Chapter 12: Descriptive Statistics for Subject-Level Variables

The MEANS Procedure

Analysis Variable : SMage age: Subject Age in Years
older: Age Group
(0=young, 1=old)		 N Obs N Mean Std Dev Minimum Maximum
0 96 96 19.7083333 2.2660732 18.0000000 32.0000000
1 57 57 75.7017544 5.3684426 63.0000000 86.0000000


Chapter 12: Descriptive Statistics for Item-Level Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
IMrelevance
IMsalience
relevance: Item Relevance to Driving (0-5)
salience: Item Salience (0-5)
51
51
2.6470588
3.0196078
1.9060276
1.1043586
0
1.0000000
5.0000000
5.0000000


Chapter 12: Descriptive Statistics for Trial-Level Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
rt
logrt
rt: Response Time in Seconds
logrt: Natural Log RT in Seconds
7646
7646
7.3766882
1.6120577
8.0891400
0.8284638
1.1560000
0.1449658
59.9690000
4.0938278


Eq 12.8: Empty Means, Single-Level Model for Log RT

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Diagonal
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Residual

Dimensions
Covariance Parameters 1
Columns in X 1
Columns in Z 0
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 0.6864 0.01110 61.83 <.0001

Fit Statistics
-2 Res Log Likelihood 18827.2
AIC (smaller is better) 18829.2
AICC (smaller is better) 18829.2
BIC (smaller is better) 18836.1

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
18827.2 1 18829.2 18829.2 18831.6 18836.1 18837.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6121 0.009475 7645 170.15 <.0001 0.05 1.5935 1.6306


Eq 12.9: Add Subject Random Intercept Variance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effect SubjectID
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 153
Max Obs Per Subject 51

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 18827.20667592  
1 2 17080.72619866 0.00000042
2 1 17080.72556394 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.1746 0.02124 8.22 <.0001
Residual   0.5157 0.008426 61.21 <.0001

Fit Statistics
-2 Res Log Likelihood 17080.7
AIC (smaller is better) 17084.7
AICC (smaller is better) 17084.7
BIC (smaller is better) 17090.8

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 1746.48 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
17080.7 2 17084.7 17084.7 17087.2 17090.8 17092.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6194 0.03477 152 46.57 <.0001 0.05 1.5507 1.6881


Eq 12.10: Add Item Random Intercept Variance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 1
Columns in Z Per Subject 204
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 18827.20667592  
1 2 15182.04194698 0.00000826
2 1 15182.03723125 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.1802 0.02159 8.35 <.0001
UN(1,1) ItemID 0.1259 0.02570 4.90 <.0001
Residual   0.3899 0.006391 61.00 <.0001

Fit Statistics
-2 Res Log Likelihood 15182.0
AIC (smaller is better) 15188.0
AICC (smaller is better) 15188.0
BIC (smaller is better) 15182.0

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 3645.17 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
15182.0 3 15188.0 15188.0 15182.0 15182.0 15185.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6226 0.06081 99.8 26.68 <.0001 0.05 1.5020 1.7433


Likelihood Ratio Test for FitEmpty2 vs. FitEmpty3

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitEmpty2 17080.7 2 17084.7 17090.8 . . .
FitEmpty3 15182.0 3 15188.0 15182.0 1898.69 1 0


Eq 12.11: Add Fixed Effects of Item Predictors

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 4
Columns in Z Per Subject 204
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 18446.12022735  
1 2 15181.07715990 0.00000422
2 1 15181.07474638 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.1803 0.02159 8.35 <.0001
UN(1,1) ItemID 0.09411 0.01995 4.72 <.0001
Residual   0.3899 0.006391 61.00 <.0001

Fit Statistics
-2 Res Log Likelihood 15181.1
AIC (smaller is better) 15187.1
AICC (smaller is better) 15187.1
BIC (smaller is better) 15181.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 3265.05 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
15181.1 3 15187.1 15187.1 15181.1 15181.1 15184.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6126 0.05695 104 28.32 <.0001 0.05 1.4997 1.7255
rel3 -0.05027 0.02375 47 -2.12 0.0396 0.05 -0.09804 -0.00250
sal3 -0.1377 0.04214 47 -3.27 0.0020 0.05 -0.2225 -0.05296
rel3*sal3 -0.01147 0.01997 47 -0.57 0.5686 0.05 -0.05164 0.02871

