Chapter 2: Descriptive Statistics for Example Variables

The MEANS Procedure

Variable Label N Mean Std Dev Minimum Maximum
age
grip
cognition
age: Age in Years
grip: Grip Strength in Pounds
cognition: Information Test Cognitive Outcome
550
550
550
84.9267863
9.1127273
24.8218182
3.4300288
2.9829543
10.9890273
80.0164932
0
0
96.9672832
19.0000000
44.0000000


Chapter 2: Descriptive Statistics for Example Variables

The FREQ Procedure

Frequency
Percent
Row Pct
Col Pct
Table of sexMW by demgroup
sexMW(sexMW: Sex
(0=Men, 1=Women))		 demgroup(demgroup: Dementia Diagnosis
(1=None, 2=Future, 3=Current))
1None 2Future 3Current Total
0
168
30.55
74.01
42.11
40
7.27
17.62
36.70
19
3.45
8.37
45.24
227
41.27
 
 
1
231
42.00
71.52
57.89
69
12.55
21.36
63.30
23
4.18
7.12
54.76
323
58.73
 
 
Total
399
72.55
109
19.82
42
7.64
550
100.00


Chapter 2: Descriptive Statistics for Example Variables

The CORR Procedure

4 Variables: age grip sexMW cognition

Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum Label
age 550 84.92679 3.43003 46710 80.01649 96.96728 age: Age in Years
grip 550 9.11273 2.98295 5012 0 19.00000 grip: Grip Strength in Pounds
sexMW 550 0.58727 0.49277 323.00000 0 1.00000 sexMW: Sex (0=Men, 1=Women)
cognition 550 24.82182 10.98903 13652 0 44.00000 cognition: Information Test Cognitive Outcome

Pearson Correlation Coefficients, N = 550
Prob > |r| under H0: Rho=0
  age grip sexMW cognition
age
age: Age in Years
1.00000
 
-0.18414
<.0001
0.04560
0.2858
-0.17045
<.0001
grip
grip: Grip Strength in Pounds
-0.18414
<.0001
1.00000
 
-0.40324
<.0001
0.24183
<.0001
sexMW
sexMW: Sex (0=Men, 1=Women)
0.04560
0.2858
-0.40324
<.0001
1.00000
 
-0.23628
<.0001
cognition
cognition: Information Test Cognitive Outcome
-0.17045
<.0001
0.24183
<.0001
-0.23628
<.0001
1.00000
 


Eq 2.3: Empty Means Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 120.76 7.2887 16.57 <.0001

Fit Statistics
-2 Res Log Likelihood 4196.1
AIC (Smaller is Better) 4198.1
AICC (Smaller is Better) 4198.1
BIC (Smaller is Better) 4202.4

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4196.1 1 4198.1 4198.1 4199.8 4202.4 4203.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 24.8218 0.4686 549 52.97 <.0001 0.05 23.9014 25.7422


Eq 2.4: Adding Age (0=85)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 2
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 117.46 7.0963 16.55 <.0001

Fit Statistics
-2 Res Log Likelihood 4182.1
AIC (Smaller is Better) 4184.1
AICC (Smaller is Better) 4184.1
BIC (Smaller is Better) 4188.4

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4182.1 1 4184.1 4184.1 4185.8 4188.4 4189.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 24.7818 0.4622 548 53.61 <.0001 0.05 23.8739 25.6898
age85 -0.5461 0.1349 548 -4.05 <.0001 0.05 -0.8110 -0.2812

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 548 16.40 16.40 <.0001 <.0001


R2 (% Reduction) Overall and for CovEmpty vs. CovAge

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.000000 .
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.000000 .
CovAge Residual 117.46 7.0963 16.55 <.0001 0.027282 0.027282


Eq 2.4: Adding Original Age Instead

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 2
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 117.46 7.0963 16.55 <.0001

Fit Statistics
-2 Res Log Likelihood 4182.1
AIC (Smaller is Better) 4184.1
AICC (Smaller is Better) 4184.1
BIC (Smaller is Better) 4188.4

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4182.1 1 4184.1 4184.1 4185.8 4188.4 4189.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 71.1995 11.4622 548 6.21 <.0001 0.05 48.6844 93.7147
age -0.5461 0.1349 548 -4.05 <.0001 0.05 -0.8110 -0.2812

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age 1 548 16.40 16.40 <.0001 <.0001


Eq 2.6: Adding Grip (0=9)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 3
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 112.12 6.7798 16.54 <.0001

Fit Statistics
-2 Res Log Likelihood 4157.5
AIC (Smaller is Better) 4159.5
AICC (Smaller is Better) 4159.5
BIC (Smaller is Better) 4163.8

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4157.5 1 4159.5 4159.5 4161.2 4163.8 4164.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 24.7008 0.4519 547 54.66 <.0001 0.05 23.8132 25.5884
age85 -0.4176 0.1340 547 -3.12 0.0019 0.05 -0.6809 -0.1543
grip9 0.8025 0.1541 547 5.21 <.0001 0.05 0.4997 1.1053

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 547 9.70 9.70 0.0018 0.0019
grip9 1 547 27.11 27.11 <.0001 <.0001

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 2 547 44.28 22.14 <.0001 <.0001


R2 (% Reduction) Overall and for CovAge vs. CovGrip

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.000000 .
CovAge Residual 117.46 7.0963 16.55 <.0001 0.027282 .
CovGrip Residual 112.12 6.7798 16.54 <.0001 0.071514 0.044231


Eq 2.7: Adding Sex (0=M, 1=W)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 4
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 109.38 6.6200 16.52 <.0001

Fit Statistics
-2 Res Log Likelihood 4141.1
AIC (Smaller is Better) 4143.1
AICC (Smaller is Better) 4143.1
BIC (Smaller is Better) 4147.4

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4141.1 1 4143.1 4143.1 4144.8 4147.4 4148.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 26.9594 0.7389 546 36.49 <.0001 0.05 25.5080 28.4108
age85 -0.4338 0.1325 546 -3.27 0.0011 0.05 -0.6940 -0.1736
grip9 0.5460 0.1663 546 3.28 0.0011 0.05 0.2194 0.8726
sexMW -3.7988 0.9904 546 -3.84 0.0001 0.05 -5.7442 -1.8534

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 546 10.72 10.72 0.0011 0.0011
grip9 1 546 10.78 10.78 0.0010 0.0011
sexMW 1 546 14.71 14.71 0.0001 0.0001

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 3 546 60.11 20.04 <.0001 <.0001


