
0.00
0.00
26
6.34
100.00
19.85
26
6.34
 
 
16
0
0.00
0.00
0.00
0
0.00
0.00
0.00
12
2.93
100.00
9.16
12
2.93
 
 
17
0
0.00
0.00
0.00
0
0.00
0.00
0.00
22
5.37
100.00
16.79
22
5.37
 
 
18
0
0.00
0.00
0.00
0
0.00
0.00
0.00
21
5.12
100.00
16.03
21
5.12
 
 
19
0
0.00
0.00
0.00
0
0.00
0.00
0.00
27
6.59
100.00
20.61
27
6.59
 
 
20
0
0.00
0.00
0.00
0
0.00
0.00
0.00
23
5.61
100.00
17.56
23
5.61
 
 
Total
141
34.39
138
33.66
131
31.95
410
100.00
Frequency Missing = 76

Frequency
Percent
Row Pct
Col Pct
Table of ClassID_year1 by grade_year1
ClassID_year1(ClassID_year1:
Class ID Variable
at Year 1)		 grade_year1(grade_year1: Class is Grade
3, 4, or 5 at Year 1)
4 5 6 Total
21
22
5.46
100.00
17.89
0
0.00
0.00
0.00
0
0.00
0.00
0.00
22
5.46
 
 
23
18
4.47
100.00
14.63
0
0.00
0.00
0.00
0
0.00
0.00
0.00
18
4.47
 
 
24
21
5.21
100.00
17.07
0
0.00
0.00
0.00
0
0.00
0.00
0.00
21
5.21
 
 
25
21
5.21
100.00
17.07
0
0.00
0.00
0.00
0
0.00
0.00
0.00
21
5.21
 
 
26
21
5.21
100.00
17.07
0
0.00
0.00
0.00
0
0.00
0.00
0.00
21
5.21
 
 
27
20
4.96
100.00
16.26
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.96
 
 
28
0
0.00
0.00
0.00
24
5.96
100.00
16.22
0
0.00
0.00
0.00
24
5.96
 
 
29
0
0.00
0.00
0.00
11
2.73
100.00
7.43
0
0.00
0.00
0.00
11
2.73
 
 
30
0
0.00
0.00
0.00
21
5.21
100.00
14.19
0
0.00
0.00
0.00
21
5.21
 
 
31
0
0.00
0.00
0.00
24
5.96
100.00
16.22
0
0.00
0.00
0.00
24
5.96
 
 
32
0
0.00
0.00
0.00
23
5.71
100.00
15.54
0
0.00
0.00
0.00
23
5.71
 
 
33
0
0.00
0.00
0.00
21
5.21
100.00
14.19
0
0.00
0.00
0.00
21
5.21
 
 
34
0
0.00
0.00
0.00
24
5.96
100.00
16.22
0
0.00
0.00
0.00
24
5.96
 
 
35
0
0.00
0.00
0.00
0
0.00
0.00
0.00
23
5.71
100.00
17.42
23
5.71
 
 
36
0
0.00
0.00
0.00
0
0.00
0.00
0.00
22
5.46
100.00
16.67
22
5.46
 
 
37
0
0.00
0.00
0.00
0
0.00
0.00
0.00
19
4.71
100.00
14.39
19
4.71
 
 
38
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.96
100.00
15.15
20
4.96
 
 
39
0
0.00
0.00
0.00
0
0.00
0.00
0.00
17
4.22
100.00
12.88
17
4.22
 
 
40
0
0.00
0.00
0.00
0
0.00
0.00
0.00
13
3.23
100.00
9.85
13
3.23
 
 
41
0
0.00
0.00
0.00
0
0.00
0.00
0.00
18
4.47
100.00
13.64
18
4.47
 
 
Total
123
30.52
148
36.72
132
32.75
403
100.00
Frequency Missing = 83

Frequency
Percent
Row Pct
Col Pct
Table of ClassID_year2 by grade_year2
ClassID_year2(ClassID_year2:
Class ID Variable
at Year 2)		 grade_year2(grade_year2: Class is Grade
3, 4, or 5 at Year 2)
5 6 7 Total
42
15
3.74
100.00
11.63
0
0.00
0.00
0.00
0
0.00
0.00
0.00
15
3.74
 
 
43
13
3.24
100.00
10.08
0
0.00
0.00
0.00
0
0.00
0.00
0.00
13
3.24
 
 
44
17
4.24
100.00
13.18
0
0.00
0.00
0.00
0
0.00
0.00
0.00
17
4.24
 
 
45
24
5.99
100.00
18.60
0
0.00
0.00
0.00
0
0.00
0.00
0.00
24
5.99
 
 
46
24
5.99
100.00
18.60
0
0.00
0.00
0.00
0
0.00
0.00
0.00
24
5.99
 
 
47
20
4.99
100.00
15.50
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.99
 
 
48
16
3.99
100.00
12.40
0
0.00
0.00
0.00
0
0.00
0.00
0.00
16
3.99
 
 
49
0
0.00
0.00
0.00
26
6.48
100.00
16.25
0
0.00
0.00
0.00
26
6.48
 
 
50
0
0.00
0.00
0.00
26
6.48
100.00
16.25
0
0.00
0.00
0.00
26
6.48
 
 
51
0
0.00
0.00
0.00
25
6.23
100.00
15.63
0
0.00
0.00
0.00
25
6.23
 
 
52
0
0.00
0.00
0.00
20
4.99
100.00
12.50
0
0.00
0.00
0.00
20
4.99
 
 
53
0
0.00
0.00
0.00
25
6.23
100.00
15.63
0
0.00
0.00
0.00
25
6.23
 
 
54
0
0.00
0.00
0.00
12
2.99
100.00
7.50
0
0.00
0.00
0.00
12
2.99
 
 
55
0
0.00
0.00
0.00
26
6.48
100.00
16.25
0
0.00
0.00
0.00
26
6.48
 
 
56
0
0.00
0.00
0.00
0
0.00
0.00
0.00
17
4.24
100.00
15.18
17
4.24
 
 
57
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.99
100.00
17.86
20
4.99
 
 
59
0
0.00
0.00
0.00
0
0.00
0.00
0.00
16
3.99
100.00
14.29
16
3.99
 
 
60
0
0.00
0.00
0.00
0
0.00
0.00
0.00
19
4.74
100.00
16.96
19
4.74
 
 
61
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.99
100.00
17.86
20
4.99
 
 
63
0
0.00
0.00
0.00
0
0.00
0.00
0.00
20
4.99
100.00
17.86
20
4.99
 
 
Total
129
32.17
160
39.90
112
27.93
401
100.00
Frequency Missing = 85


Chapter 11b: Descriptive Statistics for Level-1 Time-Varying Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
CMgirl
effort
aggression
CMgirl: Class Proportion of Girls
effort: Teacher-Perceived Student Effort
aggression: Teacher-Perceived Student Aggression
1214
1214
1214
0.4588138
3.9925865
1.5348435
0.0672026
0.9862525
0.7536234
0.2941176
1.0000000
1.0000000
0.6500000
5.0000000
5.0000000


Ch 11b: Empty Means, Two-Level Model of Years Within Students
Predicting Teacher-Perceived Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 1
Columns in Z Per Subject 1
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3415.86365599  
1 2 3075.50193474 0.00005427
2 1 3075.47866838 0.00000002
3 1 3075.47865885 0.00000000

Convergence criteria met.