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47 4.48 4.48 0.0342 0.0396
sal3 1 47 10.68 10.68 0.0011 0.0020
rel3*sal3 1 47 0.33 0.33 0.5658 0.5686

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of 3 Item Predictor Effects 3 47 19.44 6.48 0.0002 0.0009


PsuedoR2 (% Reduction) for CovEmpty vs. CovItem

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovEmpty UN(1,1) SubjectID 0.1802 0.02159 8.35 <.0001 .
CovEmpty UN(1,1) ItemID 0.1259 0.02570 4.90 <.0001 .
CovEmpty Residual   0.3899 0.006391 61.00 <.0001 .
CovItem UN(1,1) SubjectID 0.1803 0.02159 8.35 <.0001 -0.00018
CovItem UN(1,1) ItemID 0.09411 0.01995 4.72 <.0001 0.25258
CovItem Residual   0.3899 0.006391 61.00 <.0001 0.00000


Ch 12: Remove Item Random Intercept Variance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effect SubjectID
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 4
Columns in Z Per Subject 1
Subjects 153
Max Obs Per Subject 51

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 18446.12022735  
1 2 16539.02013330 0.00000058
2 1 16539.01940761 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.1770 0.02142 8.26 <.0001
Residual   0.4782 0.007814 61.20 <.0001

Fit Statistics
-2 Res Log Likelihood 16539.0
AIC (smaller is better) 16543.0
AICC (smaller is better) 16543.0
BIC (smaller is better) 16549.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 1907.10 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
16539.0 2 16543.0 16543.0 16545.5 16549.1 16551.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.6105 0.03500 153 46.02 <.0001 0.05 1.5413 1.6796
rel3 -0.05023 0.004327 7490 -11.61 <.0001 0.05 -0.05871 -0.04174
sal3 -0.1378 0.007673 7490 -17.96 <.0001 0.05 -0.1528 -0.1228
rel3*sal3 -0.01046 0.003647 7490 -2.87 0.0042 0.05 -0.01760 -0.00331

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 7490 134.75 134.75 <.0001 <.0001
sal3 1 7490 322.47 322.47 <.0001 <.0001
rel3*sal3 1 7490 8.22 8.22 0.0041 0.0042


Likelihood Ratio Test for FitNoRandItem vs. FitItem

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitNoRandItem 16539.0 2 16543.0 16549.1 . . .
FitItem 15181.1 3 15187.1 15181.1 1357.94 1 0


Eq 12.12: Add Fixed Main Effects of Subject Predictors

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 6
Columns in Z Per Subject 204
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16427.18336920  
1 2 14919.90464906 0.00000006
2 1 14919.90462053 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.02333 0.003600 6.48 <.0001
UN(1,1) ItemID 0.09408 0.01994 4.72 <.0001
Residual   0.3899 0.006391 61.00 <.0001

Fit Statistics
-2 Res Log Likelihood 14919.9
AIC (smaller is better) 14925.9
AICC (smaller is better) 14925.9
BIC (smaller is better) 14919.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 1507.28 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14919.9 3 14925.9 14925.9 14919.9 14919.9 14922.9

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3123 0.04833 59.7 27.15 <.0001 0.05 1.2156 1.4090
rel3 -0.05031 0.02374 47 -2.12 0.0394 0.05 -0.09807 -0.00254
sal3 -0.1377 0.04214 47 -3.27 0.0020 0.05 -0.2225 -0.05298
rel3*sal3 -0.01149 0.01997 47 -0.58 0.5677 0.05 -0.05166 0.02867
older 0.5899 0.05556 150 10.62 <.0001 0.05 0.4801 0.6997
yrs65 0.02021 0.004406 152 4.59 <.0001 0.05 0.01151 0.02892

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47 4.49 4.49 0.0341 0.0394
sal3 1 47 10.69 10.69 0.0011 0.0020
rel3*sal3 1 47 0.33 0.33 0.5649 0.5677
older 1 150 112.72 112.72 <.0001 <.0001
yrs65 1 152 21.05 21.05 <.0001 <.0001

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Multivariate Test of 2 Subject Predictor Effects 2 151 765.18 382.59 <.0001 <.0001