R2 (% Reduction) Overall and for CovGrip vs. CovSex

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.000000 .
CovGrip Residual 112.12 6.7798 16.54 <.0001 0.071514 .
CovSex Residual 109.38 6.6200 16.52 <.0001 0.094221 0.022707


Eq 2.7: Adding Sex (1=M 0=W)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 4
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 109.38 6.6200 16.52 <.0001

Fit Statistics
-2 Res Log Likelihood 4141.1
AIC (Smaller is Better) 4143.1
AICC (Smaller is Better) 4143.1
BIC (Smaller is Better) 4147.4

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4141.1 1 4143.1 4143.1 4144.8 4147.4 4148.4

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.1607 0.6003 546 38.58 <.0001 0.05 21.9814 24.3399
age85 -0.4338 0.1325 546 -3.27 0.0011 0.05 -0.6940 -0.1736
grip9 0.5460 0.1663 546 3.28 0.0011 0.05 0.2194 0.8726
sexWM 3.7988 0.9904 546 3.84 0.0001 0.05 1.8534 5.7442

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 546 10.72 10.72 0.0011 0.0011
grip9 1 546 10.78 10.78 0.0010 0.0011
sexWM 1 546 14.71 14.71 0.0001 0.0001


Eq 2.8: Adding Dementia Group
Using Manual Group Contrasts so Reference=None

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 6
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 88.0709 5.3401 16.49 <.0001

Fit Statistics
-2 Res Log Likelihood 4016.3
AIC (Smaller is Better) 4018.3
AICC (Smaller is Better) 4018.3
BIC (Smaller is Better) 4022.6

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4016.3 1 4018.3 4018.3 4019.9 4022.6 4023.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 29.2643 0.6985 544 41.90 <.0001 0.05 27.8922 30.6364
age85 -0.4057 0.1189 544 -3.41 0.0007 0.05 -0.6393 -0.1722
grip9 0.6042 0.1498 544 4.03 <.0001 0.05 0.3100 0.8984
sexMW -3.6574 0.8914 544 -4.10 <.0001 0.05 -5.4084 -1.9063
demNF -5.7220 1.0191 544 -5.61 <.0001 0.05 -7.7238 -3.7202
demNC -16.4798 1.5228 544 -10.82 <.0001 0.05 -19.4710 -13.4886

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 544 11.65 11.65 0.0006 0.0007
grip9 1 544 16.27 16.27 <.0001 <.0001
sexMW 1 544 16.83 16.83 <.0001 <.0001
demNF 1 544 31.53 31.53 <.0001 <.0001
demNC 1 544 117.12 117.12 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Future vs Current -10.7578 1.7080 544 -6.30 <.0001 0.05 -14.1128 -7.4028

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 5 544 208.76 41.75 <.0001 <.0001
Omnibus Dementia Group Test 2 544 134.11 67.06 <.0001 <.0001


R2 (% Reduction) Overall and for CovSex vs. CovDem

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovSex Residual 109.38 6.6200 16.52 <.0001 0.09422 .
CovDem Residual 88.0709 5.3401 16.49 <.0001 0.27069 0.17647


Eq 2.8: Adding Dementia Group
Categorical Predictor for Dementia Group

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 7
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 88.0709 5.3401 16.49 <.0001

Fit Statistics
-2 Res Log Likelihood 4016.3
AIC (Smaller is Better) 4018.3
AICC (Smaller is Better) 4018.3
BIC (Smaller is Better) 4022.6

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4016.3 1 4018.3 4018.3 4019.9 4022.6 4023.6

Solution for Fixed Effects
Effect demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   12.7845 1.5302 544 8.35 <.0001 0.05 9.7787 15.7903
age85   -0.4057 0.1189 544 -3.41 0.0007 0.05 -0.6393 -0.1722
grip9   0.6042 0.1498 544 4.03 <.0001 0.05 0.3100 0.8984
sexMW   -3.6574 0.8914 544 -4.10 <.0001 0.05 -5.4084 -1.9063
demgroup 1None 16.4798 1.5228 544 10.82 <.0001 0.05 13.4886 19.4710
demgroup 2Future 10.7578 1.7080 544 6.30 <.0001 0.05 7.4028 14.1128
demgroup 3Current 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 544 11.65 11.65 0.0006 0.0007
grip9 1 544 16.27 16.27 <.0001 <.0001
sexMW 1 544 16.83 16.83 <.0001 <.0001
demgroup 2 544 134.11 67.06 <.0001 <.0001

Least Squares Means
Effect demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 sexMW Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
demgroup 1None 0.00 0.00 0.00 29.2643 0.6985 544 41.90 <.0001 0.05 27.8922 30.6364
demgroup 2Future 0.00 0.00 0.00 23.5424 1.0785 544 21.83 <.0001 0.05 21.4238 25.6609
demgroup 3Current 0.00 0.00 0.00 12.7845 1.5302 544 8.35 <.0001 0.05 9.7787 15.7903

Differences of Least Squares Means
Effect demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 sexMW Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
demgroup 1None 2Future 0.00 0.00 0.00 5.7220 1.0191 544 5.61 <.0001 0.05 3.7202 7.7238
demgroup 1None 3Current 0.00 0.00 0.00 16.4798 1.5228 544 10.82 <.0001 0.05 13.4886 19.4710
demgroup 2Future 3Current 0.00 0.00 0.00 10.7578 1.7080 544 6.30 <.0001 0.05 7.4028 14.1128


Eq 2.9: Adding Age by Grip Interaction
Age (0=85), Grip (0=9)

The Mixed Procedure

Model Information
Data Set WORK.PLOTAGEGRIP
Dependent Variable cognition
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 7
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 559
Number of Observations Used 550
Number of Observations Not Used 9

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 86.7615 5.2655 16.48 <.0001

Fit Statistics
-2 Res Log Likelihood 4011.7
AIC (Smaller is Better) 4013.7
AICC (Smaller is Better) 4013.7
BIC (Smaller is Better) 4018.0

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4011.7 1 4013.7 4013.7 4015.4 4018.0 4019.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 29.4078 0.6949 543 42.32 <.0001 0.05 28.0428 30.7728
age85 -0.3340 0.1204 543 -2.77 0.0057 0.05 -0.5704 -0.09754
grip9 0.6194 0.1487 543 4.16 <.0001 0.05 0.3272 0.9116
sexMW -3.4556 0.8873 543 -3.89 0.0001 0.05 -5.1985 -1.7127
demNF -5.9225 1.0136 543 -5.84 <.0001 0.05 -7.9137 -3.9314
demNC -16.3004 1.5125 543 -10.78 <.0001 0.05 -19.2716 -13.3292
age85*grip9 0.1230 0.04054 543 3.03 0.0025 0.05 0.04339 0.2026