Estimated V Matrix for StudentID
4101
Row Col1 Col2
1 0.9858 0.5804
2 0.5804 0.9858

Estimated V Correlation Matrix
for StudentID 4101
Row Col1 Col2
1 1.0000 0.5887
2 0.5887 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5804 0.04982 11.65 <.0001
Residual   0.4055 0.02128 19.05 <.0001

Fit Statistics
-2 Res Log Likelihood 3075.5
AIC (smaller is better) 3079.5
AICC (smaller is better) 3079.5
BIC (smaller is better) 3087.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 340.38 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3075.5 2 3079.5 3079.5 3082.8 3087.9 3089.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 3.9699 0.03954 473 100.41 <.0001 0.05 3.8922 4.0476


Ch 11b: Saturated Means, Unstructured Variance Model
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 6
Columns in X 4
Columns in Z 0
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3415.14945543  
1 2 3064.21778997 0.00173519
2 1 3063.43738939 0.00002517
3 1 3063.42673670 0.00000001

Convergence criteria met.

Estimated R Matrix for StudentID
4103
Row Col1 Col2 Col3
1 0.9039 0.5942 0.5579
2 0.5942 1.0242 0.5965
3 0.5579 0.5965 1.0153

Estimated R Correlation Matrix for
StudentID 4103
Row Col1 Col2 Col3
1 1.0000 0.6176 0.5824
2 0.6176 1.0000 0.5849
3 0.5824 0.5849 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) StudentID 0.9039 0.06350 14.23 <.0001
UN(2,1) StudentID 0.5942 0.05718 10.39 <.0001
UN(2,2) StudentID 1.0242 0.07117 14.39 <.0001
UN(3,1) StudentID 0.5579 0.05495 10.15 <.0001
UN(3,2) StudentID 0.5965 0.05884 10.14 <.0001
UN(3,3) StudentID 1.0153 0.07159 14.18 <.0001

Fit Statistics
-2 Res Log Likelihood 3063.4
AIC (smaller is better) 3075.4
AICC (smaller is better) 3075.5
BIC (smaller is better) 3100.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 351.72 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3063.4 6 3075.4 3075.5 3085.3 3100.5 3106.5

Solution for Fixed Effects
Effect year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   3.9242 0.04861 436 80.74 <.0001 0.05 3.8287 4.0197
year 0 0.1527 0.04621 407 3.31 0.0010 0.05 0.06190 0.2436
year 1 -0.02107 0.04744 391 -0.44 0.6572 0.05 -0.1143 0.07221
year 2 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year 2 385 18.52 9.26 <.0001 0.0001

Least Squares Means
Effect year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
year 0 4.0770 0.04546 436 89.67 <.0001 0.05 3.9876 4.1663
year 1 3.9031 0.04866 447 80.21 <.0001 0.05 3.8075 3.9988
year 2 3.9242 0.04861 436 80.74 <.0001 0.05 3.8287 4.0197

Differences of Least Squares Means
Effect year:
Year of
Study
(0-2)		 year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
year 0 1 0.1738 0.04406 376 3.94 <.0001 0.05 0.08718 0.2604
year 0 2 0.1527 0.04621 407 3.31 0.0010 0.05 0.06190 0.2436
year 1 2 -0.02107 0.04744 391 -0.44 0.6572 0.05 -0.1143 0.07221


Ch 11b: Piecewise Means, Random Intercept Model
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 3
Columns in Z Per Subject 1
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3415.14945543  
1 2 3067.75676056 0.00005346
2 1 3067.73395421 0.00000002
3 1 3067.73394506 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5821 0.04968 11.72 <.0001
Residual   0.3979 0.02091 19.03 <.0001

Fit Statistics
-2 Res Log Likelihood 3067.7
AIC (smaller is better) 3071.7
AICC (smaller is better) 3071.7
BIC (smaller is better) 3080.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 347.42 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3067.7 2 3071.7 3071.7 3075.0 3080.1 3082.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 3.9056 0.04765 872 81.97 <.0001 0.05 3.8121 3.9991
year01 -0.1706 0.04558 764 -3.74 0.0002 0.05 -0.2601 -0.08114
year12 0.01833 0.04605 770 0.40 0.6907 0.05 -0.07206 0.1087

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 764 14.01 14.01 0.0002 0.0002
year12 1 770 0.16 0.16 0.6906 0.6907


Likelihood Ratio Test for FitPieceRI2E vs. FitSatUN2E

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2E 3067.7 2 3071.7 3080.1 . . .
FitSatUN2E 3063.4 6 3075.4 3100.5 4.30721 4 0.36602


Eq 11b.13: Adding Fixed Effects of Year-Specific Class
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 64
Columns in Z Per Subject 1
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3324.11490207  
1 2 2949.26253162 0.00076259
2 1 2948.93328602 0.00000428
3 1 2948.93151696 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5960 0.04995 11.93 <.0001
Residual   0.3255 0.01792 18.16 <.0001

Fit Statistics
-2 Res Log Likelihood 2948.9
AIC (smaller is better) 2952.9
AICC (smaller is better) 2952.9
BIC (smaller is better) 2961.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 375.18 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2948.9 2 2952.9 2952.9 2956.2 2961.3 2963.3

