Chapter 10a: Descriptive Statistics for Time-Invariant Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
PMageT0
PMytdeathT0
ageT0: Age in Years at Time 0
ytdeathT0: Years to Death at Time 0
207
207
83.3340880
-7.1746690
2.9666565
3.9784865
79.4191781
-15.9095890
97.7780822
-0.0491803


Chapter 10a: Descriptive Statistics for Time-Invariant Variables

The CORR Procedure

2 Variables: PMageT0 PMytdeathT0

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
PMageT0 207 83.33409 2.96666 17250 79.41918 97.77808 ageT0: Age in Years at Time 0
PMytdeathT0 207 -7.17467 3.97849 -1485 -15.90959 -0.04918 ytdeathT0: Years to Death at Time 0

Pearson Correlation Coefficients, N = 207
Prob > |r| under H0: Rho=0
  PMageT0 PMytdeathT0
PMageT0
ageT0: Age in Years at Time 0
1.00000
 
0.15360
0.0271
PMytdeathT0
ytdeathT0: Years to Death at Time 0
0.15360
0.0271
1.00000
 


Chapter 10a: Descriptive Statistics for Time-Varying Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
time
tvage
tvytdeath
recall
time: Years since Time 0
tvage: Time-Varying Age in Years
tvytdeath: Time-Varying Years to Death
recall: Time-Varying Prose Recall
557
557
557
557
2.6742157
85.6453437
-5.8697378
10.1938959
2.6031008
3.5572800
3.6644798
3.8265118
0
79.4191781
-15.9095890
0
8.5027322
99.8986301
-0.0491803
16.0000000


Ch 10a: Empty Means, Random Intercept Model for Prose Recall

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3074.63298487  
1 2 2859.48580069 0.00193800
2 1 2857.46542658 0.00011513
3 1 2857.35548715 0.00000049
4 1 2857.35503325 0.00000000

Convergence criteria met.

Estimated V Matrix for PersonID 2
Row Col1 Col2
1 15.6224 10.4578
2 10.4578 15.6224

Estimated V Correlation Matrix
for PersonID 2
Row Col1 Col2
1 1.0000 0.6694
2 0.6694 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.4578 1.3095 7.99 <.0001
Residual   5.1646 0.3930 13.14 <.0001

Fit Statistics
-2 Log Likelihood 2857.4
AIC (Smaller is Better) 2863.4
AICC (Smaller is Better) 2863.4
BIC (Smaller is Better) 2873.4

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 217.28 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2857.4 3 2863.4 2863.4 2867.4 2873.4 2876.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.7349 0.2506 197 38.85 <.0001 0.05 9.2408 10.2291


Ch 10a: Saturated Means by Rounded Years in Study, Random Intercept Model for Prose Recall

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 5
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3066.70547727  
1 2 2844.44869856 0.00270389
2 1 2841.61281823 0.00021138
3 1 2841.41023746 0.00000161
4 1 2841.40876706 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.6432 1.3202 8.06 <.0001
Residual   4.9201 0.3751 13.12 <.0001

Fit Statistics
-2 Log Likelihood 2841.4
AIC (Smaller is Better) 2855.4
AICC (Smaller is Better) 2855.6
BIC (Smaller is Better) 2878.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 225.30 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2841.4 7 2855.4 2855.6 2864.8 2878.7 2885.7

Solution for Fixed Effects
Effect occasion:
Occasion
of Study
(0-8)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
occasion 0 9.6767 0.2776 292 34.85 <.0001 0.05 9.1303 10.2231
occasion 2 9.9966 0.3030 365 33.00 <.0001 0.05 9.4008 10.5924
occasion 4 9.7562 0.3346 453 29.15 <.0001 0.05 9.0986 10.4139
occasion 6 9.9569 0.3818 535 26.08 <.0001 0.05 9.2068 10.7069
occasion 8 8.4618 0.4275 557 19.79 <.0001 0.05 7.6220 9.3015

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
occasion 5 353 1515.32 303.06 <.0001 <.0001


Ch 10a: Saturated Means by Rounded Age, Random Intercept Model for Prose Recall

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 17
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3058.70328588  
1 2 2832.95338974 0.00251405
2 1 2830.34219652 0.00018438
3 1 2830.16714337 0.00000123
4 1 2830.16602932 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.4738 1.2973 8.07 <.0001
Residual   4.8131 0.3669 13.12 <.0001

Fit Statistics
-2 Log Likelihood 2830.2
AIC (Smaller is Better) 2868.2
AICC (Smaller is Better) 2869.6
BIC (Smaller is Better) 2931.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 228.54 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2830.2 19 2868.2 2869.6 2893.8 2931.5 2950.5

