Chapter 7b: Descriptive Statistics for Time-Invariant Variables

The MEANS Procedure

Analysis Variable : Attitude12 Attitude12: Attitudes at Age 12
N Mean Std Dev Minimum Maximum
200 3.9505004 0.6024956 2.4373666 5.0000000


Chapter 7b: Descriptive Statistics for Time-Varying Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
age
risky
age: Exact Age at Occasion
risky: Risky Behavior at Occasion
1400
1400
15.0010317
19.3848852
2.0041741
5.3013587
11.5308790
10.0000000
18.3368796
36.2824265


Ch 7b: Empty Means, Random Intercept Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
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 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8642.32437117  
1 1 8296.61688483 0.00000000

Convergence criteria met.

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7
1 28.0843 10.8431 10.8431 10.8431 10.8431 10.8431 10.8431
2 10.8431 28.0843 10.8431 10.8431 10.8431 10.8431 10.8431
3 10.8431 10.8431 28.0843 10.8431 10.8431 10.8431 10.8431
4 10.8431 10.8431 10.8431 28.0843 10.8431 10.8431 10.8431
5 10.8431 10.8431 10.8431 10.8431 28.0843 10.8431 10.8431
6 10.8431 10.8431 10.8431 10.8431 10.8431 28.0843 10.8431
7 10.8431 10.8431 10.8431 10.8431 10.8431 10.8431 28.0843

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7
1 1.0000 0.3861 0.3861 0.3861 0.3861 0.3861 0.3861
2 0.3861 1.0000 0.3861 0.3861 0.3861 0.3861 0.3861
3 0.3861 0.3861 1.0000 0.3861 0.3861 0.3861 0.3861
4 0.3861 0.3861 0.3861 1.0000 0.3861 0.3861 0.3861
5 0.3861 0.3861 0.3861 0.3861 1.0000 0.3861 0.3861
6 0.3861 0.3861 0.3861 0.3861 0.3861 1.0000 0.3861
7 0.3861 0.3861 0.3861 0.3861 0.3861 0.3861 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.8431 1.3344 8.13 <.0001
Residual   17.2412 0.7039 24.49 <.0001

Fit Statistics
-2 Log Likelihood 8296.6
AIC (Smaller is Better) 8302.6
AICC (Smaller is Better) 8302.6
BIC (Smaller is Better) 8312.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 345.71 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
8296.6 3 8302.6 8302.6 8306.6 8312.5 8315.5

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 19.3849 0.2579 200 75.15 <.0001 0.05 18.8763 19.8935


Ch 7b: Saturated Means by Rounded Occasion, Unstructured Variance Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 28
Columns in X 8
Columns in Z 0
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8352.06367763  
1 1 7606.83220997 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7
1 20.8919 11.6035 10.7002 8.8325 9.1931 6.9827 5.8521
2 11.6035 19.5582 11.1286 9.3914 11.5883 10.5351 9.9714
3 10.7002 11.1286 20.2464 12.5830 12.9565 11.7780 9.2230
4 8.8325 9.3914 12.5830 20.8101 14.0117 15.0484 14.3849
5 9.1931 11.5883 12.9565 14.0117 21.9129 16.0068 15.2538
6 6.9827 10.5351 11.7780 15.0484 16.0068 27.1119 19.0865
7 5.8521 9.9714 9.2230 14.3849 15.2538 19.0865 29.2478