Solution for Fixed Effects
Effect ClassID_year0:
Class ID
Variable
at Year 0		 ClassID_year1:
Class ID
Variable
at Year 1		 ClassID_year2:
Class ID
Variable
at Year 2		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept       4.3076 0.1750 1063 24.62 <.0001 0.05 3.9642 4.6509
year01       0.6721 0.2225 880 3.02 0.0026 0.05 0.2353 1.1088
year12       -0.3713 0.2208 821 -1.68 0.0930 0.05 -0.8048 0.06211
aclass0*ClassID_year0 -99     0 . . . . . . .
aclass0*ClassID_year0 1     0.5249 0.2190 1098 2.40 0.0167 0.05 0.09519 0.9546
aclass0*ClassID_year0 3     0.6042 0.2185 1094 2.77 0.0058 0.05 0.1755 1.0328
aclass0*ClassID_year0 4     0.7557 0.2168 1101 3.49 0.0005 0.05 0.3303 1.1811
aclass0*ClassID_year0 5     0.3249 0.2273 1099 1.43 0.1532 0.05 -0.1211 0.7708
aclass0*ClassID_year0 6     -0.4751 0.2164 1099 -2.20 0.0283 0.05 -0.8996 -0.05054
aclass0*ClassID_year0 7     0.3401 0.2240 1097 1.52 0.1293 0.05 -0.09948 0.7796
aclass0*ClassID_year0 8     0.4521 0.2166 1085 2.09 0.0371 0.05 0.02716 0.8771
aclass0*ClassID_year0 10     0.8411 0.2166 1081 3.88 0.0001 0.05 0.4162 1.2661
aclass0*ClassID_year0 11     0.4883 0.2201 1073 2.22 0.0267 0.05 0.05655 0.9201
aclass0*ClassID_year0 12     0.6711 0.2255 1087 2.98 0.0030 0.05 0.2287 1.1136
aclass0*ClassID_year0 13     0.6557 0.2139 1081 3.07 0.0022 0.05 0.2361 1.0754
aclass0*ClassID_year0 14     0.3955 0.2206 1077 1.79 0.0733 0.05 -0.03733 0.8284
aclass0*ClassID_year0 15     0.4983 0.2028 875 2.46 0.0142 0.05 0.1002 0.8964
aclass0*ClassID_year0 16     0.6454 0.2642 980 2.44 0.0147 0.05 0.1270 1.1638
aclass0*ClassID_year0 17     0.2646 0.2121 884 1.25 0.2124 0.05 -0.1516 0.6808
aclass0*ClassID_year0 18     0.7679 0.2146 884 3.58 0.0004 0.05 0.3468 1.1890
aclass0*ClassID_year0 19     0.2087 0.1989 851 1.05 0.2943 0.05 -0.1817 0.5991
aclass0*ClassID_year0 20     0 . . . . . . .
aclass1*ClassID_year1   -99   0 . . . . . . .
aclass1*ClassID_year1   21   -0.3010 0.2359 1069 -1.28 0.2021 0.05 -0.7639 0.1618
aclass1*ClassID_year1   23   0.07002 0.2467 1058 0.28 0.7766 0.05 -0.4141 0.5541
aclass1*ClassID_year1   24   -0.3905 0.2376 1063 -1.64 0.1005 0.05 -0.8567 0.07563
aclass1*ClassID_year1   25   -0.1678 0.2368 1059 -0.71 0.4788 0.05 -0.6324 0.2969
aclass1*ClassID_year1   26   -0.4140 0.2371 1062 -1.75 0.0812 0.05 -0.8793 0.05135
aclass1*ClassID_year1   27   -0.4816 0.2389 1054 -2.02 0.0440 0.05 -0.9502 -0.01287
aclass1*ClassID_year1   28   -0.2954 0.2305 1066 -1.28 0.2004 0.05 -0.7476 0.1569
aclass1*ClassID_year1   29   -0.9708 0.3064 1155 -3.17 0.0016 0.05 -1.5720 -0.3697
aclass1*ClassID_year1   30   -0.4296 0.2365 1053 -1.82 0.0696 0.05 -0.8938 0.03453
aclass1*ClassID_year1   31   -0.4364 0.2300 1062 -1.90 0.0580 0.05 -0.8877 0.01486
aclass1*ClassID_year1   32   -0.5117 0.2318 1058 -2.21 0.0275 0.05 -0.9666 -0.05679
aclass1*ClassID_year1   33   -1.0117 0.2358 1050 -4.29 <.0001 0.05 -1.4744 -0.5489
aclass1*ClassID_year1   34   -0.2055 0.2310 1069 -0.89 0.3740 0.05 -0.6588 0.2479
aclass1*ClassID_year1   35   -0.3018 0.2243 889 -1.35 0.1788 0.05 -0.7421 0.1384
aclass1*ClassID_year1   36   -0.4828 0.2219 840 -2.18 0.0298 0.05 -0.9183 -0.04735
aclass1*ClassID_year1   37   -0.3026 0.2311 854 -1.31 0.1907 0.05 -0.7561 0.1509
aclass1*ClassID_year1   38   -0.7549 0.2294 863 -3.29 0.0010 0.05 -1.2051 -0.3047
aclass1*ClassID_year1   39   -0.6238 0.2400 877 -2.60 0.0095 0.05 -1.0949 -0.1527
aclass1*ClassID_year1   40   -0.4575 0.2684 964 -1.70 0.0887 0.05 -0.9842 0.06931
aclass1*ClassID_year1   41   0 . . . . . . .
aclass2*ClassID_year2     -99 0 . . . . . . .
aclass2*ClassID_year2     42 0.2133 0.2482 1029 0.86 0.3903 0.05 -0.2737 0.7002
aclass2*ClassID_year2     43 0.5281 0.2775 1132 1.90 0.0573 0.05 -0.01642 1.0726
aclass2*ClassID_year2     44 0.1299 0.2402 1037 0.54 0.5886 0.05 -0.3414 0.6013
aclass2*ClassID_year2     45 -0.05505 0.2224 1068 -0.25 0.8046 0.05 -0.4915 0.3814
aclass2*ClassID_year2     46 -0.07331 0.2223 1067 -0.33 0.7417 0.05 -0.5095 0.3629
aclass2*ClassID_year2     47 -0.8170 0.2312 1051 -3.53 0.0004 0.05 -1.2706 -0.3634
aclass2*ClassID_year2     48 -0.2093 0.2434 1029 -0.86 0.3900 0.05 -0.6870 0.2683
aclass2*ClassID_year2     49 0.3947 0.2203 1078 1.79 0.0735 0.05 -0.03767 0.8270
aclass2*ClassID_year2     50 -0.06578 0.2206 1081 -0.30 0.7656 0.05 -0.4986 0.3671
aclass2*ClassID_year2     51 0.2025 0.2205 1067 0.92 0.3587 0.05 -0.2302 0.6352
aclass2*ClassID_year2     52 0.2121 0.2300 1041 0.92 0.3568 0.05 -0.2393 0.6634
aclass2*ClassID_year2     53 0.1831 0.2205 1067 0.83 0.4065 0.05 -0.2495 0.6157
aclass2*ClassID_year2     54 0.04805 0.2946 1155 0.16 0.8705 0.05 -0.5299 0.6260
aclass2*ClassID_year2     55 0.4644 0.2195 1075 2.12 0.0346 0.05 0.03364 0.8952
aclass2*ClassID_year2     56 -0.05137 0.2305 848 -0.22 0.8237 0.05 -0.5037 0.4010
aclass2*ClassID_year2     57 -0.3862 0.2169 805 -1.78 0.0753 0.05 -0.8119 0.03952
aclass2*ClassID_year2     59 -0.6327 0.2340 843 -2.70 0.0070 0.05 -1.0919 -0.1734
aclass2*ClassID_year2     60 -0.2030 0.2228 838 -0.91 0.3625 0.05 -0.6404 0.2344
aclass2*ClassID_year2     61 -0.3396 0.2169 805 -1.57 0.1178 0.05 -0.7653 0.08616
aclass2*ClassID_year2     63 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 0 . . . . .
year12 0 . . . . .
aclass0*ClassID_year0 17 884 77.87 4.58 <.0001 <.0001
aclass1*ClassID_year1 19 881 47.72 2.51 0.0003 0.0004
aclass2*ClassID_year2 19 890 73.95 3.89 <.0001 <.0001