PsuedoR2 (% Reduction) for CovItem vs. CovSubject

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovItem UN(1,1) SubjectID 0.1803 0.02159 8.35 <.0001 .
CovItem UN(1,1) ItemID 0.09411 0.01995 4.72 <.0001 .
CovItem Residual   0.3899 0.006391 61.00 <.0001 .
CovSubject UN(1,1) SubjectID 0.02333 0.003600 6.48 <.0001 0.87059
CovSubject UN(1,1) ItemID 0.09408 0.01994 4.72 <.0001 0.00039
CovSubject Residual   0.3899 0.006391 61.00 <.0001 0.00000


Ch 12: Remove Subject Random Intercept Variance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effect ItemID
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 6
Columns in Z Per Subject 1
Subjects 51
Max Obs Per Subject 153

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16427.18336920  
1 2 15147.22380294 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) ItemID 0.09360 0.01988 4.71 <.0001
Residual   0.4129 0.006701 61.62 <.0001

Fit Statistics
-2 Res Log Likelihood 15147.2
AIC (smaller is better) 15151.2
AICC (smaller is better) 15151.2
BIC (smaller is better) 15155.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 1279.96 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
15147.2 2 15151.2 15151.2 15152.7 15155.1 15157.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3125 0.04569 48.4 28.72 <.0001 0.05 1.2206 1.4043
rel3 -0.05031 0.02370 47 -2.12 0.0391 0.05 -0.09799 -0.00263
sal3 -0.1373 0.04207 47 -3.26 0.0020 0.05 -0.2220 -0.05270
rel3*sal3 -0.01145 0.01993 47 -0.57 0.5685 0.05 -0.05155 0.02865
older 0.5882 0.02872 7593 20.48 <.0001 0.05 0.5319 0.6445
yrs65 0.02014 0.002290 7593 8.80 <.0001 0.05 0.01565 0.02463

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47 4.51 4.51 0.0338 0.0391
sal3 1 47 10.66 10.66 0.0011 0.0020
rel3*sal3 1 47 0.33 0.33 0.5657 0.5685
older 1 7593 419.38 419.38 <.0001 <.0001
yrs65 1 7593 77.36 77.36 <.0001 <.0001


Likelihood Ratio Test for FitNoRandSubject vs. FitSubject

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitNoRandSubject 15147.2 2 15151.2 15155.1 . . .
FitSubject 14919.9 3 14925.9 14919.9 227.319 1 0


Eq 12.13: Add Subject Random Salience Slope Variance and Covariance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
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 6
Columns in Z Per Subject 357
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16427.18336920  
1 2 14911.53761743 0.00000028
2 1 14911.53749409 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID 0.02341 0.003603 6.50 <.0001
UN(2,1) SubjectID -0.00048 0.001394 -0.35 0.7298
UN(2,2) SubjectID 0.002411 0.001026 2.35 0.0094
UN(1,1) ItemID 0.09417 0.01996 4.72 <.0001
Residual   0.3869 0.006408 60.38 <.0001

Fit Statistics
-2 Res Log Likelihood 14911.5
AIC (smaller is better) 14921.5
AICC (smaller is better) 14921.5
BIC (smaller is better) 14911.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1515.65 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14911.5 5 14921.5 14921.5 14911.5 14911.5 14916.5

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3116 0.04835 59.8 27.13 <.0001 0.05 1.2149 1.4083
rel3 -0.05035 0.02375 47 -2.12 0.0393 0.05 -0.09813 -0.00257
sal3 -0.1377 0.04234 47.8 -3.25 0.0021 0.05 -0.2228 -0.05252
rel3*sal3 -0.01151 0.01997 47 -0.58 0.5673 0.05 -0.05169 0.02867
older 0.5897 0.05554 150 10.62 <.0001 0.05 0.4799 0.6994
yrs65 0.02042 0.004404 152 4.64 <.0001 0.05 0.01172 0.02912

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47 4.50 4.50 0.0340 0.0393
sal3 1 47.8 10.57 10.57 0.0011 0.0021
rel3*sal3 1 47 0.33 0.33 0.5645 0.5673
older 1 150 112.73 112.73 <.0001 <.0001
yrs65 1 152 21.49 21.49 <.0001 <.0001