Covariance Matrix for Fixed Effects
Row Effect Col1 Col2 Col3 Col4 Col5 Col6 Col7
1 Intercept 0.4829 0.000454 -0.03075 -0.4507 -0.1820 -0.2263 0.001916
2 age85 0.000454 0.01449 0.003317 0.005024 -0.00413 -0.00115 0.000959
3 grip9 -0.03075 0.003317 0.02212 0.05374 -0.01339 -0.00030 0.000203
4 sexMW -0.4507 0.005024 0.05374 0.7873 -0.07102 0.02371 0.002695
5 demNF -0.1820 -0.00413 -0.01339 -0.07102 1.0274 0.2129 -0.00268
6 demNC -0.2263 -0.00115 -0.00030 0.02371 0.2129 2.2878 0.002396
7 age85*grip9 0.001916 0.000959 0.000203 0.002695 -0.00268 0.002396 0.001643

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 543 7.70 7.70 0.0055 0.0057
grip9 1 543 17.34 17.34 <.0001 <.0001
sexMW 1 543 15.17 15.17 <.0001 0.0001
demNF 1 543 34.14 34.14 <.0001 <.0001
demNC 1 543 116.14 116.14 <.0001 <.0001
age85*grip9 1 543 9.21 9.21 0.0024 0.0025

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Future vs Current -10.3779 1.6998 543 -6.11 <.0001 0.05 -13.7169 -7.0388
Age Slope at Grip Strength = 6 -0.7030 0.1534 543 -4.58 <.0001 0.05 -1.0043 -0.4017
Age Slope at Grip Strength = 9 -0.3340 0.1204 543 -2.77 0.0057 0.05 -0.5704 -0.09754
Age Slope at Grip Strength = 12 0.03509 0.1872 543 0.19 0.8513 0.05 -0.3325 0.4027
Grip Strength Slope at Age = 80 0.004326 0.2473 543 0.02 0.9861 0.05 -0.4815 0.4902
Grip Strength Slope at Age = 85 0.6194 0.1487 543 4.16 <.0001 0.05 0.3272 0.9116
Grip Strength Slope at Age = 90 1.2345 0.2554 543 4.83 <.0001 0.05 0.7328 1.7362
Cognition at Grip = 12 Age = 80 31.0906 1.0924 543 28.46 <.0001 0.05 28.9447 33.2364
Cognition at Grip = 12 Age = 85 31.2661 0.7053 543 44.33 <.0001 0.05 29.8805 32.6516
Cognition at Grip = 12 Age = 90 31.4415 1.2462 543 25.23 <.0001 0.05 28.9936 33.8895
Cognition at Grip = 9 Age = 80 31.0776 0.9168 543 33.90 <.0001 0.05 29.2767 32.8785
Cognition at Grip = 9 Age = 85 29.4078 0.6949 543 42.32 <.0001 0.05 28.0428 30.7728
Cognition at Grip = 9 Age = 90 27.7380 0.9217 543 30.09 <.0001 0.05 25.9274 29.5486
Cognition at Grip = 6 Age = 80 31.0646 1.2605 543 24.65 <.0001 0.05 28.5886 33.5406
Cognition at Grip = 6 Age = 85 27.5495 0.9309 543 29.60 <.0001 0.05 25.7210 29.3781
Cognition at Grip = 6 Age = 90 24.0345 1.1491 543 20.92 <.0001 0.05 21.7773 26.2917

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 6 543 221.12 36.85 <.0001 <.0001


R2 (% Reduction) Overall and for CovDem vs. CovAgeGrip

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovDem Residual 88.0709 5.3401 16.49 <.0001 0.27069 .
CovAgeGrip Residual 86.7615 5.2655 16.48 <.0001 0.28153 0.010843


Regions of significance for age85*grip9 interaction:
The effect of grip9 will be significant at centered values of age85 BELOW the lower bound
and ABOVE the upper bound, which translate to these uncentered lower and upper bounds.

CenteredLower CenteredUpper UncenteredLower UncenteredUpper
-14.8174 -2.28519 70.1826 82.7148


Regions of significance for age85*grip9 interaction:
The effect of age85 will be significant at centered values of grip9 BELOW the lower bound
and ABOVE the upper bound, which translate to these uncentered lower and upper bounds.

CenteredLower CenteredUpper UncenteredLower UncenteredUpper
0.66541 9.52041 9.66541 18.5204


Predicted Outcomes for Fake People

age85 grip9 sexMW demNF demNC Pred
-5 3 0 0 0 31.0906
0 3 0 0 0 31.2661
5 3 0 0 0 31.4415
-5 0 0 0 0 31.0776
0 0 0 0 0 29.4078
5 0 0 0 0 27.7380
-5 -3 0 0 0 31.0646
0 -3 0 0 0 27.5495
5 -3 0 0 0 24.0345


Eq 2.9: Adding Age by Grip Interaction
Age (0=80), Grip (0=12)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 7
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 86.7615 5.2655 16.48 <.0001

Fit Statistics
-2 Res Log Likelihood 4011.7
AIC (Smaller is Better) 4013.7
AICC (Smaller is Better) 4013.7
BIC (Smaller is Better) 4018.0

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4011.7 1 4013.7 4013.7 4015.4 4018.0 4019.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 31.0906 1.0924 543 28.46 <.0001 0.05 28.9447 33.2364
age80 0.03509 0.1872 543 0.19 0.8513 0.05 -0.3325 0.4027
grip12 0.004326 0.2473 543 0.02 0.9861 0.05 -0.4815 0.4902
sexMW -3.4556 0.8873 543 -3.89 0.0001 0.05 -5.1985 -1.7127
demNF -5.9225 1.0136 543 -5.84 <.0001 0.05 -7.9137 -3.9314
demNC -16.3004 1.5125 543 -10.78 <.0001 0.05 -19.2716 -13.3292
age80*grip12 0.1230 0.04054 543 3.03 0.0025 0.05 0.04339 0.2026

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age80 1 543 0.04 0.04 0.8513 0.8513
grip12 1 543 0.00 0.00 0.9860 0.9861
sexMW 1 543 15.17 15.17 <.0001 0.0001
demNF 1 543 34.14 34.14 <.0001 <.0001
demNC 1 543 116.14 116.14 <.0001 <.0001
age80*grip12 1 543 9.21 9.21 0.0024 0.0025