PsuedoR2 (% Reduction) for CovPieceRI2E vs. CovClassFixedE

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovPieceRI2E UN(1,1) StudentID 0.5821 0.04968 11.72 <.0001 .
CovPieceRI2E Residual   0.3979 0.02091 19.03 <.0001 .
CovClassFixedE UN(1,1) StudentID 0.5960 0.04995 11.93 <.0001 -0.02385
CovClassFixedE Residual   0.3255 0.01792 18.16 <.0001 0.18214


Eq 11b.14: Adding Random Acute Year-Specific Class Effects
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 3
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3415.14945543  
1 3 2984.87334748 0.00053246
2 1 2984.65390765 0.00001369
3 1 2984.64858631 0.00000002
4 1 2984.64857871 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5925 0.04922 12.04 <.0001
UN(1,1) ClassID_year0 0.08082 0.03521 2.30 0.0109
UN(1,1) ClassID_year1 0.04766 0.02511 1.90 0.0288
UN(1,1) ClassID_year2 0.08706 0.03782 2.30 0.0107
Residual   0.3262 0.01790 18.22 <.0001

Fit Statistics
-2 Res Log Likelihood 2984.6
AIC (smaller is better) 2994.6
AICC (smaller is better) 2994.7
BIC (smaller is better) 2984.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 430.50 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2984.6 5 2994.6 2994.7 2984.6 2984.6 2989.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 3.8943 0.06726 25.5 57.90 <.0001 0.05 3.7560 4.0327
year01 -0.1817 0.09303 29.2 -1.95 0.0605 0.05 -0.3719 0.008564
year12 0.02060 0.09265 30.5 0.22 0.8256 0.05 -0.1685 0.2097

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 29.2 3.81 3.81 0.0509 0.0605
year12 1 30.5 0.05 0.05 0.8241 0.8256


Likelihood Ratio Test for FitPieceRI2E vs. FitClassAcuteE

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2E 3067.7 2 3071.7 3080.1 . . .
FitClassAcuteE 2984.6 5 2994.6 2984.6 83.0854 3 0


Ch 11b: Adding Random Transfer Class Effects Instead
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 3
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3415.14945543  
1 2 3021.85861019 0.00231081
2 1 3020.75500045 0.00039873
3 1 3020.57629270 0.00002075
4 1 3020.56773998 0.00000007
5 1 3020.56771163 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5481 0.04790 11.44 <.0001
UN(1,1) ClassID_year0 0.04774 0.03019 1.58 0.0569
UN(1,1) ClassID_year1 0.04269 0.02262 1.89 0.0296
UN(1,1) ClassID_year2 0.09338 0.04032 2.32 0.0103
Residual   0.3577 0.01939 18.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3020.6
AIC (smaller is better) 3030.6
AICC (smaller is better) 3030.6
BIC (smaller is better) 3020.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 394.58 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3020.6 5 3030.6 3030.6 3020.6 3020.6 3025.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 3.8401 0.07286 46.4 52.71 <.0001 0.05 3.6935 3.9867
year01 -0.1795 0.06090 38.4 -2.95 0.0054 0.05 -0.3028 -0.05626
year12 0.02268 0.08170 21.7 0.28 0.7839 0.05 -0.1469 0.1922

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 38.4 8.69 8.69 0.0032 0.0054
year12 1 21.7 0.08 0.08 0.7813 0.7839


Likelihood Ratio Test for FitPieceRI2E vs. FitClassTransE

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2E 3067.7 2 3071.7 3080.1 . . .
FitClassTransE 3020.6 5 3030.6 3020.6 47.1662 3 3.2038E-10


Eq 11b.15: Adding Year-Specific Effects of Class Grade
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 18
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3396.74919049  
1 2 2982.73489136 0.00027312
2 1 2982.62703943 0.00000053
3 1 2982.62683428 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5909 0.04916 12.02 <.0001
UN(1,1) ClassID_year0 0.08326 0.03811 2.18 0.0144
UN(1,1) ClassID_year1 0.03880 0.02223 1.75 0.0405
UN(1,1) ClassID_year2 0.05596 0.02876 1.95 0.0258
Residual   0.3271 0.01798 18.20 <.0001

Fit Statistics
-2 Res Log Likelihood 2982.6
AIC (smaller is better) 2992.6
AICC (smaller is better) 2992.7
BIC (smaller is better) 2982.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 414.12 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2982.6 5 2992.6 2992.7 2982.6 2982.6 2987.6

Solution for Fixed Effects
Effect grade:
Class
Grade		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   3.8906 0.1102 28.8 35.29 <.0001 0.05 3.6651 4.1161
year01   -0.1341 0.1581 25 -0.85 0.4042 0.05 -0.4596 0.1914
year12   -0.2204 0.1443 25.7 -1.53 0.1388 0.05 -0.5172 0.07629
aclass0*grade 3 -0.03588 0.2018 20.4 -0.18 0.8607 0.05 -0.4564 0.3846
aclass0*grade 4 0.1878 0.2014 20.3 0.93 0.3622 0.05 -0.2320 0.6076
aclass0*grade 5 0 . . . . . . .
aclass0*grade 6 0 . . . . . . .
aclass0*grade 7 0 . . . . . . .
aclass1*grade 3 0 . . . . . . .
aclass1*grade 4 0.1435 0.1592 26.9 0.90 0.3757 0.05 -0.1834 0.4703
aclass1*grade 5 -0.1120 0.1537 27 -0.73 0.4724 0.05 -0.4273 0.2033
aclass1*grade 6 0 . . . . . . .
aclass1*grade 7 0 . . . . . . .
aclass2*grade 3 0 . . . . . . .
aclass2*grade 4 0 . . . . . . .
aclass2*grade 5 0.2073 0.1766 24.3 1.17 0.2517 0.05 -0.1569 0.5715
aclass2*grade 6 0.4819 0.1738 22.7 2.77 0.0109 0.05 0.1222 0.8416
aclass2*grade 7 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 0 . . . . .
year12 0 . . . . .
aclass0*grade 2 20.2 1.44 0.72 0.4867 0.4988
aclass1*grade 2 26.4 2.65 1.32 0.2661 0.2832
aclass2*grade 2 23.4 7.83 3.92 0.0199 0.0341