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7
1 1.0000 0.5740 0.5203 0.4236 0.4297 0.2934 0.2367
2 0.5740 1.0000 0.5592 0.4655 0.5598 0.4575 0.4169
3 0.5203 0.5592 1.0000 0.6130 0.6151 0.5027 0.3790
4 0.4236 0.4655 0.6130 1.0000 0.6562 0.6335 0.5831
5 0.4297 0.5598 0.6151 0.6562 1.0000 0.6567 0.6025
6 0.2934 0.4575 0.5027 0.6335 0.6567 1.0000 0.6778
7 0.2367 0.4169 0.3790 0.5831 0.6025 0.6778 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 20.8919 2.0892 10.00 <.0001
UN(2,1) PersonID 11.6035 1.6481 7.04 <.0001
UN(2,2) PersonID 19.5582 1.9558 10.00 <.0001
UN(3,1) PersonID 10.7002 1.6393 6.53 <.0001
UN(3,2) PersonID 11.1286 1.6122 6.90 <.0001
UN(3,3) PersonID 20.2464 2.0246 10.00 <.0001
UN(4,1) PersonID 8.8325 1.6012 5.52 <.0001
UN(4,2) PersonID 9.3914 1.5735 5.97 <.0001
UN(4,3) PersonID 12.5830 1.7024 7.39 <.0001
UN(4,4) PersonID 20.8101 2.0810 10.00 <.0001
UN(5,1) PersonID 9.1931 1.6467 5.58 <.0001
UN(5,2) PersonID 11.5883 1.6776 6.91 <.0001
UN(5,3) PersonID 12.9565 1.7486 7.41 <.0001
UN(5,4) PersonID 14.0117 1.8060 7.76 <.0001
UN(5,5) PersonID 21.9129 2.1913 10.00 <.0001
UN(6,1) PersonID 6.9827 1.7538 3.98 <.0001
UN(6,2) PersonID 10.5351 1.7906 5.88 <.0001
UN(6,3) PersonID 11.7780 1.8542 6.35 <.0001
UN(6,4) PersonID 15.0484 1.9883 7.57 <.0001
UN(6,5) PersonID 16.0068 2.0619 7.76 <.0001
UN(6,6) PersonID 27.1119 2.7112 10.00 <.0001
UN(7,1) PersonID 5.8521 1.7962 3.26 0.0011
UN(7,2) PersonID 9.9714 1.8323 5.44 <.0001
UN(7,3) PersonID 9.2230 1.8401 5.01 <.0001
UN(7,4) PersonID 14.3849 2.0194 7.12 <.0001
UN(7,5) PersonID 15.2538 2.0900 7.30 <.0001
UN(7,6) PersonID 19.0865 2.4055 7.93 <.0001
UN(7,7) PersonID 29.2478 2.9248 10.00 <.0001

Fit Statistics
-2 Log Likelihood 7606.8
AIC (Smaller is Better) 7676.8
AICC (Smaller is Better) 7678.7
BIC (Smaller is Better) 7792.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
27 745.23 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7606.8 35 7676.8 7678.7 7723.5 7792.3 7827.3

Solution for Fixed Effects
Effect occasion:
Occasion
of Measurement
(12-18)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   23.5211 0.3824 200 61.51 <.0001 0.05 22.7670 24.2752
occasion 12 -6.7988 0.4384 200 -15.51 <.0001 0.05 -7.6632 -5.9343
occasion 13 -6.3383 0.3799 200 -16.68 <.0001 0.05 -7.0874 -5.5892
occasion 14 -5.6585 0.3940 200 -14.36 <.0001 0.05 -6.4355 -4.8816
occasion 15 -4.5393 0.3263 200 -13.91 <.0001 0.05 -5.1826 -3.8959
occasion 16 -3.7482 0.3213 200 -11.66 <.0001 0.05 -4.3819 -3.1146
occasion 17 -1.8704 0.3016 200 -6.20 <.0001 0.05 -2.4650 -1.2758
occasion 18 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
occasion 6 200 332.83 55.47 <.0001 <.0001

Least Squares Means
Effect occasion:
Occasion
of Measurement
(12-18)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
occasion 12 16.7223 0.3232 200 51.74 <.0001 0.05 16.0850 17.3597
occasion 13 17.1828 0.3127 200 54.95 <.0001 0.05 16.5661 17.7994
occasion 14 17.8626 0.3182 200 56.14 <.0001 0.05 17.2352 18.4900
occasion 15 18.9818 0.3226 200 58.85 <.0001 0.05 18.3458 19.6179
occasion 16 19.7729 0.3310 200 59.74 <.0001 0.05 19.1202 20.4256
occasion 17 21.6507 0.3682 200 58.80 <.0001 0.05 20.9247 22.3767
occasion 18 23.5211 0.3824 200 61.51 <.0001 0.05 22.7670 24.2752