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Future vs Current -10.3779 1.6998 543 -6.11 <.0001 0.05 -13.7169 -7.0388


Eq 2.9: Adding Age by Grip Interaction
Age (0=90), Grip (0=6)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 7
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 86.7615 5.2655 16.48 <.0001

Fit Statistics
-2 Res Log Likelihood 4011.7
AIC (Smaller is Better) 4013.7
AICC (Smaller is Better) 4013.7
BIC (Smaller is Better) 4018.0

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
4011.7 1 4013.7 4013.7 4015.4 4018.0 4019.0

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 24.0345 1.1491 543 20.92 <.0001 0.05 21.7773 26.2917
age90 -0.7030 0.1534 543 -4.58 <.0001 0.05 -1.0043 -0.4017
grip6 1.2345 0.2554 543 4.83 <.0001 0.05 0.7328 1.7362
sexMW -3.4556 0.8873 543 -3.89 0.0001 0.05 -5.1985 -1.7127
demNF -5.9225 1.0136 543 -5.84 <.0001 0.05 -7.9137 -3.9314
demNC -16.3004 1.5125 543 -10.78 <.0001 0.05 -19.2716 -13.3292
age90*grip6 0.1230 0.04054 543 3.03 0.0025 0.05 0.04339 0.2026

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age90 1 543 21.01 21.01 <.0001 <.0001
grip6 1 543 23.36 23.36 <.0001 <.0001
sexMW 1 543 15.17 15.17 <.0001 0.0001
demNF 1 543 34.14 34.14 <.0001 <.0001
demNC 1 543 116.14 116.14 <.0001 <.0001
age90*grip6 1 543 9.21 9.21 0.0024 0.0025

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Future vs Current -10.3779 1.6998 543 -6.11 <.0001 0.05 -13.7169 -7.0388


Eq 2.13: Adding Sex by Dementia Interaction
Sex (0=Men), Dementia (0=None)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 29.0701 0.7485 541 38.84 <.0001 0.05 27.5998 30.5405
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW -2.8756 1.0112 541 -2.84 0.0046 0.05 -4.8620 -0.8892
demNF -6.0559 1.6351 541 -3.70 0.0002 0.05 -9.2679 -2.8439
demNC -11.9707 2.2450 541 -5.33 <.0001 0.05 -16.3806 -7.5608
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demNF 0.1643 2.0705 541 0.08 0.9368 0.05 -3.9029 4.2314
sexMW*demNC -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338

Covariance Matrix for Fixed Effects
Row Effect Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8 Col9
1 Intercept 0.5603 0.001604 -0.03092 -0.5874 -0.5028 -0.5098 0.001953 0.5214 0.5131
2 age85 0.001604 0.01437 0.003278 0.002989 -0.00968 -0.00296 0.000950 0.008994 0.003199
3 grip9 -0.03092 0.003278 0.02193 0.05402 -0.01063 -0.00064 0.000201 -0.00423 0.000673
4 sexMW -0.5874 0.002989 0.05402 1.0226 0.4853 0.5143 0.002578 -0.8987 -0.8822
5 demNF -0.5028 -0.00968 -0.01063 0.4853 2.6736 0.5111 -0.00270 -2.6639 -0.5149
6 demNC -0.5098 -0.00296 -0.00064 0.5143 0.5111 5.0398 0.001824 -0.5143 -5.0362
7 age85*grip9 0.001953 0.000950 0.000201 0.002578 -0.00270 0.001824 0.001628 0.000074 0.001001
8 sexMW*demNF 0.5214 0.008994 -0.00423 -0.8987 -2.6639 -0.5143 0.000074 4.2869 0.8857
9 sexMW*demNC 0.5131 0.003199 0.000673 -0.8822 -0.5149 -5.0362 0.001001 0.8857 9.1478

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 8.09 8.09 0.0045 0.0046
demNF 1 541 13.72 13.72 0.0002 0.0002
demNC 1 541 28.43 28.43 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demNF 1 541 0.01 0.01 0.9368 0.9368
sexMW*demNC 1 541 6.78 6.78 0.0092 0.0095

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Cognition for Men None 29.0701 0.7485 541 38.84 <.0001 0.05 27.5998 30.5405
Cognition for Women None 26.1946 0.6388 541 41.00 <.0001 0.05 24.9397 27.4495
Cognition for Men Future 23.0142 1.4928 541 15.42 <.0001 0.05 20.0819 25.9466
Cognition for Women Future 20.3029 1.1186 541 18.15 <.0001 0.05 18.1055 22.5003
Cognition for Men Current 17.0994 2.1402 541 7.99 <.0001 0.05 12.8953 21.3036
Cognition for Women Current 6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751
Sex Difference for No Dementia -2.8756 1.0112 541 -2.84 0.0046 0.05 -4.8620 -0.8892
Sex Difference for Future Dementia -2.7113 1.8741 541 -1.45 0.1485 0.05 -6.3927 0.9700
Sex Difference for Current Dementia -10.7507 2.8993 541 -3.71 0.0002 0.05 -16.4460 -5.0554
None-Future Difference for Men -6.0559 1.6351 541 -3.70 0.0002 0.05 -9.2679 -2.8439
None-Future Difference for Women -5.8916 1.2778 541 -4.61 <.0001 0.05 -8.4016 -3.3817
None-Current Difference for Men -11.9707 2.2450 541 -5.33 <.0001 0.05 -16.3806 -7.5608
None-Current Difference for Women -19.8458 2.0286 541 -9.78 <.0001 0.05 -23.8307 -15.8610
Future-Current Difference for Men -5.9148 2.5868 541 -2.29 0.0226 0.05 -10.9962 -0.8335
Future-Current Difference for Women -13.9542 2.2389 541 -6.23 <.0001 0.05 -18.3522 -9.5562
None-Future Sex Difference 0.1643 2.0705 541 0.08 0.9368 0.05 -3.9029 4.2314
None-Current Sex Difference -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338
Future-Current Sex Difference -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 8 541 230.14 28.77 <.0001 <.0001
Omnibus Dementia*Sex Interaction Test 2 541 6.98 3.49 0.0304 0.0311


R2 (% Reduction) Overall and for CovAgeGrip vs. CovSexDem

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovAgeGrip Residual 86.7615 5.2655 16.48 <.0001 0.28153 .
CovSexDem Residual 85.9724 5.2273 16.45 <.0001 0.28806 .006534430


Regions of significance for age85*grip9 interaction:
The effect of grip9 will be significant at centered values of age85 BELOW the lower bound
and ABOVE the upper bound, which translate to these uncentered lower and upper bounds.