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Grade 3 vs 4 at Year 0 0.2236 0.2001 19.8 1.12 0.2770 0.05 -0.1939 0.6412
Grade 3 vs 5 at Year 0 0.03588 0.2018 20.4 0.18 0.8607 0.05 -0.3846 0.4564
Grade 4 vs 5 at Year 0 -0.1878 0.2014 20.3 -0.93 0.3622 0.05 -0.6076 0.2320
Grade 4 vs 5 at Year 1 -0.2554 0.1571 25.3 -1.63 0.1163 0.05 -0.5787 0.06785
Grade 4 vs 6 at Year 1 -0.1435 0.1592 26.9 -0.90 0.3757 0.05 -0.4703 0.1834
Grade 5 vs 6 at Year 1 0.1120 0.1537 27 0.73 0.4724 0.05 -0.2033 0.4273
Grade 5 vs 6 at Year 2 0.2746 0.1683 23.3 1.63 0.1162 0.05 -0.07328 0.6224
Grade 5 vs 7 at Year 2 -0.2073 0.1766 24.3 -1.17 0.2517 0.05 -0.5715 0.1569
Grade 6 vs 7 at Year 2 -0.4819 0.1738 22.7 -2.77 0.0109 0.05 -0.8416 -0.1222


PsuedoR2 (% Reduction) for CovClassAcuteE vs. CovGradeE

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovClassAcuteE UN(1,1) StudentID 0.5925 0.04922 12.04 <.0001 .
CovClassAcuteE UN(1,1) ClassID_year0 0.08082 0.03521 2.30 0.0109 .
CovClassAcuteE UN(1,1) ClassID_year1 0.04766 0.02511 1.90 0.0288 .
CovClassAcuteE UN(1,1) ClassID_year2 0.08706 0.03782 2.30 0.0107 .
CovClassAcuteE Residual   0.3262 0.01790 18.22 <.0001 .
CovGradeE UN(1,1) StudentID 0.5909 0.04916 12.02 <.0001 0.00263
CovGradeE UN(1,1) ClassID_year0 0.08326 0.03811 2.18 0.0144 -0.03020
CovGradeE UN(1,1) ClassID_year1 0.03880 0.02223 1.75 0.0405 0.18597
CovGradeE UN(1,1) ClassID_year2 0.05596 0.02876 1.95 0.0258 0.35719
CovGradeE Residual   0.3271 0.01798 18.20 <.0001 -0.00267


Eq 11b.16: Adding Student Gender and Year-Specific Class Contextual Gender Effects
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 22
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 3377.80108341  
1 2 2968.35487287 0.00016785
2 1 2968.28948885 0.00000025
3 1 2968.28939467 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.5775 0.04825 11.97 <.0001
UN(1,1) ClassID_year0 0.08650 0.04067 2.13 0.0167
UN(1,1) ClassID_year1 0.04304 0.02439 1.76 0.0388
UN(1,1) ClassID_year2 0.06136 0.03158 1.94 0.0260
Residual   0.3265 0.01792 18.22 <.0001

Fit Statistics
-2 Res Log Likelihood 2968.3
AIC (smaller is better) 2978.3
AICC (smaller is better) 2978.3
BIC (smaller is better) 2968.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 409.51 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2968.3 5 2978.3 2978.3 2968.3 2968.3 2973.3

Solution for Fixed Effects
Effect grade:
Class
Grade		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   3.7657 0.1263 27.6 29.82 <.0001 0.05 3.5069 4.0246
year01   -0.1641 0.1731 25.1 -0.95 0.3520 0.05 -0.5205 0.1922
year12   -0.2395 0.1668 24.6 -1.44 0.1637 0.05 -0.5833 0.1043
aclass0*grade 3 -0.05791 0.2055 18.8 -0.28 0.7812 0.05 -0.4884 0.3726
aclass0*grade 4 0.2028 0.2047 18.4 0.99 0.3347 0.05 -0.2266 0.6321
aclass0*grade 5 0 . . . . . . .
aclass0*grade 6 0 . . . . . . .
aclass0*grade 7 0 . . . . . . .
aclass1*grade 3 0 . . . . . . .
aclass1*grade 4 0.1357 0.1631 24.6 0.83 0.4133 0.05 -0.2005 0.4720
aclass1*grade 5 -0.1122 0.1575 24.7 -0.71 0.4829 0.05 -0.4369 0.2125
aclass1*grade 6 0 . . . . . . .
aclass1*grade 7 0 . . . . . . .
aclass2*grade 3 0 . . . . . . .
aclass2*grade 4 0 . . . . . . .
aclass2*grade 5 0.2178 0.1844 21.7 1.18 0.2504 0.05 -0.1650 0.6006
aclass2*grade 6 0.4919 0.1795 20.7 2.74 0.0124 0.05 0.1183 0.8656
aclass2*grade 7 0 . . . . . . .
girl   0.2613 0.07767 462 3.36 0.0008 0.05 0.1087 0.4139
aclass0*CMgirl50   0.8410 1.3998 13.9 0.60 0.5576 0.05 -2.1630 3.8451
aclass1*CMgirl50   -0.1548 1.0747 16 -0.14 0.8873 0.05 -2.4332 2.1236
aclass2*CMgirl50   -0.3708 0.7948 14.8 -0.47 0.6477 0.05 -2.0673 1.3258

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 0 . . . . .
year12 0 . . . . .
aclass0*grade 2 18.4 1.75 0.88 0.4162 0.4329
aclass1*grade 2 24.1 2.38 1.19 0.3040 0.3213
aclass2*grade 2 21.2 7.66 3.83 0.0217 0.0380
girl 1 462 11.32 11.32 0.0008 0.0008
aclass0*CMgirl50 1 13.9 0.36 0.36 0.5480 0.5576
aclass1*CMgirl50 1 16 0.02 0.02 0.8855 0.8873
aclass2*CMgirl50 1 14.8 0.22 0.22 0.6409 0.6477