Differences of Least Squares Means
Effect occasion:
Occasion
of Measurement
(12-18)		 occasion:
Occasion
of Measurement
(12-18)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
occasion 12 13 -0.4604 0.2936 200 -1.57 0.1184 0.05 -1.0394 0.1186
occasion 12 14 -1.1402 0.3141 200 -3.63 0.0004 0.05 -1.7597 -0.5208
occasion 12 15 -2.2595 0.3467 200 -6.52 <.0001 0.05 -2.9431 -1.5759
occasion 12 16 -3.0505 0.3494 200 -8.73 <.0001 0.05 -3.7396 -2.3615
occasion 12 17 -4.9284 0.4125 200 -11.95 <.0001 0.05 -5.7418 -4.1149
occasion 12 18 -6.7988 0.4384 200 -15.51 <.0001 0.05 -7.6632 -5.9343
occasion 13 14 -0.6798 0.2962 200 -2.30 0.0228 0.05 -1.2639 -0.09571
occasion 13 15 -1.7991 0.3285 200 -5.48 <.0001 0.05 -2.4469 -1.1513
occasion 13 16 -2.5901 0.3024 200 -8.56 <.0001 0.05 -3.1865 -1.9937
occasion 13 17 -4.4679 0.3578 200 -12.49 <.0001 0.05 -5.1734 -3.7624
occasion 13 18 -6.3383 0.3799 200 -16.68 <.0001 0.05 -7.0874 -5.5892
occasion 14 15 -1.1193 0.2819 200 -3.97 <.0001 0.05 -1.6751 -0.5635
occasion 14 16 -1.9103 0.2850 200 -6.70 <.0001 0.05 -2.4723 -1.3483
occasion 14 17 -3.7881 0.3450 200 -10.98 <.0001 0.05 -4.4684 -3.1079
occasion 14 18 -5.6585 0.3940 200 -14.36 <.0001 0.05 -6.4355 -4.8816
occasion 15 16 -0.7910 0.2711 200 -2.92 0.0039 0.05 -1.3256 -0.2564
occasion 15 17 -2.6688 0.2985 200 -8.94 <.0001 0.05 -3.2575 -2.0802
occasion 15 18 -4.5393 0.3263 200 -13.91 <.0001 0.05 -5.1826 -3.8959
occasion 16 17 -1.8778 0.2916 200 -6.44 <.0001 0.05 -2.4529 -1.3027
occasion 16 18 -3.7482 0.3213 200 -11.66 <.0001 0.05 -4.3819 -3.1146
occasion 17 18 -1.8704 0.3016 200 -6.20 <.0001 0.05 -2.4650 -1.2758


Ch 7b: Fixed Linear Age, Random Intercept Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 2
Columns in Z per Subject 1
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8365.23464747  
1 1 7797.97384321 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 11.6594 1.3302 8.77 <.0001
Residual   11.3819 0.4647 24.49 <.0001

Fit Statistics
-2 Log Likelihood 7798.0
AIC (Smaller is Better) 7806.0
AICC (Smaller is Better) 7806.0
BIC (Smaller is Better) 7819.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 567.26 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7798.0 4 7806.0 7806.0 7811.3 7819.2 7823.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 22.7421 0.2910 321 78.16 <.0001 0.05 22.1696 23.3145
agec18 1.1194 0.04503 1200 24.86 <.0001 0.05 1.0311 1.2078