Likelihood Ratio Test for FitSubject vs. FitRandSal

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitSubject 14919.9 3 14925.9 14919.9 . . .
FitRandSal 14911.5 5 14921.5 14911.5 8.36713 2 0.015244


Ch 12: Add Subject Random Relevance Slope Variance and Covariances

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 8
Columns in X 6
Columns in Z Per Subject 510
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16427.18336920  
1 2 14908.78652591 0.00000042
2 1 14908.78634358 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID 0.02370 0.003672 6.45 <.0001
UN(2,1) SubjectID -0.00053 0.001406 -0.37 0.7087
UN(2,2) SubjectID 0.002312 0.001049 2.20 0.0137
UN(3,1) SubjectID 0.000459 0.000812 0.57 0.5718
UN(3,2) SubjectID 0.000077 0.000410 0.19 0.8513
UN(3,3) SubjectID 0.000424 0.000317 1.34 0.0901
UN(1,1) ItemID 0.09419 0.01996 4.72 <.0001
Residual   0.3855 0.006452 59.74 <.0001

Fit Statistics
-2 Res Log Likelihood 14908.8
AIC (smaller is better) 14924.8
AICC (smaller is better) 14924.8
BIC (smaller is better) 14908.8

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
7 1518.40 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14908.8 8 14924.8 14924.8 14908.8 14908.8 14916.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3132 0.04838 59.8 27.15 <.0001 0.05 1.2165 1.4100
rel3 -0.05028 0.02381 47.5 -2.11 0.0400 0.05 -0.09817 -0.00239
sal3 -0.1378 0.04233 47.8 -3.25 0.0021 0.05 -0.2229 -0.05266
rel3*sal3 -0.01152 0.01997 47 -0.58 0.5669 0.05 -0.05170 0.02866
older 0.5884 0.05551 150 10.60 <.0001 0.05 0.4787 0.6981
yrs65 0.02013 0.004402 152 4.57 <.0001 0.05 0.01143 0.02883

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47.5 4.46 4.46 0.0347 0.0400
sal3 1 47.8 10.59 10.59 0.0011 0.0021
rel3*sal3 1 47 0.33 0.33 0.5642 0.5669
older 1 150 112.38 112.38 <.0001 <.0001
yrs65 1 152 20.91 20.91 <.0001 <.0001


Likelihood Ratio Test for FitRandSal vs. FitRandMean

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitRandSal 14911.5 5 14921.5 14911.5 . . .
FitRandMean 14908.8 8 14924.8 14908.8 2.75115 3 0.43160


Eq 12.14: Add All Possible Fixed Effect Interactions

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
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 12
Columns in Z Per Subject 357
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16447.90113179  
1 2 14924.32264863 0.00000033
2 1 14924.32250095 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID 0.02341 0.003599 6.50 <.0001
UN(2,1) SubjectID -0.00041 0.001335 -0.30 0.7614
UN(2,2) SubjectID 0.002049 0.000988 2.07 0.0190
UN(1,1) ItemID 0.09432 0.01999 4.72 <.0001
Residual   0.3853 0.006383 60.36 <.0001

Fit Statistics
-2 Res Log Likelihood 14924.3
AIC (smaller is better) 14934.3
AICC (smaller is better) 14934.3
BIC (smaller is better) 14924.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1523.58 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14924.3 5 14934.3 14934.3 14924.3 14924.3 14929.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3038 0.04841 59.9 26.93 <.0001 0.05 1.2070 1.4006
rel3 -0.06398 0.02395 48.4 -2.67 0.0102 0.05 -0.1121 -0.01585
sal3 -0.1425 0.04275 49.5 -3.33 0.0016 0.05 -0.2284 -0.05667
rel3*sal3 -0.00273 0.02014 48.4 -0.14 0.8928 0.05 -0.04321 0.03775
older 0.6067 0.05620 158 10.80 <.0001 0.05 0.4957 0.7177
yrs65 0.02083 0.004457 159 4.67 <.0001 0.05 0.01203 0.02964
rel3*older 0.01424 0.01523 7301 0.94 0.3496 0.05 -0.01561 0.04409
sal3*older -0.01487 0.03057 184 -0.49 0.6272 0.05 -0.07518 0.04543
rel3*sal3*older -0.02530 0.01287 7309 -1.97 0.0494 0.05 -0.05054 -0.00007
rel3*yrs65 0.002225 0.001218 7309 1.83 0.0678 0.05 -0.00016 0.004612
sal3*yrs65 0.002572 0.002430 188 1.06 0.2912 0.05 -0.00222 0.007366
rel3*sal3*yrs65 0.000042 0.001027 7314 0.04 0.9675 0.05 -0.00197 0.002056