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Grade 3 vs 4 at Year 0 0.2607 0.2073 18 1.26 0.2247 0.05 -0.1749 0.6963
Grade 3 vs 5 at Year 0 0.05791 0.2055 18.8 0.28 0.7812 0.05 -0.3726 0.4884
Grade 4 vs 5 at Year 0 -0.2028 0.2047 18.4 -0.99 0.3347 0.05 -0.6321 0.2266
Grade 4 vs 5 at Year 1 -0.2480 0.1607 23.1 -1.54 0.1364 0.05 -0.5804 0.08441
Grade 4 vs 6 at Year 1 -0.1357 0.1631 24.6 -0.83 0.4133 0.05 -0.4720 0.2005
Grade 5 vs 6 at Year 1 0.1122 0.1575 24.7 0.71 0.4829 0.05 -0.2125 0.4369
Grade 5 vs 6 at Year 2 0.2741 0.1729 21.3 1.59 0.1276 0.05 -0.08515 0.6334
Grade 5 vs 7 at Year 2 -0.2178 0.1844 21.7 -1.18 0.2504 0.05 -0.6006 0.1650
Grade 6 vs 7 at Year 2 -0.4919 0.1795 20.7 -2.74 0.0124 0.05 -0.8656 -0.1183
Between-Class Gender Effect at Year 0 1.1023 1.4007 13.9 0.79 0.4445 0.05 -1.9029 4.1075
Between-Class Gender Effect at Year 1 0.1065 1.0760 16.1 0.10 0.9224 0.05 -2.1738 2.3867
Between-Class Gender Effect at Year 2 -0.1095 0.7964 14.9 -0.14 0.8925 0.05 -1.8083 1.5893

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Year-Specific Class Contextual Gender Effects 3 14.8 0.60 0.20 0.8956 0.8939


PsuedoR2 (% Reduction) for CovGradeE vs. CovGirlE

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovGradeE UN(1,1) StudentID 0.5909 0.04916 12.02 <.0001 .
CovGradeE UN(1,1) ClassID_year0 0.08326 0.03811 2.18 0.0144 .
CovGradeE UN(1,1) ClassID_year1 0.03880 0.02223 1.75 0.0405 .
CovGradeE UN(1,1) ClassID_year2 0.05596 0.02876 1.95 0.0258 .
CovGradeE Residual   0.3271 0.01798 18.20 <.0001 .
CovGirlE UN(1,1) StudentID 0.5775 0.04825 11.97 <.0001 0.02277
CovGirlE UN(1,1) ClassID_year0 0.08650 0.04067 2.13 0.0167 -0.03890
CovGirlE UN(1,1) ClassID_year1 0.04304 0.02439 1.76 0.0388 -0.10938
CovGirlE UN(1,1) ClassID_year2 0.06136 0.03158 1.94 0.0260 -0.09637
CovGirlE Residual   0.3265 0.01792 18.22 <.0001 0.00197


Ch 11b: Empty Means, Two-Level Model of Years Within Students
Predicting Teacher-Perceived Student Aggression

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable aggression
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 1
Columns in Z Per Subject 1
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2763.22197622  
1 2 2534.61046982 0.00186919
2 1 2534.31224174 0.00000967
3 1 2534.31076138 0.00000000

Convergence criteria met.

Estimated V Matrix for StudentID
4101
Row Col1 Col2
1 0.5848 0.3017
2 0.3017 0.5848

Estimated V Correlation Matrix
for StudentID 4101
Row Col1 Col2
1 1.0000 0.5159
2 0.5159 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.3017 0.02900 10.40 <.0001
Residual   0.2831 0.01508 18.78 <.0001

Fit Statistics
-2 Res Log Likelihood 2534.3
AIC (smaller is better) 2538.3
AICC (smaller is better) 2538.3
BIC (smaller is better) 2546.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 228.91 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2534.3 2 2538.3 2538.3 2541.6 2546.7 2548.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.5519 0.02959 449 52.44 <.0001 0.05 1.4938 1.6101


Ch 11b: Saturated Means, Unstructured Variance Model
Predicting Student Aggression

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable aggression
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 6
Columns in X 4
Columns in Z 0
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2767.82158403  
1 2 2538.85166579 0.03747846
2 1 2532.03886521 0.00355264
3 1 2531.45818707 0.00004271
4 1 2531.45160174 0.00000001

Convergence criteria met.

Estimated R Matrix for StudentID
4103
Row Col1 Col2 Col3
1 0.5937 0.3126 0.2659
2 0.3126 0.6123 0.3279
3 0.2659 0.3279 0.5458

Estimated R Correlation Matrix for
StudentID 4103
Row Col1 Col2 Col3
1 1.0000 0.5185 0.4672
2 0.5185 1.0000 0.5672
3 0.4672 0.5672 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) StudentID 0.5937 0.04300 13.81 <.0001
UN(2,1) StudentID 0.3126 0.03737 8.37 <.0001
UN(2,2) StudentID 0.6123 0.04316 14.19 <.0001
UN(3,1) StudentID 0.2659 0.03221 8.26 <.0001
UN(3,2) StudentID 0.3279 0.03410 9.62 <.0001
UN(3,3) StudentID 0.5458 0.03902 13.99 <.0001

Fit Statistics
-2 Res Log Likelihood 2531.5
AIC (smaller is better) 2543.5
AICC (smaller is better) 2543.5
BIC (smaller is better) 2568.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 236.37 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2531.5 6 2543.5 2543.5 2553.3 2568.6 2574.6

Solution for Fixed Effects
Effect year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   1.5741 0.03587 422 43.89 <.0001 0.05 1.5036 1.6446
year 0 -0.07228 0.03978 430 -1.82 0.0699 0.05 -0.1505 0.005901
year 1 0.009864 0.03664 376 0.27 0.7879 0.05 -0.06217 0.08190
year 2 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year 2 374 5.05 2.52 0.0801 0.0815

Least Squares Means
Effect year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
year 0 1.5018 0.03724 408 40.33 <.0001 0.05 1.4286 1.5750
year 1 1.5840 0.03783 433 41.87 <.0001 0.05 1.5096 1.6583
year 2 1.5741 0.03587 422 43.89 <.0001 0.05 1.5036 1.6446

Differences of Least Squares Means
Effect year:
Year of
Study
(0-2)		 year:
Year of
Study
(0-2)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
year 0 1 -0.08214 0.03880 351 -2.12 0.0349 0.05 -0.1584 -0.00584
year 0 2 -0.07228 0.03978 430 -1.82 0.0699 0.05 -0.1505 0.005901
year 1 2 0.009864 0.03664 376 0.27 0.7879 0.05 -0.06217 0.08190


Ch 11b: Piecewise Means, Random Intercept Model
Predicting Student Aggression

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable aggression
Covariance Structure Unstructured
Subject Effect StudentID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 3
Columns in Z Per Subject 1
Subjects 486
Max Obs Per Subject 3

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2767.82158403  
1 2 2539.10231760 0.00178532
2 1 2538.80996160 0.00000907
3 1 2538.80853697 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.3011 0.02894 10.41 <.0001
Residual   0.2823 0.01505 18.75 <.0001

Fit Statistics
-2 Res Log Likelihood 2538.8
AIC (smaller is better) 2542.8
AICC (smaller is better) 2542.8
BIC (smaller is better) 2551.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 229.01 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2538.8 2 2542.8 2542.8 2546.1 2551.2 2553.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.5825 0.03706 929 42.70 <.0001 0.05 1.5097 1.6552
year01 0.07988 0.03827 750 2.09 0.0372 0.05 0.004757 0.1550
year12 -0.01018 0.03864 757 -0.26 0.7922 0.05 -0.08603 0.06566