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1200 618.06 618.06 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Age=12 16.0254 0.2910 321 55.07 <.0001 0.05 15.4529 16.5979
Intercept at Age=13 17.1448 0.2730 251 62.79 <.0001 0.05 16.6071 17.6826
Intercept at Age=14 18.2643 0.2616 212 69.81 <.0001 0.05 17.7485 18.7800
Intercept at Age=15 19.3837 0.2577 200 75.21 <.0001 0.05 18.8755 19.8920
Intercept at Age=16 20.5032 0.2616 212 78.37 <.0001 0.05 19.9875 21.0189
Intercept at Age=17 21.6226 0.2730 251 79.20 <.0001 0.05 21.0850 22.1603
Intercept at Age=18 22.7421 0.2910 321 78.16 <.0001 0.05 22.1696 23.3145


PsuedoR2 (% Reduction) for CovEmpty vs. CovFixLin

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovEmpty UN(1,1) PersonID 10.8431 1.3344 8.13 <.0001 .
CovEmpty Residual   17.2412 0.7039 24.49 <.0001 .
CovFixLin UN(1,1) PersonID 11.6594 1.3302 8.77 <.0001 -0.07528
CovFixLin Residual   11.3819 0.4647 24.49 <.0001 0.33984


Ch 7b: Random Linear Age Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 2
Columns in Z per Subject 2
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8365.23464747  
1 2 7677.18878202 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 21.5137 2.5634 8.39 <.0001
UN(2,1) PersonID 2.4328 0.4139 5.88 <.0001
UN(2,2) PersonID 0.5699 0.08919 6.39 <.0001
Residual   8.7179 0.3898 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7677.2
AIC (Smaller is Better) 7689.2
AICC (Smaller is Better) 7689.2
BIC (Smaller is Better) 7709.0

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 688.05 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7677.2 6 7689.2 7689.2 7697.2 7709.0 7715.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 22.7434 0.3575 200 63.62 <.0001 0.05 22.0385 23.4484
agec18 1.1199 0.06638 200 16.87 <.0001 0.05 0.9890 1.2508

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 200 284.59 284.59 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Age=12 16.0241 0.2906 200 55.14 <.0001 0.05 15.4511 16.5971
Intercept at Age=13 17.1440 0.2639 200 64.97 <.0001 0.05 16.6237 17.6644
Intercept at Age=14 18.2639 0.2523 200 72.40 <.0001 0.05 17.7664 18.7613
Intercept at Age=15 19.3838 0.2578 200 75.19 <.0001 0.05 18.8754 19.8921
Intercept at Age=16 20.5037 0.2795 200 73.37 <.0001 0.05 19.9526 21.0547
Intercept at Age=17 21.6236 0.3139 200 68.88 <.0001 0.05 21.0045 22.2426
Intercept at Age=18 22.7434 0.3575 200 63.62 <.0001 0.05 22.0385 23.4484


Likelihood Ratio Test for FitFixLin vs. FitRandLin

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFixLin 7798.0 4 7806.0 7819.2 . . .
FitRandLin 7677.2 6 7689.2 7709.0 120.785 2 0


Eq 7b.8: Fixed Quadratic, Random Linear Age Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 3
Columns in Z per Subject 2
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8349.74953754  
1 2 7634.77022089 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 21.6917 2.5636 8.46 <.0001
UN(2,1) PersonID 2.4754 0.4142 5.98 <.0001
UN(2,2) PersonID 0.5846 0.08927 6.55 <.0001
Residual   8.3520 0.3735 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7634.8
AIC (Smaller is Better) 7648.8
AICC (Smaller is Better) 7648.9
BIC (Smaller is Better) 7671.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 714.98 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7634.8 7 7648.8 7648.9 7658.1 7671.9 7678.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.4655 0.3740 239 62.74 <.0001 0.05 22.7287 24.2023
agec18 1.9877 0.1476 1188 13.47 <.0001 0.05 1.6981 2.2773
agec18*agec18 0.1446 0.02197 1010 6.58 <.0001 0.05 0.1015 0.1877