Solution for Fixed Effects
Effect roundage:
Age Rounded
to Nearest
Year		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
roundage 79 13.4913 1.7433 384 7.74 <.0001 0.05 10.0636 16.9189
roundage 80 10.4504 0.6119 554 17.08 <.0001 0.05 9.2485 11.6523
roundage 81 9.7446 0.4498 529 21.66 <.0001 0.05 8.8610 10.6282
roundage 82 10.1338 0.4841 543 20.93 <.0001 0.05 9.1829 11.0848
roundage 83 9.8820 0.4284 514 23.07 <.0001 0.05 9.0405 10.7236
roundage 84 9.8499 0.4243 521 23.22 <.0001 0.05 9.0164 10.6834
roundage 85 9.6093 0.4344 525 22.12 <.0001 0.05 8.7559 10.4627
roundage 86 9.9802 0.4556 533 21.90 <.0001 0.05 9.0851 10.8753
roundage 87 9.8731 0.4344 536 22.73 <.0001 0.05 9.0198 10.7264
roundage 88 9.5781 0.4984 555 19.22 <.0001 0.05 8.5992 10.5570
roundage 89 8.9692 0.4584 546 19.57 <.0001 0.05 8.0688 9.8697
roundage 90 9.6277 0.5908 555 16.30 <.0001 0.05 8.4673 10.7881
roundage 91 7.6922 0.6317 531 12.18 <.0001 0.05 6.4512 8.9333
roundage 92 9.5189 0.7213 509 13.20 <.0001 0.05 8.1018 10.9360
roundage 93 7.7879 0.9904 492 7.86 <.0001 0.05 5.8418 9.7339
roundage 94 10.4949 1.1593 427 9.05 <.0001 0.05 8.2162 12.7736
roundage 95 10.7399 1.2192 515 8.81 <.0001 0.05 8.3447 13.1351

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
roundage 17 439 1552.71 91.34 <.0001 <.0001


Ch 10a: Saturated Means by Rounded Years to Death, Random Intercept Model for Prose Recall

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 16
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3061.72466716  
1 2 2838.37730302 0.00286693
2 1 2835.37224000 0.00023570
3 1 2835.14655440 0.00000199
4 1 2835.14473907 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.6060 1.3154 8.06 <.0001
Residual   4.8487 0.3700 13.10 <.0001

Fit Statistics
-2 Log Likelihood 2835.1
AIC (Smaller is Better) 2871.1
AICC (Smaller is Better) 2872.4
BIC (Smaller is Better) 2931.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 226.58 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2835.1 18 2871.1 2872.4 2895.4 2931.1 2949.1

Solution for Fixed Effects
Effect roundytdeath:
Years to
Death Rounded
to Nearest
Year		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
roundytdeath -15 9.5567 1.3045 419 7.33 <.0001 0.05 6.9926 12.1209
roundytdeath -14 10.0984 0.9505 456 10.62 <.0001 0.05 8.2304 11.9664
roundytdeath -13 10.2943 0.6990 509 14.73 <.0001 0.05 8.9209 11.6676
roundytdeath -12 10.5085 0.7228 528 14.54 <.0001 0.05 9.0887 11.9284
roundytdeath -11 10.2265 0.5685 549 17.99 <.0001 0.05 9.1098 11.3431
roundytdeath -10 10.4025 0.5464 554 19.04 <.0001 0.05 9.3293 11.4758
roundytdeath -9 9.6930 0.4608 555 21.04 <.0001 0.05 8.7879 10.5981
roundytdeath -8 10.1762 0.5152 556 19.75 <.0001 0.05 9.1643 11.1881
roundytdeath -7 10.2214 0.4297 547 23.79 <.0001 0.05 9.3774 11.0654
roundytdeath -6 10.6927 0.4705 557 22.73 <.0001 0.05 9.7685 11.6169
roundytdeath -5 9.6427 0.4168 529 23.14 <.0001 0.05 8.8239 10.4615
roundytdeath -4 9.5659 0.4473 551 21.38 <.0001 0.05 8.6872 10.4446
roundytdeath -3 9.3987 0.4192 528 22.42 <.0001 0.05 8.5753 10.2222
roundytdeath -2 9.9846 0.4640 540 21.52 <.0001 0.05 9.0732 10.8960
roundytdeath -1 8.4481 0.4493 539 18.80 <.0001 0.05 7.5656 9.3306
roundytdeath 0 8.9842 0.6850 555 13.11 <.0001 0.05 7.6386 10.3298

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
roundytdeath 16 438 1529.74 95.61 <.0001 <.0001


Ch 10a: Empty Means, Random Intercept Model for Years since Birth

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable tvage
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 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 2993.35839344  
1 2 2920.48038351 0.00005476
2 1 2920.42677338 0.00000014
3 1 2920.42664094 0.00000000

Convergence criteria met.

Estimated V Matrix for PersonID 2
Row Col1 Col2
1 12.8640 5.0911
2 5.0911 12.8640

Estimated V Correlation Matrix
for PersonID 2
Row Col1 Col2
1 1.0000 0.3958
2 0.3958 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 5.0911 0.8861 5.75 <.0001
Residual   7.7728 0.5870 13.24 <.0001

Fit Statistics
-2 Log Likelihood 2920.4
AIC (Smaller is Better) 2926.4
AICC (Smaller is Better) 2926.5
BIC (Smaller is Better) 2936.4

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 72.93 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2920.4 3 2926.4 2926.5 2930.5 2936.4 2939.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 85.4024 0.2041 186 418.49 <.0001 0.05 84.9998 85.8050


Ch 10a: Empty Means, Random Intercept Model for Years to Death

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable tvytdeath
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 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3026.43327568  
1 2 2939.14096342 0.00021216
2 1 2938.92586472 0.00000190
3 1 2938.92403573 0.00000000

Convergence criteria met.