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 750 4.36 4.36 0.0368 0.0372
year12 1 757 0.07 0.07 0.7921 0.7922


Likelihood Ratio Test for FitPieceRI2A vs. FitSatUN2A

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2A 2538.8 2 2542.8 2551.2 . . .
FitSatUN2A 2531.5 6 2543.5 2568.6 7.35694 4 0.11819


Ch 11b: Adding Random Acute Year-Specific Class Effects
Predicting Student Aggression

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable aggression
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 3
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2767.82158403  
1 2 2305.62126084 0.00924899
2 1 2305.23274057 0.00006127
3 1 2305.23029231 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.3016 0.02719 11.09 <.0001
UN(1,1) ClassID_year0 0.1490 0.05519 2.70 0.0035
UN(1,1) ClassID_year1 0.08689 0.03572 2.43 0.0075
UN(1,1) ClassID_year2 0.07612 0.02931 2.60 0.0047
Residual   0.1869 0.01050 17.80 <.0001

Fit Statistics
-2 Res Log Likelihood 2305.2
AIC (smaller is better) 2315.2
AICC (smaller is better) 2315.3
BIC (smaller is better) 2305.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 462.59 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2305.2 5 2315.2 2315.3 2305.2 2305.2 2310.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6072 0.07416 19 21.67 <.0001 0.05 1.4520 1.7625
year01 0.1091 0.1169 29.8 0.93 0.3578 0.05 -0.1296 0.3479
year12 -0.03178 0.09599 31.8 -0.33 0.7428 0.05 -0.2274 0.1638

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 29.8 0.87 0.87 0.3503 0.3578
year12 1 31.8 0.11 0.11 0.7406 0.7428


Likelihood Ratio Test for FitPieceRI2A vs. FitClassAcuteA

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2A 2538.8 2 2542.8 2551.2 . . .
FitClassAcuteA 2305.2 5 2315.2 2305.2 233.578 3 0


Ch 11b: Adding Random Transfer Class Effects Instead
Predicting Student Aggression

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable aggression
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 3
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2767.82158403  
1 2 2445.36602117 0.01124362
2 1 2443.92556292 0.00142562
3 1 2443.75234786 0.00005915
4 1 2443.74569247 0.00000015
5 1 2443.74567621 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.2421 0.02541 9.53 <.0001
UN(1,1) ClassID_year0 0.06029 0.02921 2.06 0.0195
UN(1,1) ClassID_year1 0.06736 0.02962 2.27 0.0115
UN(1,1) ClassID_year2 0.08502 0.03414 2.49 0.0064
Residual   0.2474 0.01366 18.11 <.0001

Fit Statistics
-2 Res Log Likelihood 2443.7
AIC (smaller is better) 2453.7
AICC (smaller is better) 2453.8
BIC (smaller is better) 2443.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 324.08 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2443.7 5 2453.7 2453.8 2443.7 2443.7 2448.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6798 0.06953 75.4 24.16 <.0001 0.05 1.5413 1.8183
year01 0.09880 0.06123 43.4 1.61 0.1138 0.05 -0.02464 0.2222
year12 -0.02392 0.07509 21.7 -0.32 0.7531 0.05 -0.1798 0.1319

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 1 43.4 2.60 2.60 0.1066 0.1138
year12 1 21.7 0.10 0.10 0.7500 0.7531


Likelihood Ratio Test for FitPieceRI2A vs. FitClassTransA

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitPieceRI2A 2538.8 2 2542.8 2551.2 . . .
FitClassTransA 2443.7 5 2453.7 2443.7 95.0629 3 0


Ch 11b: Adding Time-Varying, Student Mean, and Year-Specific Class Contextual Effects of Student Aggression
Predicting Student Effort

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER11B
Dependent Variable effort
Covariance Structure Unstructured
Subject Effects StudentID, ClassID_year0, ClassID_year1, ClassID_year2
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 5
Columns in X 27
Columns in Z Per Subject 547
Subjects 1
Max Obs Per Subject 1214

Number of Observations
Number of Observations Read 1214
Number of Observations Used 1214
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 2901.94001410  
1 3 2596.63267715 0.00042742
2 1 2596.54045098 0.00001011
3 1 2596.53839250 0.00000001
4 1 2596.53839020 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) StudentID 0.3441 0.03080 11.17 <.0001
UN(1,1) ClassID_year0 0.01282 0.01200 1.07 0.1427
UN(1,1) ClassID_year1 0.02433 0.01601 1.52 0.0642
UN(1,1) ClassID_year2 0.03659 0.02125 1.72 0.0426
Residual   0.2664 0.01449 18.39 <.0001

Fit Statistics
-2 Res Log Likelihood 2596.5
AIC (smaller is better) 2606.5
AICC (smaller is better) 2606.6
BIC (smaller is better) 2596.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 305.40 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2596.5 5 2606.5 2606.6 2596.5 2596.5 2601.5

Solution for Fixed Effects
Effect grade:
Class
Grade		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   3.5931 0.1159 25.6 31.00 <.0001 0.05 3.3547 3.8315
year01   -0.05146 0.1307 26.2 -0.39 0.6970 0.05 -0.3201 0.2172
year12   -0.2437 0.1537 25.1 -1.59 0.1252 0.05 -0.5601 0.07268
aclass0*grade 3 0.004914 0.1151 20.8 0.04 0.9663 0.05 -0.2345 0.2444
aclass0*grade 4 0.1181 0.1165 19.1 1.01 0.3232 0.05 -0.1256 0.3619
aclass0*grade 5 0 . . . . . . .
aclass0*grade 6 0 . . . . . . .
aclass0*grade 7 0 . . . . . . .
aclass1*grade 3 0 . . . . . . .
aclass1*grade 4 0.04193 0.1328 22 0.32 0.7551 0.05 -0.2334 0.3172
aclass1*grade 5 -0.08934 0.1247 22.3 -0.72 0.4810 0.05 -0.3477 0.1690
aclass1*grade 6 0 . . . . . . .
aclass1*grade 7 0 . . . . . . .
aclass2*grade 3 0 . . . . . . .
aclass2*grade 4 0 . . . . . . .
aclass2*grade 5 0.2015 0.1475 19.4 1.37 0.1874 0.05 -0.1067 0.5098
aclass2*grade 6 0.4110 0.1472 18.4 2.79 0.0119 0.05 0.1022 0.7199
aclass2*grade 7 0 . . . . . . .
girl   0.07658 0.06301 464 1.22 0.2249 0.05 -0.04724 0.2004
aclass0*CMgirl50   1.2541 0.7318 11.7 1.71 0.1129 0.05 -0.3450 2.8532
aclass1*CMgirl50   -0.1972 0.8857 15.7 -0.22 0.8267 0.05 -2.0782 1.6839
aclass2*CMgirl50   0.01186 0.6591 13.8 0.02 0.9859 0.05 -1.4036 1.4273
agg2   -0.6055 0.04390 783 -13.79 <.0001 0.05 -0.6917 -0.5194
SMagg2   -0.1977 0.06243 1058 -3.17 0.0016 0.05 -0.3202 -0.07515
aclass0*CMagg2   0.004472 0.1087 14.7 0.04 0.9677 0.05 -0.2276 0.2366
aclass1*CMagg2   0.1260 0.1372 22.9 0.92 0.3679 0.05 -0.1579 0.4099
aclass2*CMagg2   0.06775 0.1808 15.2 0.37 0.7130 0.05 -0.3170 0.4525