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1188 181.34 181.34 <.0001 <.0001
agec18*agec18 1 1010 43.35 43.35 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Age=12 16.7458 0.3108 260 53.88 <.0001 0.05 16.1339 17.3578
Intercept at Age=13 17.1426 0.2640 200 64.93 <.0001 0.05 16.6220 17.6633
Intercept at Age=14 17.8287 0.2609 228 68.35 <.0001 0.05 17.3147 18.3427
Intercept at Age=15 18.8040 0.2724 249 69.02 <.0001 0.05 18.2674 19.3406
Intercept at Age=16 20.0686 0.2872 223 69.88 <.0001 0.05 19.5027 20.6345
Intercept at Age=17 21.6224 0.3139 200 68.87 <.0001 0.05 21.0033 22.2415
Intercept at Age=18 23.4655 0.3740 239 62.74 <.0001 0.05 22.7287 24.2023
Linear Slope at Age=12 0.2522 0.1476 1188 1.71 0.0878 0.05 -0.03740 0.5417
Linear Slope at Age=13 0.5414 0.1102 932 4.92 <.0001 0.05 0.3253 0.7576
Linear Slope at Age=14 0.8307 0.07965 396 10.43 <.0001 0.05 0.6741 0.9873
Linear Slope at Age=15 1.1199 0.06645 200 16.86 <.0001 0.05 0.9889 1.2510
Linear Slope at Age=16 1.4092 0.07966 397 17.69 <.0001 0.05 1.2526 1.5658
Linear Slope at Age=17 1.6985 0.1102 932 15.42 <.0001 0.05 1.4823 1.9147
Linear Slope at Age=18 1.9877 0.1476 1188 13.47 <.0001 0.05 1.6981 2.2773


PsuedoR2 (% Reduction) for CovRandLin vs. CovFixQuad

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovRandLin UN(1,1) PersonID 21.5137 2.5634 8.39 <.0001 .
CovRandLin UN(2,2) PersonID 0.5699 0.08919 6.39 <.0001 .
CovRandLin Residual   8.7179 0.3898 22.36 <.0001 .
CovFixQuad UN(1,1) PersonID 21.6917 2.5636 8.46 <.0001 -0.008274
CovFixQuad UN(2,2) PersonID 0.5846 0.08927 6.55 <.0001 -0.025771
CovFixQuad Residual   8.3520 0.3735 22.36 <.0001 0.041969


Total R2 (% Reduction) for PredEmpty vs. PredAge

Name PredCorr TotalR2 TotalR2Diff
PredEmpty . . .
PredAge 0.43427 0.18859 .


Ch 7b: Random Quadratic Age Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 7
Columns in X 3
Columns in Z per Subject 3
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8349.74953754  
1 2 7629.51112306 0.00000207
2 1 7629.50582660 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 21.2827 2.7450 7.75 <.0001
UN(2,1) PersonID 2.4761 0.9474 2.61 0.0090
UN(2,2) PersonID 1.3561 0.5325 2.55 0.0054
UN(3,1) PersonID -0.00542 0.1309 -0.04 0.9670
UN(3,2) PersonID 0.1277 0.07761 1.65 0.0999
UN(3,3) PersonID 0.02152 0.01240 1.74 0.0414
Residual   7.9778 0.3996 19.97 <.0001

Fit Statistics
-2 Log Likelihood 7629.5
AIC (Smaller is Better) 7649.5
AICC (Smaller is Better) 7649.7
BIC (Smaller is Better) 7682.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
6 720.24 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7629.5 10 7649.5 7649.7 7662.9 7682.5 7692.5

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.4688 0.3695 200 63.51 <.0001 0.05 22.7402 24.1974
agec18 1.9912 0.1577 193 12.62 <.0001 0.05 1.6800 2.3023
agec18*agec18 0.1451 0.02389 191 6.07 <.0001 0.05 0.09797 0.1922