Estimated V Matrix for PersonID 2
Row Col1 Col2
1 13.7588 6.0425
2 6.0425 13.7588

Estimated V Correlation Matrix
for PersonID 2
Row Col1 Col2
1 1.0000 0.4392
2 0.4392 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 6.0425 0.9770 6.18 <.0001
Residual   7.7164 0.5823 13.25 <.0001

Fit Statistics
-2 Log Likelihood 2938.9
AIC (Smaller is Better) 2944.9
AICC (Smaller is Better) 2945.0
BIC (Smaller is Better) 2954.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 87.51 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2938.9 3 2944.9 2945.0 2949.0 2954.9 2957.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept -5.4868 0.2153 190 -25.48 <.0001 0.05 -5.9115 -5.0621


Ch 10a: Empty Means, Random Intercept Model for Years in Study

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable time
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 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 2645.46417963  
1 4 2645.46417963 0.00000000

Convergence criteria met.

Estimated V Matrix for PersonID 2
Row Col1 Col2
1 6.7640  
2   6.7640

Estimated V Correlation Matrix
for PersonID 2
Row Col1 Col2
1 1.0000  
2   1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 0 . . .
Residual   6.7640 0.4053 16.69 <.0001

Fit Statistics
-2 Log Likelihood 2645.5
AIC (Smaller is Better) 2649.5
AICC (Smaller is Better) 2649.5
BIC (Smaller is Better) 2656.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
0 0.00 1.0000

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2645.5 2 2649.5 2649.5 2652.2 2656.1 2658.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 2.6742 0.1102 557 24.27 <.0001 0.05 2.4578 2.8907


Ch 10a: Fixed Quadratic, Random Intercept Model using Years since Birth

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 3
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3071.86487418  
1 2 2852.79982760 0.00198091
2 1 2850.74067468 0.00011948
3 1 2850.62692918 0.00000053
4 1 2850.62644462 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.4803 1.3075 8.02 <.0001
Residual   5.0716 0.3860 13.14 <.0001

Fit Statistics
-2 Log Likelihood 2850.6
AIC (Smaller is Better) 2860.6
AICC (Smaller is Better) 2860.7
BIC (Smaller is Better) 2877.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 221.24 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2850.6 5 2860.6 2860.7 2867.4 2877.3 2882.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.8197 0.2634 231 37.28 <.0001 0.05 9.3006 10.3387
tvage84 -0.1190 0.05165 465 -2.30 0.0217 0.05 -0.2205 -0.01749
tvage84*tvage84 0.004792 0.007579 475 0.63 0.5275 0.05 -0.01010 0.01968

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvage84 1 465 5.31 5.31 0.0212 0.0217
tvage84*tvage84 1 475 0.40 0.40 0.5272 0.5275


Eq 10a.1: Random Linear Model using Years since Birth

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3072.41724440  
1 2 2846.27209661 0.00525284
2 1 2840.52949936 0.00082021
3 1 2839.70601528 0.00002752
4 1 2839.68041740 0.00000004
5 1 2839.68038031 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 11.2652 1.4730 7.65 <.0001
UN(2,1) PersonID -0.3275 0.1776 -1.84 0.0653
UN(2,2) PersonID 0.09000 0.03427 2.63 0.0043
Residual   4.2752 0.3841 11.13 <.0001

Fit Statistics
-2 Log Likelihood 2839.7
AIC (Smaller is Better) 2851.7
AICC (Smaller is Better) 2851.8
BIC (Smaller is Better) 2871.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 232.74 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2839.7 6 2851.7 2851.8 2859.8 2871.7 2877.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.8119 0.2642 181 37.13 <.0001 0.05 9.2905 10.3332
tvage84 -0.09011 0.04471 131 -2.02 0.0459 0.05 -0.1786 -0.00167

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvage84 1 131 4.06 4.06 0.0439 0.0459


Eq 10a.1: Fixed Quadratic, Random Linear Model using Years since Birth

The Mixed Procedure

Model Information
Data Set WORK.PLOTUNCTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 564
Number of Observations Used 557
Number of Observations Not Used 7

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3071.86487418  
1 2 2845.92572465 0.00499790
2 1 2840.45732392 0.00080525
3 1 2839.64517913 0.00002995
4 1 2839.61725721 0.00000005
5 1 2839.61721035 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 11.2627 1.4730 7.65 <.0001
UN(2,1) PersonID -0.3315 0.1792 -1.85 0.0643
UN(2,2) PersonID 0.09223 0.03567 2.59 0.0049
Residual   4.2627 0.3859 11.05 <.0001

Fit Statistics
-2 Log Likelihood 2839.6
AIC (Smaller is Better) 2853.6
AICC (Smaller is Better) 2853.8
BIC (Smaller is Better) 2877.0

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 232.25 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2839.6 7 2853.6 2853.8 2863.1 2877.0 2884.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.8246 0.2690 197 36.53 <.0001 0.05 9.2942 10.3550
tvage84 -0.08079 0.05755 212 -1.40 0.1618 0.05 -0.1942 0.03265
tvage84*tvage84 -0.00220 0.008481 185 -0.26 0.7952 0.05 -0.01894 0.01453

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvage84 1 212 1.97 1.97 0.1603 0.1618
tvage84*tvage84 1 185 0.07 0.07 0.7949 0.7952


Likelihood Ratio Test for FitFQRIAge vs. FitFQRLAge

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRIAge 2850.6 5 2860.6 2877.3 . . .
FitFQRLAge 2839.6 7 2853.6 2877.0 11.0092 2 .004067946


Total R2 (% Reduction) for PredEmpty vs. PredFQRLAge

Name PredCorr TotalR2 TotalR2Diff
PredEmpty . . .
PredFQRLAge 0.059270 .003512990 .