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 48.4 7.14 7.14 0.0075 0.0102
sal3 1 49.5 11.12 11.12 0.0009 0.0016
rel3*sal3 1 48.4 0.02 0.02 0.8922 0.8928
older 1 158 116.55 116.55 <.0001 <.0001
yrs65 1 159 21.85 21.85 <.0001 <.0001
rel3*older 1 7301 0.87 0.87 0.3496 0.3496
sal3*older 1 184 0.24 0.24 0.6266 0.6272
rel3*sal3*older 1 7309 3.86 3.86 0.0493 0.0494
rel3*yrs65 1 7309 3.34 3.34 0.0678 0.0678
sal3*yrs65 1 188 1.12 1.12 0.2899 0.2912
rel3*sal3*yrs65 1 7314 0.00 0.00 0.9675 0.9675


PsuedoR2 (% Reduction) for CovRandSal vs. CovAllInt

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovRandSal UN(1,1) SubjectID 0.02341 0.003603 6.50 <.0001 .
CovRandSal UN(2,2) SubjectID 0.002411 0.001026 2.35 0.0094 .
CovRandSal UN(1,1) ItemID 0.09417 0.01996 4.72 <.0001 .
CovRandSal Residual   0.3869 0.006408 60.38 <.0001 .
CovAllInt UN(1,1) SubjectID 0.02341 0.003599 6.50 <.0001 -0.00005
CovAllInt UN(2,2) SubjectID 0.002049 0.000988 2.07 0.0190 0.15018
CovAllInt UN(1,1) ItemID 0.09432 0.01999 4.72 <.0001 -0.00156
CovAllInt Residual   0.3853 0.006383 60.36 <.0001 0.00419


Eq 12.15: Keep Significant Fixed Effect Interactions

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
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 9
Columns in Z Per Subject 357
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16419.72511067  
1 2 14896.09052205 0.00000034
2 1 14896.09037463 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID 0.02341 0.003600 6.50 <.0001
UN(2,1) SubjectID -0.00041 0.001347 -0.30 0.7611
UN(2,2) SubjectID 0.002129 0.000993 2.14 0.0160
UN(1,1) ItemID 0.09433 0.01999 4.72 <.0001
Residual   0.3854 0.006383 60.37 <.0001

Fit Statistics
-2 Res Log Likelihood 14896.1
AIC (smaller is better) 14906.1
AICC (smaller is better) 14906.1
BIC (smaller is better) 14896.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1523.63 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14896.1 5 14906.1 14906.1 14896.1 14896.1 14901.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3038 0.04841 59.9 26.93 <.0001 0.05 1.2070 1.4007
rel3 -0.06398 0.02395 48.4 -2.67 0.0102 0.05 -0.1121 -0.01584
sal3 -0.1425 0.04276 49.6 -3.33 0.0016 0.05 -0.2285 -0.05664
rel3*sal3 -0.00273 0.02014 48.4 -0.14 0.8927 0.05 -0.04321 0.03775
older 0.6120 0.05571 152 10.99 <.0001 0.05 0.5019 0.7221
yrs65 0.02036 0.004402 152 4.62 <.0001 0.05 0.01166 0.02905
rel3*older 0.03786 0.008089 7305 4.68 <.0001 0.05 0.02200 0.05371
sal3*older 0.01276 0.01629 184 0.78 0.4345 0.05 -0.01938 0.04490
rel3*sal3*older -0.02481 0.006829 7314 -3.63 0.0003 0.05 -0.03819 -0.01142