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 193 159.34 159.34 <.0001 <.0001
agec18*agec18 1 191 36.89 36.89 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Age=12 16.7453 0.3062 200 54.69 <.0001 0.05 16.1415 17.3490
Intercept at Age=13 17.1404 0.2642 200 64.87 <.0001 0.05 16.6194 17.6614
Intercept at Age=14 17.8257 0.2686 200 66.37 <.0001 0.05 17.2961 18.3553
Intercept at Age=15 18.8012 0.2829 200 66.46 <.0001 0.05 18.2433 19.3590
Intercept at Age=16 20.0669 0.2943 200 68.18 <.0001 0.05 19.4865 20.6472
Intercept at Age=17 21.6227 0.3140 200 68.85 <.0001 0.05 21.0035 22.2420
Intercept at Age=18 23.4688 0.3695 200 63.51 <.0001 0.05 22.7402 24.1974
Linear Slope at Age=12 0.2500 0.1583 192 1.58 0.1158 0.05 -0.06217 0.5622
Linear Slope at Age=13 0.5402 0.1167 194 4.63 <.0001 0.05 0.3101 0.7703
Linear Slope at Age=14 0.8304 0.08205 198 10.12 <.0001 0.05 0.6686 0.9922
Linear Slope at Age=15 1.1206 0.06649 200 16.85 <.0001 0.05 0.9895 1.2517
Linear Slope at Age=16 1.4108 0.08170 196 17.27 <.0001 0.05 1.2496 1.5719
Linear Slope at Age=17 1.7010 0.1162 194 14.64 <.0001 0.05 1.4718 1.9301
Linear Slope at Age=18 1.9912 0.1577 193 12.62 <.0001 0.05 1.6800 2.3023


Likelihood Ratio Test for FitFixQuad vs. FitRandQuad

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFixQuad 7634.8 7 7648.8 7671.9 . . .
FitRandQuad 7629.5 10 7649.5 7682.5 5.26439 3 0.15343


Ch 7b: Fixed Cubic, Random Linear Age Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 4
Columns in Z per Subject 2
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8349.67357749  
1 2 7634.18510365 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 21.7093 2.5651 8.46 <.0001
UN(2,1) PersonID 2.4806 0.4146 5.98 <.0001
UN(2,2) PersonID 0.5861 0.08941 6.56 <.0001
Residual   8.3449 0.3732 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7634.2
AIC (Smaller is Better) 7650.2
AICC (Smaller is Better) 7650.3
BIC (Smaller is Better) 7676.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 715.49 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7634.2 8 7650.2 7650.3 7660.9 7676.6 7684.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.5251 0.3821 259 61.57 <.0001 0.05 22.7727 24.2775
agec18 2.1937 0.3069 1108 7.15 <.0001 0.05 1.5914 2.7959
agec18*agec18 0.2374 0.1232 1028 1.93 0.0542 0.05 -0.00431 0.4790
agec18*agec18*agec18 0.01027 0.01343 1030 0.77 0.4443 0.05 -0.01607 0.03662

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1108 51.08 51.08 <.0001 <.0001
agec18*agec18 1 1028 3.71 3.71 0.0539 0.0542
agec18*agec18*agec18 1 1030 0.59 0.59 0.4441 0.4443


Ch 7b: Fixed Quadratic, Random Linear Age Model
Attitudes Predicting Intercept

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 4
Columns in Z per Subject 2
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8291.03631296  
1 2 7625.56201695 0.00000004
2 1 7625.56192245 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 19.2978 2.3948 8.06 <.0001
UN(2,1) PersonID 2.2276 0.3995 5.58 <.0001
UN(2,2) PersonID 0.5846 0.08930 6.55 <.0001
Residual   8.3519 0.3735 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7625.6
AIC (Smaller is Better) 7641.6
AICC (Smaller is Better) 7641.7
BIC (Smaller is Better) 7667.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 665.47 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7625.6 8 7641.6 7641.7 7652.2 7667.9 7675.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.3998 0.3582 229 65.32 <.0001 0.05 22.6940 24.1056
agec18 1.9880 0.1476 1188 13.47 <.0001 0.05 1.6984 2.2776
agec18*agec18 0.1447 0.02197 1010 6.59 <.0001 0.05 0.1016 0.1878
att4 -1.3325 0.4098 200 -3.25 0.0013 0.05 -2.1407 -0.5244