Predicted Outcomes for Fake People

tvage84 Pred
-2 9.97738
0 9.82462
2 9.65422
4 9.46619
6 9.26052
8 9.03721
10 8.79626


Ch 10a: Fixed Quadratic, Random Intercept Model using Years to Death

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 3
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3067.13291859  
1 2 2847.76487777 0.00215474
2 1 2845.52343893 0.00013918
3 1 2845.39094685 0.00000071
4 1 2845.39029699 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.4403 1.3005 8.03 <.0001
Residual   5.0122 0.3815 13.14 <.0001

Fit Statistics
-2 Log Likelihood 2845.4
AIC (Smaller is Better) 2855.4
AICC (Smaller is Better) 2855.5
BIC (Smaller is Better) 2872.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 221.74 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2845.4 5 2855.4 2855.5 2862.1 2872.1 2877.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.1328 0.2825 286 35.87 <.0001 0.05 9.5767 10.6888
tvytdeath7 -0.09922 0.03843 504 -2.58 0.0101 0.05 -0.1747 -0.02371
tvytdeath7*tvytdeath7 -0.01487 0.007874 413 -1.89 0.0597 0.05 -0.03034 0.000612

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvytdeath7 1 504 6.67 6.67 0.0098 0.0101
tvytdeath7*tvytdeath7 1 413 3.56 3.56 0.0590 0.0597


Eq 10a.1: Fixed Quadratic, Random Linear Model using Years to Death

The Mixed Procedure

Model Information
Data Set WORK.PLOTUNCTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 564
Number of Observations Used 557
Number of Observations Not Used 7

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3067.13291859  
1 2 2832.43640925 0.00299601
2 1 2829.23797734 0.00037726
3 1 2828.86616689 0.00000939
4 1 2828.85753383 0.00000001

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 9.8168 1.3865 7.08 <.0001
UN(2,1) PersonID -0.07116 0.1592 -0.45 0.6549
UN(2,2) PersonID 0.1202 0.03962 3.03 0.0012
Residual   4.0670 0.3656 11.12 <.0001

Fit Statistics
-2 Log Likelihood 2828.9
AIC (Smaller is Better) 2842.9
AICC (Smaller is Better) 2843.1
BIC (Smaller is Better) 2866.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 238.28 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2828.9 7 2842.9 2843.1 2852.3 2866.2 2873.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.1471 0.2750 202 36.90 <.0001 0.05 9.6049 10.6893
tvytdeath7 -0.08670 0.04752 112 -1.82 0.0707 0.05 -0.1809 0.007445
tvytdeath7*tvytdeath7 -0.02026 0.008693 268 -2.33 0.0205 0.05 -0.03738 -0.00315

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvytdeath7 1 112 3.33 3.33 0.0681 0.0707
tvytdeath7*tvytdeath7 1 268 5.43 5.43 0.0197 0.0205


Likelihood Ratio Test for FitFQRIYTD vs. FitFQRLYTD

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRIYTD 2845.4 5 2855.4 2872.1 . . .
FitFQRLYTD 2828.9 7 2842.9 2866.2 16.5328 2 .000257014


Total R2 (% Reduction) for PredEmpty vs. PredFQRLYTD

Name PredCorr TotalR2 TotalR2Diff
PredEmpty . . .
PredFQRLYTD 0.11014 0.012131 .


Predicted Outcomes for Fake People

tvytdeath7 Pred
-4 10.1697
-2 10.2395
0 10.1471
2 9.8926
4 9.4761
6 8.8974
. .


Ch 10a: Fixed Quadratic, Random Intercept Model using Years in Study

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER10A
Dependent Variable recall
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 3
Columns in Z per Subject 1
Subjects 207
Max Obs per Subject 5

Number of Observations
Number of Observations Read 557
Number of Observations Used 557
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3069.63719766  
1 2 2848.81114983 0.00250491
2 1 2846.18630053 0.00018416
3 1 2846.00989775 0.00000123
4 1 2846.00876934 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 10.6213 1.3203 8.04 <.0001
Residual   4.9831 0.3797 13.12 <.0001

Fit Statistics
-2 Log Likelihood 2846.0
AIC (Smaller is Better) 2856.0
AICC (Smaller is Better) 2856.1
BIC (Smaller is Better) 2872.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 223.63 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2846.0 5 2856.0 2856.1 2862.7 2872.7 2877.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.6610 0.2750 282 35.13 <.0001 0.05 9.1197 10.2023
time 0.2613 0.1192 378 2.19 0.0290 0.05 0.02687 0.4958
time*time -0.04691 0.01583 367 -2.96 0.0032 0.05 -0.07803 -0.01579

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 378 4.80 4.80 0.0284 0.0290
time*time 1 367 8.79 8.79 0.0030 0.0032


Eq 10a.1: Fixed Quadratic, Random Linear Model using Years in Study

The Mixed Procedure

Model Information
Data Set WORK.PLOTUNCTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 564
Number of Observations Used 557
Number of Observations Not Used 7

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3069.63719766  
1 2 2830.46489182 0.00232645
2 1 2828.03397660 0.00020406
3 1 2827.83797850 0.00000234
4 1 2827.83584858 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 13.0673 1.6536 7.90 <.0001
UN(2,1) PersonID -0.6553 0.2343 -2.80 0.0052
UN(2,2) PersonID 0.1336 0.04442 3.01 0.0013
Residual   3.9575 0.3610 10.96 <.0001