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
year01 0 . . . . .
year12 0 . . . . .
aclass0*grade 2 19.5 1.27 0.64 0.5287 0.5393
aclass1*grade 2 21.3 1.08 0.54 0.5834 0.5911
aclass2*grade 2 18.8 7.84 3.92 0.0199 0.0378
girl 1 464 1.48 1.48 0.2242 0.2249
aclass0*CMgirl50 1 11.7 2.94 2.94 0.0866 0.1129
aclass1*CMgirl50 1 15.7 0.05 0.05 0.8239 0.8267
aclass2*CMgirl50 1 13.8 0.00 0.00 0.9856 0.9859
agg2 1 783 190.27 190.27 <.0001 <.0001
SMagg2 1 1058 10.02 10.02 0.0015 0.0016
aclass0*CMagg2 1 14.7 0.00 0.00 0.9672 0.9677
aclass1*CMagg2 1 22.9 0.84 0.84 0.3583 0.3679
aclass2*CMagg2 1 15.2 0.14 0.14 0.7078 0.7130

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Grade 3 vs 4 at Year 0 0.1132 0.1189 18.7 0.95 0.3529 0.05 -0.1358 0.3623
Grade 3 vs 5 at Year 0 -0.00491 0.1151 20.8 -0.04 0.9663 0.05 -0.2444 0.2345
Grade 4 vs 5 at Year 0 -0.1181 0.1165 19.1 -1.01 0.3232 0.05 -0.3619 0.1256
Grade 4 vs 5 at Year 1 -0.1313 0.1315 19.8 -1.00 0.3303 0.05 -0.4059 0.1433
Grade 4 vs 6 at Year 1 -0.04193 0.1328 22 -0.32 0.7551 0.05 -0.3172 0.2334
Grade 5 vs 6 at Year 1 0.08934 0.1247 22.3 0.72 0.4810 0.05 -0.1690 0.3477
Grade 5 vs 6 at Year 2 0.2095 0.1399 18.7 1.50 0.1508 0.05 -0.08350 0.5025
Grade 5 vs 7 at Year 2 -0.2015 0.1475 19.4 -1.37 0.1874 0.05 -0.5098 0.1067
Grade 6 vs 7 at Year 2 -0.4110 0.1472 18.4 -2.79 0.0119 0.05 -0.7199 -0.1022
Between-Class Gender Effect at Year 0 1.3307 0.7325 11.7 1.82 0.0949 0.05 -0.2691 2.9305
Between-Class Gender Effect at Year 1 -0.1206 0.8865 15.7 -0.14 0.8935 0.05 -2.0027 1.7616
Between-Class Gender Effect at Year 2 0.08844 0.6601 13.9 0.13 0.8953 0.05 -1.3283 1.5052
Between-Class Aggression Effect at Year 0 -0.7987 0.1144 18.1 -6.98 <.0001 0.05 -1.0390 -0.5584
Between-Class Aggression Effect at Year 1 -0.6772 0.1391 24.4 -4.87 <.0001 0.05 -0.9640 -0.3903
Between-Class Aggression Effect at Year 2 -0.7354 0.1838 16.3 -4.00 0.0010 0.05 -1.1244 -0.3465
Between-Student Aggression Effect -0.8032 0.04846 550 -16.58 <.0001 0.05 -0.8984 -0.7080

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Year-Specific Class Contextual Aggression Effects 3 17.7 0.94 0.31 0.8160 0.8157


PsuedoR2 (% Reduction) for CovGirlE vs. CovAggE

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovGirlE UN(1,1) StudentID 0.5775 0.04825 11.97 <.0001 .
CovGirlE UN(1,1) ClassID_year0 0.08650 0.04067 2.13 0.0167 .
CovGirlE UN(1,1) ClassID_year1 0.04304 0.02439 1.76 0.0388 .
CovGirlE UN(1,1) ClassID_year2 0.06136 0.03158 1.94 0.0260 .
CovGirlE Residual   0.3265 0.01792 18.22 <.0001 .
CovAggE UN(1,1) StudentID 0.3441 0.03080 11.17 <.0001 0.40418
CovAggE UN(1,1) ClassID_year0 0.01282 0.01200 1.07 0.1427 0.85182
CovAggE UN(1,1) ClassID_year1 0.02433 0.01601 1.52 0.0642 0.43468
CovAggE UN(1,1) ClassID_year2 0.03659 0.02125 1.72 0.0426 0.40363
CovAggE Residual   0.2664 0.01449 18.39 <.0001 0.18386


PsuedoR2 (% Reduction) for CovClassAcuteE vs. CovAggE

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovClassAcuteE UN(1,1) StudentID 0.5925 0.04922 12.04 <.0001 .
CovClassAcuteE UN(1,1) ClassID_year0 0.08082 0.03521 2.30 0.0109 .
CovClassAcuteE UN(1,1) ClassID_year1 0.04766 0.02511 1.90 0.0288 .
CovClassAcuteE UN(1,1) ClassID_year2 0.08706 0.03782 2.30 0.0107 .
CovClassAcuteE Residual   0.3262 0.01790 18.22 <.0001 .
CovAggE UN(1,1) StudentID 0.3441 0.03080 11.17 <.0001 0.41927
CovAggE UN(1,1) ClassID_year0 0.01282 0.01200 1.07 0.1427 0.84140
CovAggE UN(1,1) ClassID_year1 0.02433 0.01601 1.52 0.0642 0.48948
CovAggE UN(1,1) ClassID_year2 0.03659 0.02125 1.72 0.0426 0.57970
CovAggE Residual   0.2664 0.01449 18.39 <.0001 0.18330


Total R2 (% Reduction) for PredEmpty2E vs. PredFinalE

Name PredCorr TotalR2 TotalR2Diff
PredEmpty2E . . .
PredFinalE 0.60524 0.36632 .