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1188 181.38 181.38 <.0001 <.0001
agec18*agec18 1 1010 43.37 43.37 <.0001 <.0001
att4 1 200 10.57 10.57 0.0011 0.0013


PsuedoR2 (% Reduction) for CovFixQuad vs. CovAttInt

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovFixQuad UN(1,1) PersonID 21.6917 2.5636 8.46 <.0001 .
CovFixQuad UN(2,2) PersonID 0.5846 0.08927 6.55 <.0001 .
CovFixQuad Residual   8.3520 0.3735 22.36 <.0001 .
CovAttInt UN(1,1) PersonID 19.2978 2.3948 8.06 <.0001 0.11036
CovAttInt UN(2,2) PersonID 0.5846 0.08930 6.55 <.0001 -0.00003
CovAttInt Residual   8.3519 0.3735 22.36 <.0001 0.00001


Total R2 (% Reduction) for PredAge vs. PredAttInt

Name PredCorr TotalR2 TotalR2Diff
PredAge 0.43427 0.18859 .
PredAttInt 0.47014 0.22103 0.032447


Ch 7b: Fixed Quadratic, Random Linear Age Model
Attitudes Predicting Linear Age Slope

The Mixed Procedure

Model Information
Data Set WORK.PLOTAGEATT
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 5
Columns in Z per Subject 2
Subjects 201
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1414
Number of Observations Used 1400
Number of Observations Not Used 14

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8265.86865661  
1 2 7602.53277799 0.00000001

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 18.0772 2.2040 8.20 <.0001
UN(2,1) PersonID 1.8838 0.3563 5.29 <.0001
UN(2,2) PersonID 0.4878 0.07976 6.12 <.0001
Residual   8.3535 0.3736 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7602.5
AIC (Smaller is Better) 7620.5
AICC (Smaller is Better) 7620.7
BIC (Smaller is Better) 7650.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 663.34 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7602.5 9 7620.5 7620.7 7632.6 7650.3 7659.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.3120 0.3500 245 66.60 <.0001 0.05 22.6226 24.0015
agec18 1.9649 0.1460 1196 13.46 <.0001 0.05 1.6784 2.2514
agec18*agec18 0.1450 0.02196 1011 6.60 <.0001 0.05 0.1019 0.1881
att4 -3.1555 0.5512 200 -5.72 <.0001 0.05 -4.2425 -2.0685
agec18*att4 -0.5154 0.1043 199 -4.94 <.0001 0.05 -0.7211 -0.3098

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1196 181.09 181.09 <.0001 <.0001
agec18*agec18 1 1011 43.61 43.61 <.0001 <.0001
att4 1 200 32.77 32.77 <.0001 <.0001
agec18*att4 1 199 24.43 24.43 <.0001 <.0001


PsuedoR2 (% Reduction) for CovAttInt vs. CovAttLin

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovAttInt UN(1,1) PersonID 19.2978 2.3948 8.06 <.0001 .
CovAttInt UN(2,2) PersonID 0.5846 0.08930 6.55 <.0001 .
CovAttInt Residual   8.3519 0.3735 22.36 <.0001 .
CovAttLin UN(1,1) PersonID 18.0772 2.2040 8.20 <.0001 0.06325
CovAttLin UN(2,2) PersonID 0.4878 0.07976 6.12 <.0001 0.16562
CovAttLin Residual   8.3535 0.3736 22.36 <.0001 -0.00018