Fit Statistics
-2 Log Likelihood 2827.8
AIC (Smaller is Better) 2841.8
AICC (Smaller is Better) 2842.0
BIC (Smaller is Better) 2865.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 241.80 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2827.8 7 2841.8 2842.0 2851.3 2865.2 2872.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.6383 0.2877 219 33.50 <.0001 0.05 9.0714 10.2053
time 0.2807 0.1115 356 2.52 0.0122 0.05 0.06149 0.4999
time*time -0.04792 0.01495 342 -3.21 0.0015 0.05 -0.07733 -0.01852

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 356 6.34 6.34 0.0118 0.0122
time*time 1 342 10.28 10.28 0.0013 0.0015


Likelihood Ratio Test for FitFQRIYIS vs. FitFQRLYIS

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRIYIS 2846.0 5 2856.0 2872.7 . . .
FitFQRLYIS 2827.8 7 2841.8 2865.2 18.1729 2 .000113188


Total R2 (% Reduction) for PredEmpty vs. PredFQRLYIS

Name PredCorr TotalR2 TotalR2Diff
PredEmpty . . .
PredFQRLYIS 0.059205 .003505261 .


Predicted Outcomes for Fake People

time Pred
0 9.6383
2 10.0081
4 9.9944
6 9.5974
8 8.8169
. .
. .


Eq 10a.2: Fixed Quadratic, Random Linear Model using Years since Birth
Controlling for Birth Cohort

The Mixed Procedure

Model Information
Data Set WORK.PLOTCONDTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 578
Number of Observations Used 557
Number of Observations Not Used 21

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3056.81856637  
1 2 2831.15953321 0.00565689
2 1 2824.95644956 0.00105293
3 1 2823.89167981 0.00004957
4 1 2823.84559244 0.00000013
5 1 2823.84547297 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 11.1546 1.4481 7.70 <.0001
UN(2,1) PersonID -0.3424 0.1770 -1.93 0.0530
UN(2,2) PersonID 0.09072 0.03435 2.64 0.0041
Residual   4.1108 0.3745 10.98 <.0001

Fit Statistics
-2 Log Likelihood 2823.8
AIC (Smaller is Better) 2843.8
AICC (Smaller is Better) 2844.2
BIC (Smaller is Better) 2877.2

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 232.97 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2823.8 10 2843.8 2844.2 2857.3 2877.2 2887.2

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.4141 0.3510 256 26.82 <.0001 0.05 8.7230 10.1053
tvage84 0.2959 0.1135 354 2.61 0.0095 0.05 0.07277 0.5190
tvage84*tvage84 -0.04539 0.01508 333 -3.01 0.0028 0.05 -0.07506 -0.01572
ageT084 -0.5793 0.1544 522 -3.75 0.0002 0.05 -0.8826 -0.2761
ageT084*ageT084 -0.07749 0.03065 162 -2.53 0.0124 0.05 -0.1380 -0.01696
tvage84*ageT084 0.1256 0.03450 357 3.64 0.0003 0.05 0.05776 0.1934

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvage84 1 354 6.80 6.80 0.0091 0.0095
tvage84*tvage84 1 333 9.06 9.06 0.0026 0.0028
ageT084 1 522 14.08 14.08 0.0002 0.0002
ageT084*ageT084 1 162 6.39 6.39 0.0115 0.0124
tvage84*ageT084 1 357 13.26 13.26 0.0003 0.0003

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Contextual Linear Birth Cohort on Intercept -0.5793 0.1544 522 -3.75 0.0002 0.05 -0.8826 -0.2761
Contextual Quadratic Birth Cohort on Intercept -0.07749 0.03065 162 -2.53 0.0124 0.05 -0.1380 -0.01696
Contextual Linear Birth Cohort on Linear Slope 0.1256 0.03450 357 3.64 0.0003 0.05 0.05776 0.1934
Total Linear Birth Cohort on Intercept -0.2834 0.1044 234 -2.72 0.0071 0.05 -0.4891 -0.07779
Total Quadratic Birth Cohort on Intercept 0.002724 0.02156 81.3 0.13 0.8998 0.05 -0.04017 0.04562
Total Linear Birth Cohort on Linear Slope 0.03483 0.02018 146 1.73 0.0866 0.05 -0.00506 0.07471

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Birth Cohort Contextual Effects 3 155 16.03 5.34 0.0011 0.0016


Likelihood Ratio Test for FitFQRLAge vs. FitCohAge

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRLAge 2839.6 7 2853.6 2877.0 . . .
FitCohAge 2823.8 10 2843.8 2877.2 15.7717 3 .001262953


Total R2 (% Reduction) for PredFQRLAge vs. PredCohAge

Name PredCorr TotalR2 TotalR2Diff
PredFQRLAge . . .
PredCohAge 0.15701 0.024652 .