CenteredLower CenteredUpper UncenteredLower UncenteredUpper
-14.9450 -2.29760 70.0550 82.7024


Regions of significance for age85*grip9 interaction:
The effect of age85 will be significant at centered values of grip9 BELOW the lower bound
and ABOVE the upper bound, which translate to these uncentered lower and upper bounds.

CenteredLower CenteredUpper UncenteredLower UncenteredUpper
0.68049 9.64497 9.68049 18.6450


Eq 2.13: Adding Sex by Dementia Interaction
Sex (0=Women), Dementia (0=None)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 26.1946 0.6388 541 41.00 <.0001 0.05 24.9397 27.4495
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexWM 2.8756 1.0112 541 2.84 0.0046 0.05 0.8892 4.8620
demNF -5.8916 1.2778 541 -4.61 <.0001 0.05 -8.4016 -3.3817
demNC -19.8458 2.0286 541 -9.78 <.0001 0.05 -23.8307 -15.8610
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexWM*demNF -0.1643 2.0705 541 -0.08 0.9368 0.05 -4.2314 3.9029
sexWM*demNC 7.8751 3.0245 541 2.60 0.0095 0.05 1.9338 13.8164

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexWM 1 541 8.09 8.09 0.0045 0.0046
demNF 1 541 21.26 21.26 <.0001 <.0001
demNC 1 541 95.71 95.71 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexWM*demNF 1 541 0.01 0.01 0.9368 0.9368
sexWM*demNC 1 541 6.78 6.78 0.0092 0.0095


Eq 2.15: Adding Sex by Dementia Interaction
Sex (0=Men), Dementia (0=Future)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 23.0142 1.4928 541 15.42 <.0001 0.05 20.0819 25.9466
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW -2.7113 1.8741 541 -1.45 0.1485 0.05 -6.3927 0.9700
demFN 6.0559 1.6351 541 3.70 0.0002 0.05 2.8439 9.2679
demFC -5.9148 2.5868 541 -2.29 0.0226 0.05 -10.9962 -0.8335
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demFN -0.1643 2.0705 541 -0.08 0.9368 0.05 -4.2314 3.9029
sexMW*demFC -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 2.09 2.09 0.1480 0.1485
demFN 1 541 13.72 13.72 0.0002 0.0002
demFC 1 541 5.23 5.23 0.0222 0.0226
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demFN 1 541 0.01 0.01 0.9368 0.9368
sexMW*demFC 1 541 5.54 5.54 0.0186 0.0189


Eq 2.15: Adding Sex by Dementia Interaction
Sex (0=Women), Dementia (0=Future)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 20.3029 1.1186 541 18.15 <.0001 0.05 18.1055 22.5003
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexWM 2.7113 1.8741 541 1.45 0.1485 0.05 -0.9700 6.3927
demFN 5.8916 1.2778 541 4.61 <.0001 0.05 3.3817 8.4016
demFC -13.9542 2.2389 541 -6.23 <.0001 0.05 -18.3522 -9.5562
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexWM*demFN 0.1643 2.0705 541 0.08 0.9368 0.05 -3.9029 4.2314
sexWM*demFC 8.0394 3.4152 541 2.35 0.0189 0.05 1.3308 14.7480

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexWM 1 541 2.09 2.09 0.1480 0.1485
demFN 1 541 21.26 21.26 <.0001 <.0001
demFC 1 541 38.84 38.84 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexWM*demFN 1 541 0.01 0.01 0.9368 0.9368
sexWM*demFC 1 541 5.54 5.54 0.0186 0.0189


Eq 2.16: Adding Sex by Dementia Interaction
Sex (0=Men), Dementia (0=Current)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 17.0994 2.1402 541 7.99 <.0001 0.05 12.8953 21.3036
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW -10.7507 2.8993 541 -3.71 0.0002 0.05 -16.4460 -5.0554
demCN 11.9707 2.2450 541 5.33 <.0001 0.05 7.5608 16.3806
demCF 5.9148 2.5868 541 2.29 0.0226 0.05 0.8335 10.9962
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demCN 7.8751 3.0245 541 2.60 0.0095 0.05 1.9338 13.8164
sexMW*demCF 8.0394 3.4152 541 2.35 0.0189 0.05 1.3308 14.7480

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 13.75 13.75 0.0002 0.0002
demCN 1 541 28.43 28.43 <.0001 <.0001
demCF 1 541 5.23 5.23 0.0222 0.0226
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demCN 1 541 6.78 6.78 0.0092 0.0095
sexMW*demCF 1 541 5.54 5.54 0.0186 0.0189


Eq 2.16: Adding Sex by Dementia Interaction
Sex (0=Women), Dementia (0=Current)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexWM 10.7507 2.8993 541 3.71 0.0002 0.05 5.0554 16.4460
demCN 19.8458 2.0286 541 9.78 <.0001 0.05 15.8610 23.8307
demCF 13.9542 2.2389 541 6.23 <.0001 0.05 9.5562 18.3522
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexWM*demCN -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338
sexWM*demCF -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexWM 1 541 13.75 13.75 0.0002 0.0002
demCN 1 541 95.71 95.71 <.0001 <.0001
demCF 1 541 38.84 38.84 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexWM*demCN 1 541 6.78 6.78 0.0092 0.0095
sexWM*demCF 1 541 5.54 5.54 0.0186 0.0189


Eq 2.16: Adding Sex by Dementia Interaction
Categorical Sex and Dementia

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 15
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept     6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751
age85     -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9     0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW 0   10.7507 2.8993 541 3.71 0.0002 0.05 5.0554 16.4460
sexMW 1   0 . . . . . . .
demgroup   1None 19.8458 2.0286 541 9.78 <.0001 0.05 15.8610 23.8307
demgroup   2Future 13.9542 2.2389 541 6.23 <.0001 0.05 9.5562 18.3522
demgroup   3Current 0 . . . . . . .
age85*grip9     0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demgroup 0 1None -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338
sexMW*demgroup 0 2Future -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308
sexMW*demgroup 0 3Current 0 . . . . . . .
sexMW*demgroup 1 1None 0 . . . . . . .
sexMW*demgroup 1 2Future 0 . . . . . . .
sexMW*demgroup 1 3Current 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 19.45 19.45 <.0001 <.0001
demgroup 2 541 129.24 64.62 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demgroup 2 541 6.98 3.49 0.0304 0.0311