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 48.4 7.14 7.14 0.0075 0.0102
sal3 1 49.6 11.11 11.11 0.0009 0.0016
rel3*sal3 1 48.4 0.02 0.02 0.8922 0.8927
older 1 152 120.68 120.68 <.0001 <.0001
yrs65 1 152 21.38 21.38 <.0001 <.0001
rel3*older 1 7305 21.91 21.91 <.0001 <.0001
sal3*older 1 184 0.61 0.61 0.4335 0.4345
rel3*sal3*older 1 7314 13.20 13.20 0.0003 0.0003


PsuedoR2 (% Reduction) for CovRandSal vs. CovSigInt

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovRandSal UN(1,1) SubjectID 0.02341 0.003603 6.50 <.0001 .
CovRandSal UN(2,2) SubjectID 0.002411 0.001026 2.35 0.0094 .
CovRandSal UN(1,1) ItemID 0.09417 0.01996 4.72 <.0001 .
CovRandSal Residual   0.3869 0.006408 60.38 <.0001 .
CovSigInt UN(1,1) SubjectID 0.02341 0.003600 6.50 <.0001 -0.00008
CovSigInt UN(2,2) SubjectID 0.002129 0.000993 2.14 0.0160 0.11690
CovSigInt UN(1,1) ItemID 0.09433 0.01999 4.72 <.0001 -0.00170
CovSigInt Residual   0.3854 0.006383 60.37 <.0001 0.00404


Ch 12: Remove Subject Random Slope Variance and Covariance

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structure Unstructured
Subject Effects SubjectID, ItemID
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 3
Columns in X 9
Columns in Z Per Subject 204
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16419.72511067  
1 2 14902.78352942 0.00000007
2 1 14902.78349945 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) SubjectID 0.02333 0.003596 6.49 <.0001
UN(1,1) ItemID 0.09425 0.01998 4.72 <.0001
Residual   0.3880 0.006361 60.99 <.0001

Fit Statistics
-2 Res Log Likelihood 14902.8
AIC (smaller is better) 14908.8
AICC (smaller is better) 14908.8
BIC (smaller is better) 14902.8

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 1516.94 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14902.8 3 14908.8 14908.8 14902.8 14902.8 14905.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3038 0.04839 59.8 26.94 <.0001 0.05 1.2070 1.4006
rel3 -0.06399 0.02394 48.5 -2.67 0.0102 0.05 -0.1121 -0.01587
sal3 -0.1425 0.04249 48.4 -3.35 0.0016 0.05 -0.2279 -0.05709
rel3*sal3 -0.00272 0.02013 48.5 -0.14 0.8929 0.05 -0.04319 0.03774
older 0.6139 0.05571 152 11.02 <.0001 0.05 0.5038 0.7239
yrs65 0.02017 0.004403 152 4.58 <.0001 0.05 0.01147 0.02887
rel3*older 0.03796 0.008114 7442 4.68 <.0001 0.05 0.02205 0.05387
sal3*older 0.01272 0.01439 7443 0.88 0.3770 0.05 -0.01550 0.04093
rel3*sal3*older -0.02480 0.006850 7443 -3.62 0.0003 0.05 -0.03823 -0.01137

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 48.5 7.14 7.14 0.0075 0.0102
sal3 1 48.4 11.25 11.25 0.0008 0.0016
rel3*sal3 1 48.5 0.02 0.02 0.8923 0.8929
older 1 152 121.40 121.40 <.0001 <.0001
yrs65 1 152 20.99 20.99 <.0001 <.0001
rel3*older 1 7442 21.88 21.88 <.0001 <.0001
sal3*older 1 7443 0.78 0.78 0.3770 0.3770
rel3*sal3*older 1 7443 13.11 13.11 0.0003 0.0003


Likelihood Ratio Test for FitNoRandSal vs. FitSigInt

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitNoRandSal 14902.8 3 14908.8 14902.8 . . .
FitSigInt 14896.1 5 14906.1 14896.1 6.69312 2 0.035205


Ch 12: Add Separate Residual Variances by Age Group

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER12
Dependent Variable logrt
Covariance Structures Unstructured, Variance Components
Subject Effects SubjectID, ItemID, SubjectID*ItemID
Group Effect agegroup
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 9
Columns in Z 357
Subjects 1
Max Obs Per Subject 7646