Predicted Outcomes for Fake People

tvage84 ageT084 Pred
-2 -4 10.7231
0 -4 10.4916
2 -4 9.8971
4 -4 8.9394
6 -4 7.6187
8 -4 5.9348
10 -4 3.8878
-2 0 8.6408
0 0 9.4141
2 0 9.8244
4 0 9.8715
6 0 9.5556
8 0 8.8765
10 0 7.8344
-2 4 4.0788
0 4 5.8570
2 4 7.2720
4 4 8.3240
6 4 9.0128
8 4 9.3386
10 4 9.3012


Eq 10a.2: Fixed Quadratic, Random Linear Model using Years in Study
Controlling for Birth Cohort

The Mixed Procedure

Model Information
Data Set WORK.PLOTCONDTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 578
Number of Observations Used 557
Number of Observations Not Used 21

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3056.81856637  
1 2 2821.03174109 0.00221927
2 1 2818.72904547 0.00019031
3 1 2818.54723266 0.00000219
4 1 2818.54525290 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 12.4837 1.5959 7.82 <.0001
UN(2,1) PersonID -0.5964 0.2256 -2.64 0.0082
UN(2,2) PersonID 0.1272 0.04321 2.94 0.0016
Residual   3.9406 0.3597 10.96 <.0001

Fit Statistics
-2 Log Likelihood 2818.5
AIC (Smaller is Better) 2838.5
AICC (Smaller is Better) 2838.9
BIC (Smaller is Better) 2871.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 238.27 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2818.5 10 2838.5 2838.9 2852.0 2871.9 2881.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.3402 0.3516 230 26.57 <.0001 0.05 8.6475 10.0329
time 0.3132 0.1124 366 2.79 0.0056 0.05 0.09226 0.5342
time*time -0.04555 0.01497 340 -3.04 0.0025 0.05 -0.07500 -0.01611
ageT084 -0.2972 0.1051 205 -2.83 0.0051 0.05 -0.5044 -0.09003
ageT084*ageT084 0.009130 0.01832 230 0.50 0.6187 0.05 -0.02697 0.04523
time*ageT084 0.04427 0.02080 126 2.13 0.0352 0.05 0.003117 0.08543

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 366 7.77 7.77 0.0053 0.0056
time*time 1 340 9.26 9.26 0.0023 0.0025
ageT084 1 205 8.00 8.00 0.0047 0.0051
ageT084*ageT084 1 230 0.25 0.25 0.6182 0.6187
time*ageT084 1 126 4.53 4.53 0.0333 0.0352

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Contextual Linear Birth Cohort on Intercept -0.6105 0.1577 464 -3.87 0.0001 0.05 -0.9204 -0.3006
Contextual Quadratic Birth Cohort on Intercept -0.08070 0.02972 285 -2.72 0.0070 0.05 -0.1392 -0.02221
Contextual Linear Birth Cohort on Linear Slope 0.1354 0.03482 344 3.89 0.0001 0.05 0.06690 0.2039
Total Linear Birth Cohort on Intercept -0.2972 0.1051 205 -2.83 0.0051 0.05 -0.5044 -0.09003
Total Quadratic Birth Cohort on Intercept 0.009130 0.01832 230 0.50 0.6187 0.05 -0.02697 0.04523
Total Linear Birth Cohort on Linear Slope 0.04427 0.02080 126 2.13 0.0352 0.05 0.003117 0.08543

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Birth Cohort Total Effects 3 183 9.44 3.15 0.0240 0.0264


Likelihood Ratio Test for FitFQRLYIS vs. FitCohAgeYIS

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRLYIS 2827.8 7 2841.8 2865.2 . . .
FitCohAgeYIS 2818.5 10 2838.5 2871.9 9.29060 3 0.025667


Total R2 (% Reduction) for PredFQRLYIS vs. PredCohAgeYIS

Name PredCorr TotalR2 TotalR2Diff
PredFQRLYIS . . .
PredCohAgeYIS 0.16146 0.026068 .


Predicted Outcomes for Fake People

time ageT084 Pred
0 -4 10.6752
2 -4 10.7653
4 -4 10.4909
6 -4 9.8521
8 -4 8.8489
. -4 .
. -4 .
0 0 9.3402
2 0 9.7844
4 0 9.8643
6 0 9.5797
8 0 8.9306
. 0 .
. 0 .
0 4 8.2973
2 4 9.0958
4 4 9.5298
6 4 9.5994
8 4 9.3046
. 4 .
. 4 .


Eq 10a.2: Fixed Quadratic, Random Linear Model using Years to Death
Controlling for Death Cohort

The Mixed Procedure

Model Information
Data Set WORK.PLOTCONDTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 578
Number of Observations Used 557
Number of Observations Not Used 21

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3059.67543471  
1 2 2823.81437543 0.00306326
2 1 2820.56051438 0.00038340
3 1 2820.18469683 0.00000938
4 1 2820.17611866 0.00000001

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 9.6998 1.3658 7.10 <.0001
UN(2,1) PersonID -0.05722 0.1559 -0.37 0.7136
UN(2,2) PersonID 0.1168 0.03786 3.08 0.0010
Residual   3.9992 0.3579 11.17 <.0001

Fit Statistics
-2 Log Likelihood 2820.2
AIC (Smaller is Better) 2840.2
AICC (Smaller is Better) 2840.6
BIC (Smaller is Better) 2873.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 239.50 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2820.2 10 2840.2 2840.6 2853.7 2873.6 2883.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.7494 0.3682 196 26.48 <.0001 0.05 9.0234 10.4755
tvytdeath7 0.2133 0.1141 358 1.87 0.0623 0.05 -0.01105 0.4377
tvytdeath7*tvytdeath7 -0.05638 0.01598 321 -3.53 0.0005 0.05 -0.08783 -0.02494
ytdeathT07 -0.3522 0.1295 533 -2.72 0.0068 0.05 -0.6066 -0.09775
ytdeathT07*ytdeathT07 -0.03493 0.02282 435 -1.53 0.1265 0.05 -0.07978 0.009915
tvytdeath7*ytdeathT07 0.08467 0.03095 366 2.74 0.0065 0.05 0.02381 0.1455