Contrasts
Label Num DF Den DF F Value Pr > F
Sex by None-Future Interaction 1 541 0.01 0.9368
Sex by None-Current Interaction 1 541 6.78 0.0095
Sex by Future-Current Interaction 1 541 5.54 0.0189

Least Squares Means
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
sexMW*demgroup 0 1None 0.00 0.00 29.0701 0.7485 541 38.84 <.0001 0.05 27.5998 30.5405
sexMW*demgroup 0 2Future 0.00 0.00 23.0142 1.4928 541 15.42 <.0001 0.05 20.0819 25.9466
sexMW*demgroup 0 3Current 0.00 0.00 17.0994 2.1402 541 7.99 <.0001 0.05 12.8953 21.3036
sexMW*demgroup 1 1None 0.00 0.00 26.1946 0.6388 541 41.00 <.0001 0.05 24.9397 27.4495
sexMW*demgroup 1 2Future 0.00 0.00 20.3029 1.1186 541 18.15 <.0001 0.05 18.1055 22.5003
sexMW*demgroup 1 3Current 0.00 0.00 6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751

Differences of Least Squares Means
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
sexMW*demgroup 0 1None 0 2Future 0.00 0.00 6.0559 1.6351 541 3.70 0.0002 0.05 2.8439 9.2679
sexMW*demgroup 0 1None 0 3Current 0.00 0.00 11.9707 2.2450 541 5.33 <.0001 0.05 7.5608 16.3806
sexMW*demgroup 0 1None 1 1None 0.00 0.00 2.8756 1.0112 541 2.84 0.0046 0.05 0.8892 4.8620
sexMW*demgroup 0 1None 1 2Future 0.00 0.00 8.7672 1.3522 541 6.48 <.0001 0.05 6.1109 11.4235
sexMW*demgroup 0 1None 1 3Current 0.00 0.00 22.7214 2.0981 541 10.83 <.0001 0.05 18.6000 26.8429
sexMW*demgroup 0 2Future 0 3Current 0.00 0.00 5.9148 2.5868 541 2.29 0.0226 0.05 0.8335 10.9962
sexMW*demgroup 0 2Future 1 1None 0.00 0.00 -3.1803 1.6509 541 -1.93 0.0546 0.05 -6.4233 0.06273
sexMW*demgroup 0 2Future 1 2Future 0.00 0.00 2.7113 1.8741 541 1.45 0.1485 0.05 -0.9700 6.3927
sexMW*demgroup 0 2Future 1 3Current 0.00 0.00 16.6655 2.4724 541 6.74 <.0001 0.05 11.8088 21.5222
sexMW*demgroup 0 3Current 1 1None 0.00 0.00 -9.0951 2.2436 541 -4.05 <.0001 0.05 -13.5024 -4.6879
sexMW*demgroup 0 3Current 1 2Future 0.00 0.00 -3.2035 2.4179 541 -1.32 0.1858 0.05 -7.9531 1.5461
sexMW*demgroup 0 3Current 1 3Current 0.00 0.00 10.7507 2.8993 541 3.71 0.0002 0.05 5.0554 16.4460
sexMW*demgroup 1 1None 1 2Future 0.00 0.00 5.8916 1.2778 541 4.61 <.0001 0.05 3.3817 8.4016
sexMW*demgroup 1 1None 1 3Current 0.00 0.00 19.8458 2.0286 541 9.78 <.0001 0.05 15.8610 23.8307
sexMW*demgroup 1 2Future 1 3Current 0.00 0.00 13.9542 2.2389 541 6.23 <.0001 0.05 9.5562 18.3522

Tests of Effect Slices
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Num DF Den DF F Value Pr > F
sexMW*demgroup   1None 0.00 0.00 1 541 8.09 0.0046
sexMW*demgroup   2Future 0.00 0.00 1 541 2.09 0.1485
sexMW*demgroup   3Current 0.00 0.00 1 541 13.75 0.0002
sexMW*demgroup 0   0.00 0.00 2 541 18.69 <.0001
sexMW*demgroup 1   0.00 0.00 2 541 53.16 <.0001


Eq 2.17: Adding Age by Sex and Grip by Sex Interactions
Age (0=85), Grip (0=9), Sex (0=Men), Dementia (0=None)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 11
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 86.2234 5.2523 16.42 <.0001

Fit Statistics
-2 Res Log Likelihood 3998.3
AIC (Smaller is Better) 4000.3
AICC (Smaller is Better) 4000.3
BIC (Smaller is Better) 4004.6

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3998.3 1 4000.3 4000.3 4002.0 4004.6 4005.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 28.9051 0.7980 539 36.22 <.0001 0.05 27.3377 30.4726
age85 -0.3839 0.1947 539 -1.97 0.0492 0.05 -0.7664 -0.00141
grip9 0.7231 0.2366 539 3.06 0.0024 0.05 0.2583 1.1879
sexMW -2.7551 1.0297 539 -2.68 0.0077 0.05 -4.7777 -0.7325
demNF -6.0832 1.6399 539 -3.71 0.0002 0.05 -9.3045 -2.8619
demNC -11.9467 2.2494 539 -5.31 <.0001 0.05 -16.3654 -7.5280
age85*grip9 0.1295 0.04597 539 2.82 0.0050 0.05 0.03918 0.2198
sexMW*demNF 0.2270 2.0804 539 0.11 0.9132 0.05 -3.8598 4.3137
sexMW*demNC -7.8890 3.0293 539 -2.60 0.0095 0.05 -13.8397 -1.9383
age85*sexMW 0.07884 0.2744 539 0.29 0.7740 0.05 -0.4602 0.6179
grip9*sexMW -0.1641 0.3043 539 -0.54 0.5898 0.05 -0.7619 0.4336

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 539 3.89 3.89 0.0487 0.0492
grip9 1 539 9.34 9.34 0.0022 0.0024
sexMW 1 539 7.16 7.16 0.0075 0.0077
demNF 1 539 13.76 13.76 0.0002 0.0002
demNC 1 539 28.21 28.21 <.0001 <.0001
age85*grip9 1 539 7.93 7.93 0.0049 0.0050
sexMW*demNF 1 539 0.01 0.01 0.9131 0.9132
sexMW*demNC 1 539 6.78 6.78 0.0092 0.0095
age85*sexMW 1 539 0.08 0.08 0.7739 0.7740
grip9*sexMW 1 539 0.29 0.29 0.5896 0.5898