Number of Observations
Number of Observations Read 7646
Number of Observations Used 7646
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16419.72511067  
1 2 14726.28077507 0.00001438
2 1 14726.27578291 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Group Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID   0.02148 0.003474 6.18 <.0001
UN(2,1) SubjectID   -0.00072 0.001320 -0.54 0.5875
UN(2,2) SubjectID   0.001929 0.000939 2.05 0.0200
UN(1,1) ItemID   0.09542 0.02019 4.73 <.0001
Residual SubjectID*ItemID agegroup 0 0.3202 0.006682 47.92 <.0001
Residual SubjectID*ItemID agegroup 1 0.5020 0.01395 35.98 <.0001

Fit Statistics
-2 Res Log Likelihood 14726.3
AIC (smaller is better) 14738.3
AICC (smaller is better) 14738.3
BIC (smaller is better) 14726.3

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 1693.45 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14726.3 6 14738.3 14738.3 14726.3 14726.3 14732.3

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3038 0.04830 58.1 27.00 <.0001 0.05 1.2072 1.4005
rel3 -0.06402 0.02400 47.9 -2.67 0.0104 0.05 -0.1123 -0.01576
sal3 -0.1425 0.04282 48.9 -3.33 0.0017 0.05 -0.2286 -0.05645
rel3*sal3 -0.00272 0.02018 47.9 -0.13 0.8935 0.05 -0.04329 0.03786
older 0.6111 0.05575 165 10.96 <.0001 0.05 0.5010 0.7212
yrs65 0.02041 0.004431 168 4.60 <.0001 0.05 0.01166 0.02915
rel3*older 0.03790 0.008606 4510 4.40 <.0001 0.05 0.02103 0.05477
sal3*older 0.01286 0.01694 238 0.76 0.4486 0.05 -0.02051 0.04623
rel3*sal3*older -0.02488 0.007269 4493 -3.42 0.0006 0.05 -0.03913 -0.01063

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47.9 7.12 7.12 0.0076 0.0104
sal3 1 48.9 11.07 11.07 0.0009 0.0017
rel3*sal3 1 47.9 0.02 0.02 0.8929 0.8935
older 1 165 120.16 120.16 <.0001 <.0001
yrs65 1 168 21.20 21.20 <.0001 <.0001
rel3*older 1 4510 19.39 19.39 <.0001 <.0001
sal3*older 1 238 0.58 0.58 0.4478 0.4486
rel3*sal3*older 1 4493 11.71 11.71 0.0006 0.0006


Likelihood Ratio Test for FitSigInt vs. FitHetResVar

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitSigInt 14896.1 5 14906.1 14896.1 . . .
FitHetResVar 14726.3 6 14738.3 14726.3 169.815 1 0


Ch 12: Add Separate Subject Random Effects Variances and Covariance by Age Group

The Mixed Procedure

Model Information
Data Set WORK.PLOTFAKEPEOPLE
Dependent Variable logrt
Covariance Structures Unstructured, Variance Components
Subject Effects SubjectID, ItemID, SubjectID*ItemID
Group Effects agegroup, agegroup
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 9
Columns in X 9
Columns in Z 668
Subjects 1
Max Obs Per Subject 7676

Number of Observations
Number of Observations Read 7676
Number of Observations Used 7646
Number of Observations Not Used 30

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 16419.72511067  
1 2 14705.12452034 0.00000529
2 1 14705.12274958 0.00000000

Convergence criteria met.

Covariance Parameter Estimates
Cov Parm Subject Group Estimate Standard Error Z Value Pr Z
UN(1,1) SubjectID agegroup 0 0.01097 0.002518 4.36 <.0001
UN(2,1) SubjectID agegroup 0 -0.00134 0.001137 -1.18 0.2384
UN(2,2) SubjectID agegroup 0 0.001656 0.001015 1.63 0.0514
UN(1,1) SubjectID agegroup 1 0.04497 0.01051 4.28 <.0001
UN(2,1) SubjectID agegroup 1 0.001258 0.003420 0.37 0.7129
UN(2,2) SubjectID agegroup 1 0.002944 0.002168 1.36 0.0872
UN(1,1) ItemID   0.09543 0.02019 4.73 <.0001
Residual SubjectID*ItemID agegroup 0 0.3211 0.006727 47.73 <.0001
Residual SubjectID*ItemID agegroup 1 0.4985 0.01385 35.99 <.0001