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
tvytdeath7 1 358 3.50 3.50 0.0615 0.0623
tvytdeath7*tvytdeath7 1 321 12.45 12.45 0.0004 0.0005
ytdeathT07 1 533 7.39 7.39 0.0065 0.0068
ytdeathT07*ytdeathT07 1 435 2.34 2.34 0.1258 0.1265
tvytdeath7*ytdeathT07 1 366 7.48 7.48 0.0062 0.0065

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Contextual Linear Death Cohort on Intercept -0.3522 0.1295 533 -2.72 0.0068 0.05 -0.6066 -0.09775
Contextual Quadratic Death Cohort on Intercept -0.03493 0.02282 435 -1.53 0.1265 0.05 -0.07978 0.009915
Contextual Linear Death Cohort on Linear Slope 0.08467 0.03095 366 2.74 0.0065 0.05 0.02381 0.1455
Total Linear Death Cohort on Intercept -0.1389 0.07316 244 -1.90 0.0589 0.05 -0.2830 0.005247
Total Quadratic Death Cohort on Intercept -0.00664 0.01763 205 -0.38 0.7067 0.05 -0.04140 0.02811
Total Linear Death Cohort on Linear Slope -0.02809 0.01819 230 -1.54 0.1238 0.05 -0.06393 0.007744

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Death Cohort Contextual Effects 3 363 8.76 2.92 0.0327 0.0340


Likelihood Ratio Test for FitFQRLYTD vs. FitCohYTD

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRLYTD 2828.9 7 2842.9 2866.2 . . .
FitCohYTD 2820.2 10 2840.2 2873.6 8.68142 3 0.033841


Total R2 (% Reduction) for PredFQRLYTD vs. PredCohYTD

Name PredCorr TotalR2 TotalR2Diff
PredFQRLYTD . . .
PredCohYTD 0.15142 0.022929 .


Predicted Outcomes for Fake People

tvytdeath7 ytdeathT07 Pred
-4 -4 10.1986
-2 -4 10.6245
0 -4 10.5993
2 -4 10.1230
4 -4 9.1956
6 -4 7.8172
. . .
-4 0 7.9940
-2 0 9.0973
0 0 9.7494
2 0 9.9505
4 0 9.7006
6 0 8.9996
. . .
-4 4 4.6716
-2 4 6.4522
0 4 7.7818
2 4 8.6603
4 4 9.0877
6 4 9.0641
. . .


Eq 10a.2: Fixed Quadratic, Random Linear Model using Years in Study
Controlling for Death Cohort

The Mixed Procedure

Model Information
Data Set WORK.PLOTCONDTIME
Dependent Variable recall
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 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 578
Number of Observations Used 557
Number of Observations Not Used 21

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3059.67543471  
1 2 2821.48909201 0.00215491
2 1 2819.26024407 0.00017169
3 1 2819.09700590 0.00000162
4 1 2819.09554381 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 12.7122 1.6133 7.88 <.0001
UN(2,1) PersonID -0.6415 0.2297 -2.79 0.0052
UN(2,2) PersonID 0.1320 0.04393 3.00 0.0013
Residual   3.9184 0.3567 10.99 <.0001

Fit Statistics
-2 Log Likelihood 2819.1
AIC (Smaller is Better) 2839.1
AICC (Smaller is Better) 2839.5
BIC (Smaller is Better) 2872.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 240.58 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2819.1 10 2839.1 2839.5 2852.6 2872.5 2882.5

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.7469 0.3930 231 24.80 <.0001 0.05 8.9727 10.5211
time 0.2357 0.1126 363 2.09 0.0370 0.05 0.01432 0.4572
time*time -0.05550 0.01586 323 -3.50 0.0005 0.05 -0.08670 -0.02431
ytdeathT07 -0.1469 0.07199 214 -2.04 0.0426 0.05 -0.2888 -0.00496
ytdeathT07*ytdeathT07 -0.00769 0.01709 226 -0.45 0.6530 0.05 -0.04136 0.02598
time*ytdeathT07 -0.02327 0.01829 201 -1.27 0.2048 0.05 -0.05934 0.01280

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 363 4.38 4.38 0.0363 0.0370
time*time 1 323 12.25 12.25 0.0005 0.0005
ytdeathT07 1 214 4.16 4.16 0.0414 0.0426
ytdeathT07*ytdeathT07 1 226 0.20 0.20 0.6526 0.6530
time*ytdeathT07 1 201 1.62 1.62 0.2034 0.2048

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Contextual Linear Birth Cohort on Intercept -0.3826 0.1296 528 -2.95 0.0033 0.05 -0.6373 -0.1279
Contextual Quadratic Birth Cohort on Intercept -0.03993 0.02270 361 -1.76 0.0795 0.05 -0.08457 0.004717
Contextual Linear Birth Cohort on Linear Slope 0.08773 0.03070 370 2.86 0.0045 0.05 0.02737 0.1481
Total Linear Birth Cohort on Intercept -0.1469 0.07199 214 -2.04 0.0426 0.05 -0.2888 -0.00496
Total Quadratic Birth Cohort on Intercept -0.00769 0.01709 226 -0.45 0.6530 0.05 -0.04136 0.02598
Total Linear Birth Cohort on Linear Slope -0.02327 0.01829 201 -1.27 0.2048 0.05 -0.05934 0.01280