PsuedoR2 (% Reduction) for CovFixQuad vs. CovAttLin

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovFixQuad UN(1,1) PersonID 21.6917 2.5636 8.46 <.0001 .
CovFixQuad UN(2,2) PersonID 0.5846 0.08927 6.55 <.0001 .
CovFixQuad Residual   8.3520 0.3735 22.36 <.0001 .
CovAttLin UN(1,1) PersonID 18.0772 2.2040 8.20 <.0001 0.16663
CovAttLin UN(2,2) PersonID 0.4878 0.07976 6.12 <.0001 0.16560
CovAttLin Residual   8.3535 0.3736 22.36 <.0001 -0.00017


Total R2 (% Reduction) for PredAge vs. PredAttLin

Name PredCorr TotalR2 TotalR2Diff
PredAge 0.43427 0.18859 .
PredAttLin 0.48557 0.23578 0.047190


Predicted Outcomes for Fake People

agec18 att4 Pred
-6 -2 16.8703
-5 -2 18.2705
-4 -2 19.9608
-3 -2 21.9412
-2 -2 24.2117
-1 -2 26.7723
0 -2 29.6230
-6 1 16.6815
-5 1 16.5354
-4 1 16.6794
-3 1 17.1136
-2 1 17.8378
-1 1 18.8521
0 1 20.1565


Eq 7b.9: Fixed Quadratic, Random Linear Age Model
Attitudes Predicting Quadratic Age Slope

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER7B
Dependent Variable risky
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 6
Columns in Z per Subject 2
Subjects 200
Max Obs per Subject 7

Number of Observations
Number of Observations Read 1400
Number of Observations Used 1400
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 8264.63897324  
1 2 7599.43195412 0.00000001

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 18.0843 2.2033 8.21 <.0001
UN(2,1) PersonID 1.8873 0.3564 5.30 <.0001
UN(2,2) PersonID 0.4895 0.07983 6.13 <.0001
Residual   8.3260 0.3724 22.36 <.0001

Fit Statistics
-2 Log Likelihood 7599.4
AIC (Smaller is Better) 7619.4
AICC (Smaller is Better) 7619.6
BIC (Smaller is Better) 7652.4

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 665.21 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
7599.4 10 7619.4 7619.6 7632.8 7652.4 7662.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.2993 0.3500 245 66.57 <.0001 0.05 22.6099 23.9887
agec18 1.9480 0.1461 1197 13.33 <.0001 0.05 1.6613 2.2347
agec18*agec18 0.1422 0.02199 1011 6.46 <.0001 0.05 0.09901 0.1853
att4 -3.4764 0.5805 245 -5.99 <.0001 0.05 -4.6197 -2.3330
agec18*att4 -0.9004 0.2421 1196 -3.72 0.0002 0.05 -1.3754 -0.4255
agec18*agec18*att4 -0.06409 0.03636 1011 -1.76 0.0783 0.05 -0.1354 0.007268

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
agec18 1 1197 177.67 177.67 <.0001 <.0001
agec18*agec18 1 1011 41.79 41.79 <.0001 <.0001
att4 1 245 35.87 35.87 <.0001 <.0001
agec18*att4 1 1196 13.83 13.83 0.0002 0.0002
agec18*agec18*att4 1 1011 3.11 3.11 0.0780 0.0783


PsuedoR2 (% Reduction) for CovAttLin vs. CovAttQuad

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovAttLin UN(1,1) PersonID 18.0772 2.2040 8.20 <.0001 .
CovAttLin UN(2,2) PersonID 0.4878 0.07976 6.12 <.0001 .
CovAttLin Residual   8.3535 0.3736 22.36 <.0001 .
CovAttQuad UN(1,1) PersonID 18.0843 2.2033 8.21 <.0001 -.000389743
CovAttQuad UN(2,2) PersonID 0.4895 0.07983 6.13 <.0001 -.003579850
CovAttQuad Residual   8.3260 0.3724 22.36 <.0001 0.003286887


Total R2 (% Reduction) for PredAge vs. PredAttQuad

Name PredCorr TotalR2 TotalR2Diff
PredAge 0.43427 0.18859 .
PredAttQuad 0.48626 0.23645 0.047861