Fit Statistics
-2 Res Log Likelihood 14705.1
AIC (smaller is better) 14723.1
AICC (smaller is better) 14723.1
BIC (smaller is better) 14705.1

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
8 1714.60 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
14705.1 9 14723.1 14723.1 14705.1 14705.1 14714.1

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 1.3039 0.04715 53 27.65 <.0001 0.05 1.2093 1.3984
rel3 -0.06400 0.02400 47.9 -2.67 0.0104 0.05 -0.1123 -0.01575
sal3 -0.1425 0.04279 48.7 -3.33 0.0017 0.05 -0.2285 -0.05652
rel3*sal3 -0.00270 0.02018 47.9 -0.13 0.8942 0.05 -0.04328 0.03788
older 0.6179 0.07122 59.7 8.68 <.0001 0.05 0.4754 0.7604
yrs65 0.01981 0.005845 55.3 3.39 0.0013 0.05 0.008094 0.03152
rel3*older 0.03787 0.008587 4545 4.41 <.0001 0.05 0.02103 0.05470
sal3*older 0.01286 0.01735 117 0.74 0.4601 0.05 -0.02150 0.04722
rel3*sal3*older -0.02493 0.007254 4530 -3.44 0.0006 0.05 -0.03915 -0.01071

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
rel3 1 47.9 7.11 7.11 0.0077 0.0104
sal3 1 48.7 11.09 11.09 0.0009 0.0017
rel3*sal3 1 47.9 0.02 0.02 0.8936 0.8942
older 1 59.7 75.26 75.26 <.0001 <.0001
yrs65 1 55.3 11.48 11.48 0.0007 0.0013
rel3*older 1 4545 19.45 19.45 <.0001 <.0001
sal3*older 1 117 0.55 0.55 0.4587 0.4601
rel3*sal3*older 1 4530 11.81 11.81 0.0006 0.0006

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Relevance Effect at Salience=3 for Younger -0.06400 0.02400 47.9 -2.67 0.0104 0.05 -0.1123 -0.01575
Relevance Effect at Salience=3 for Older -0.02613 0.02470 53.7 -1.06 0.2948 0.05 -0.07567 0.02340
Salience Effect at Relevance=3 for Younger -0.1425 0.04279 48.7 -3.33 0.0017 0.05 -0.2285 -0.05652
Salience Effect at Relevance=3 for Older -0.1297 0.04443 56.1 -2.92 0.0051 0.05 -0.2187 -0.04067
Relevance by Salience for Younger -0.00270 0.02018 47.9 -0.13 0.8942 0.05 -0.04328 0.03788
Relevance by Salience for Older -0.02763 0.02079 53.9 -1.33 0.1894 0.05 -0.06930 0.01405


Likelihood Ratio Test for FitHetResVar vs. FitHetRandVar

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitHetResVar 14726.3 6 14738.3 14726.3 . . .
FitHetRandVar 14705.1 9 14723.1 14705.1 21.1530 3 .000097846


Predicted Outcomes for Fake People

rel3 sal3 older yrs65 agegroup Pred
-2 -2 1 15 1 2.41995
-1 -2 1 15 1 2.44907
0 -2 1 15 1 2.47819
1 -2 1 15 1 2.50731
2 -2 1 15 1 2.53642
-2 -2 1 0 1 2.12286
-1 -2 1 0 1 2.15197
0 -2 1 0 1 2.18109
1 -2 1 0 1 2.21021
2 -2 1 0 1 2.23933
-2 -2 0 0 0 1.70612
-1 -2 0 0 0 1.64752
0 -2 0 0 0 1.58891
1 -2 0 0 0 1.53031
2 -2 0 0 0 1.47170
-2 1 1 15 1 2.19670
-1 1 1 15 1 2.14294
0 1 1 15 1 2.08918
1 1 1 15 1 2.03542
2 1 1 15 1 1.98166
-2 1 1 0 1 1.89961
-1 1 1 0 1 1.84584
0 1 1 0 1 1.79208
1 1 1 0 1 1.73832
2 1 1 0 1 1.68456
-2 1 0 0 0 1.29473
-1 1 0 0 0 1.22803
0 1 0 0 0 1.16133
1 1 0 0 0 1.09463
2 1 0 0 0 1.02793