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Age for Men -0.3839 0.1947 539 -1.97 0.0492 0.05 -0.7664 -0.00141
Age for Women -0.3051 0.1710 539 -1.78 0.0749 0.05 -0.6409 0.03074
Grip for Men 0.7231 0.2366 539 3.06 0.0024 0.05 0.2583 1.1879
Grip for Women 0.5590 0.1920 539 2.91 0.0037 0.05 0.1819 0.9360
Sex for None -2.7551 1.0297 539 -2.68 0.0077 0.05 -4.7777 -0.7325
Sex for Future -2.5281 1.9014 539 -1.33 0.1842 0.05 -6.2632 1.2070
Sex for Current -10.6441 2.9082 539 -3.66 0.0003 0.05 -16.3569 -4.9313
Men: None vs Future -6.0832 1.6399 539 -3.71 0.0002 0.05 -9.3045 -2.8619
Men: None vs Current -11.9467 2.2494 539 -5.31 <.0001 0.05 -16.3654 -7.5280
Men: Future vs Current -5.8635 2.5918 539 -2.26 0.0241 0.05 -10.9547 -0.7723
Women: None vs Future -5.8562 1.2823 539 -4.57 <.0001 0.05 -8.3752 -3.3373
Women: None vs Current -19.8357 2.0317 539 -9.76 <.0001 0.05 -23.8268 -15.8446
Women: Future vs Current -13.9795 2.2441 539 -6.23 <.0001 0.05 -18.3878 -9.5711
Sex by None vs Future 0.2270 2.0804 539 0.11 0.9132 0.05 -3.8598 4.3137
Sex by None vs Current -7.8890 3.0293 539 -2.60 0.0095 0.05 -13.8397 -1.9383
Sex by Future vs Current -8.1160 3.4236 539 -2.37 0.0181 0.05 -14.8412 -1.3908


R2 (% Reduction) Overall and for CovSexDem vs. Cov2AgeSexGrip

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovSexDem Residual 85.9724 5.2273 16.45 <.0001 0.28806 .
Cov2AgeSexGrip Residual 86.2234 5.2523 16.42 <.0001 0.28599 -.002078457


Eq 2.18: Adding Adding Age by Grip by Sex Three-Way Interaction
Age (0=85), Grip (0=9), Sex (0=Men), Dementia (0=None)

The Mixed Procedure

Model Information
Data Set WORK.PLOTAGEGRIPSEX
Dependent Variable cognition
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 12
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 568
Number of Observations Used 550
Number of Observations Not Used 18

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9433 5.2401 16.40 <.0001

Fit Statistics
-2 Res Log Likelihood 3998.4
AIC (Smaller is Better) 4000.4
AICC (Smaller is Better) 4000.4
BIC (Smaller is Better) 4004.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3998.4 1 4000.4 4000.4 4002.1 4004.7 4005.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 28.9558 0.7972 538 36.32 <.0001 0.05 27.3898 30.5219
age85 -0.4983 0.2063 538 -2.42 0.0160 0.05 -0.9034 -0.09313
grip9 0.7393 0.2364 538 3.13 0.0019 0.05 0.2749 1.2037
sexMW -2.9735 1.0364 538 -2.87 0.0043 0.05 -5.0093 -0.9377
demNF -6.1654 1.6379 538 -3.76 0.0002 0.05 -9.3830 -2.9479
demNC -11.7837 2.2479 538 -5.24 <.0001 0.05 -16.1994 -7.3680
age85*grip9 0.2300 0.07595 538 3.03 0.0026 0.05 0.08077 0.3791
sexMW*demNF 0.3969 2.0796 538 0.19 0.8487 0.05 -3.6882 4.4820
sexMW*demNC -8.1457 3.0283 538 -2.69 0.0074 0.05 -14.0945 -2.1969
age85*sexMW 0.09507 0.2742 538 0.35 0.7289 0.05 -0.4435 0.6336
grip9*sexMW -0.2001 0.3046 538 -0.66 0.5115 0.05 -0.7984 0.3982
age85*grip9*sexMW -0.1583 0.09532 538 -1.66 0.0974 0.05 -0.3455 0.02898

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 538 5.84 5.84 0.0157 0.0160
grip9 1 538 9.78 9.78 0.0018 0.0019
sexMW 1 538 8.23 8.23 0.0041 0.0043
demNF 1 538 14.17 14.17 0.0002 0.0002
demNC 1 538 27.48 27.48 <.0001 <.0001
age85*grip9 1 538 9.17 9.17 0.0025 0.0026
sexMW*demNF 1 538 0.04 0.04 0.8486 0.8487
sexMW*demNC 1 538 7.24 7.24 0.0071 0.0074
age85*sexMW 1 538 0.12 0.12 0.7288 0.7289
grip9*sexMW 1 538 0.43 0.43 0.5112 0.5115
age85*grip9*sexMW 1 538 2.76 2.76 0.0968 0.0974

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Age for Men -0.4983 0.2063 538 -2.42 0.0160 0.05 -0.9034 -0.09313
Age for Women -0.4032 0.1806 538 -2.23 0.0260 0.05 -0.7580 -0.04841
Grip for Men 0.7393 0.2364 538 3.13 0.0019 0.05 0.2749 1.2037
Grip for Women 0.5392 0.1920 538 2.81 0.0052 0.05 0.1620 0.9164
Sex for None -2.9735 1.0364 538 -2.87 0.0043 0.05 -5.0093 -0.9377
Sex for Future -2.5766 1.8986 538 -1.36 0.1753 0.05 -6.3061 1.1529
Sex for Current -11.1192 2.9176 538 -3.81 0.0002 0.05 -16.8504 -5.3880
Men: None vs Future -6.1654 1.6379 538 -3.76 0.0002 0.05 -9.3830 -2.9479
Men: None vs Current -11.7837 2.2479 538 -5.24 <.0001 0.05 -16.1994 -7.3680
Men: Future vs Current -5.6183 2.5918 538 -2.17 0.0306 0.05 -10.7095 -0.5271
Women: None vs Future -5.7685 1.2813 538 -4.50 <.0001 0.05 -8.2856 -3.2515
Women: None vs Current -19.9294 2.0292 538 -9.82 <.0001 0.05 -23.9156 -15.9433
Women: Future vs Current -14.1609 2.2432 538 -6.31 <.0001 0.05 -18.5673 -9.7545
Sex by None vs Future 0.3969 2.0796 538 0.19 0.8487 0.05 -3.6882 4.4820
Sex by None vs Current -8.1457 3.0283 538 -2.69 0.0074 0.05 -14.0945 -2.1969
Sex by Future vs Current -8.5426 3.4277 538 -2.49 0.0130 0.05 -15.2759 -1.8093
Age by Grip for Men 0.2300 0.07595 538 3.03 0.0026 0.05 0.08077 0.3791
Age by Grip for Women 0.07169 0.05761 538 1.24 0.2139 0.05 -0.04148 0.1849