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of Death Cohort Total Effects 3 204 8.82 2.94 0.0317 0.0342


Likelihood Ratio Test for FitFQRLYIS vs. FitCohYTDYIS

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFQRLYIS 2827.8 7 2841.8 2865.2 . . .
FitCohYTDYIS 2819.1 10 2839.1 2872.5 8.74030 3 0.032951


Total R2 (% Reduction) for PredFQRLYIS vs. PredCohYTDYIS

Name PredCorr TotalR2 TotalR2Diff
PredFQRLYIS . . .
PredCohYTDYIS 0.15585 0.024290 .


Predicted Outcomes for Fake People

time ytdeathT07 Pred
0 -4 10.2113
2 -4 10.6469
4 -4 10.6385
6 -4 10.1861
8 -4 9.2897
. -4 .
. . .
0 0 9.7469
2 0 9.9964
4 0 9.8018
6 0 9.1633
8 0 8.0807
. 0 .
. . .
0 4 9.0363
2 4 9.0997
4 4 8.7190
6 4 7.8943
8 4 6.6255
. 4 .
. . .


Eq 10a.4: Fixed Quadratic, Random Linear Model using Years in Study
Controlling for Birth Cohort and Death Cohort

The Mixed Procedure

Model Information
Data Set WORK.PLOTBOTHTIME
Dependent Variable recall
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 9
Columns in Z per Subject 2
Subjects 208
Max Obs per Subject 5

Number of Observations
Number of Observations Read 587
Number of Observations Used 557
Number of Observations Not Used 30

Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 3048.65681160  
1 2 2812.93244536 0.00210835
2 1 2810.76340079 0.00016749
3 1 2810.60480317 0.00000163
4 1 2810.60333536 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 12.2436 1.5668 7.81 <.0001
UN(2,1) PersonID -0.5893 0.2222 -2.65 0.0080
UN(2,2) PersonID 0.1257 0.04269 2.94 0.0016
Residual   3.8967 0.3547 10.98 <.0001

Fit Statistics
-2 Log Likelihood 2810.6
AIC (Smaller is Better) 2836.6
AICC (Smaller is Better) 2837.3
BIC (Smaller is Better) 2880.0

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 238.05 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
2810.6 13 2836.6 2837.3 2854.1 2880.0 2893.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 9.4932 0.4270 232 22.23 <.0001 0.05 8.6518 10.3345
time 0.2686 0.1133 369 2.37 0.0182 0.05 0.04588 0.4913
time*time -0.05404 0.01582 323 -3.42 0.0007 0.05 -0.08517 -0.02291
ageT084 -0.2782 0.1054 205 -2.64 0.0089 0.05 -0.4861 -0.07041
ageT084*ageT084 0.01093 0.01824 231 0.60 0.5494 0.05 -0.02500 0.04686
time*ageT084 0.04634 0.02077 127 2.23 0.0274 0.05 0.005239 0.08745
ytdeathT07 -0.1231 0.07160 212 -1.72 0.0869 0.05 -0.2643 0.01801
ytdeathT07*ytdeathT07 -0.01042 0.01697 225 -0.61 0.5398 0.05 -0.04386 0.02302
time*ytdeathT07 -0.02799 0.01822 200 -1.54 0.1262 0.05 -0.06392 0.007948

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 369 5.62 5.62 0.0177 0.0182
time*time 1 323 11.66 11.66 0.0006 0.0007
ageT084 1 205 6.97 6.97 0.0083 0.0089
ageT084*ageT084 1 231 0.36 0.36 0.5488 0.5494
time*ageT084 1 127 4.98 4.98 0.0257 0.0274
ytdeathT07 1 212 2.96 2.96 0.0855 0.0869
ytdeathT07*ytdeathT07 1 225 0.38 0.38 0.5392 0.5398
time*ytdeathT07 1 200 2.36 2.36 0.1246 0.1262


Total R2 (% Reduction) for PredFQRLYIS vs. PredBothYIS

Name PredCorr TotalR2 TotalR2Diff
PredFQRLYIS . . .
PredBothYIS 0.20840 0.043430 .


Predicted Outcomes for Fake People

time ageT084 ytdeathT07 Pred
0 -4 -4 11.1069
2 -4 -4 11.2810
4 -4 -4 11.0228
6 -4 -4 10.3323
8 -4 -4 9.2095
0 -4 0 10.7811
2 -4 0 10.7313
4 -4 0 10.2493
6 -4 0 9.3348
8 -4 0 7.9881
0 0 -4 9.8189
2 0 -4 10.3638
4 0 -4 10.4764
6 0 -4 10.1566
8 0 -4 9.4045
0 0 0 9.4932
2 0 0 9.8142
4 0 0 9.7028
6 0 0 9.1591
8 0 0 8.1831
0 4 -4 8.8809
2 4 -4 9.7965
4 4 -4 10.2798
6 4 -4 10.3308
8 4 -4 9.9494
0 4 0 8.5551
2 4 0 9.2468
4 4 0 9.5062
6 4 0 9.3333
8 4 0 8.7280