R2 (% Reduction) Overall and for Cov2AgeSexGrip vs. Cov3AgeSexGrip

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
Cov2AgeSexGrip Residual 86.2234 5.2523 16.42 <.0001 0.28599 .
Cov3AgeSexGrip Residual 85.9433 5.2401 16.40 <.0001 0.28831 .002319510


Predicted Outcomes for Fake People

age85 grip9 sexMW demNF demNC Pred
-5 3 0 0 0 30.2157
0 3 0 0 0 31.1737
5 3 0 0 0 32.1316
-5 0 0 0 0 31.4473
0 0 0 0 0 28.9558
5 0 0 0 0 26.4644
-5 -3 0 0 0 32.6788
0 -3 0 0 0 26.7380
5 -3 0 0 0 20.7972
-5 3 1 0 0 28.5407
0 3 1 0 0 27.6000
5 3 1 0 0 26.6592
-5 0 1 0 0 27.9984
0 0 1 0 0 25.9824
5 0 1 0 0 23.9663
-5 -3 1 0 0 27.4561
0 -3 1 0 0 24.3648
5 -3 1 0 0 21.2734


Eq 2.13: Final Reported Model
Age (0=85), Grip (0=9), Sex (0=Men), Dementia (0=None)

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 9
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 29.0701 0.7485 541 38.84 <.0001 0.05 27.5998 30.5405
age85 -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9 0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW -2.8756 1.0112 541 -2.84 0.0046 0.05 -4.8620 -0.8892
demNF -6.0559 1.6351 541 -3.70 0.0002 0.05 -9.2679 -2.8439
demNC -11.9707 2.2450 541 -5.33 <.0001 0.05 -16.3806 -7.5608
age85*grip9 0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demNF 0.1643 2.0705 541 0.08 0.9368 0.05 -3.9029 4.2314
sexMW*demNC -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 8.09 8.09 0.0045 0.0046
demNF 1 541 13.72 13.72 0.0002 0.0002
demNC 1 541 28.43 28.43 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demNF 1 541 0.01 0.01 0.9368 0.9368
sexMW*demNC 1 541 6.78 6.78 0.0092 0.0095

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Sex Difference for No Dementia -2.8756 1.0112 541 -2.84 0.0046 0.05 -4.8620 -0.8892
Sex Difference for Future Dementia -2.7113 1.8741 541 -1.45 0.1485 0.05 -6.3927 0.9700
Sex Difference for Current Dementia -10.7507 2.8993 541 -3.71 0.0002 0.05 -16.4460 -5.0554
None-Future Difference for Men -6.0559 1.6351 541 -3.70 0.0002 0.05 -9.2679 -2.8439
None-Future Difference for Women -5.8916 1.2778 541 -4.61 <.0001 0.05 -8.4016 -3.3817
None-Current Difference for Men -11.9707 2.2450 541 -5.33 <.0001 0.05 -16.3806 -7.5608
None-Current Difference for Women -19.8458 2.0286 541 -9.78 <.0001 0.05 -23.8307 -15.8610
Future-Current Difference for Men -5.9148 2.5868 541 -2.29 0.0226 0.05 -10.9962 -0.8335
Future-Current Difference for Women -13.9542 2.2389 541 -6.23 <.0001 0.05 -18.3522 -9.5562
None-Future Sex Difference 0.1643 2.0705 541 0.08 0.9368 0.05 -3.9029 4.2314
None-Current Sex Difference -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338
Future-Current Sex Difference -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308

Contrasts
Label Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
Model R2 Test 8 541 230.14 28.77 <.0001 <.0001
Omnibus Dementia*Sex Interaction Test 2 541 6.98 3.49 0.0304 0.0311


R2 (% Reduction) Overall and for CovEmpty vs. CovSexDem

Name CovParm Estimate StdErr ZValue ProbZ R2_from_Base R2_Increment
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovEmpty Residual 120.76 7.2887 16.57 <.0001 -0.00000 .
CovSexDem Residual 85.9724 5.2273 16.45 <.0001 0.28806 0.28806


Eq 2.13: Final Reported Model
Categorical Variables for Sex and Dementia

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER2
Dependent Variable cognition
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 15
Columns in Z 0
Subjects 1
Max Obs per Subject 550

Number of Observations
Number of Observations Read 550
Number of Observations Used 550
Number of Observations Not Used 0

Covariance Parameter Estimates
Cov Parm Estimate Standard Error Z Value Pr > Z
Residual 85.9724 5.2273 16.45 <.0001

Fit Statistics
-2 Res Log Likelihood 3997.4
AIC (Smaller is Better) 3999.4
AICC (Smaller is Better) 3999.4
BIC (Smaller is Better) 4003.7

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
3997.4 1 3999.4 3999.4 4001.1 4003.7 4004.7

Solution for Fixed Effects
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept     6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751
age85     -0.3348 0.1199 541 -2.79 0.0054 0.05 -0.5703 -0.09930
grip9     0.6179 0.1481 541 4.17 <.0001 0.05 0.3270 0.9088
sexMW 0   10.7507 2.8993 541 3.71 0.0002 0.05 5.0554 16.4460
sexMW 1   0 . . . . . . .
demgroup   1None 19.8458 2.0286 541 9.78 <.0001 0.05 15.8610 23.8307
demgroup   2Future 13.9542 2.2389 541 6.23 <.0001 0.05 9.5562 18.3522
demgroup   3Current 0 . . . . . . .
age85*grip9     0.1222 0.04035 541 3.03 0.0026 0.05 0.04288 0.2014
sexMW*demgroup 0 1None -7.8751 3.0245 541 -2.60 0.0095 0.05 -13.8164 -1.9338
sexMW*demgroup 0 2Future -8.0394 3.4152 541 -2.35 0.0189 0.05 -14.7480 -1.3308
sexMW*demgroup 0 3Current 0 . . . . . . .
sexMW*demgroup 1 1None 0 . . . . . . .
sexMW*demgroup 1 2Future 0 . . . . . . .
sexMW*demgroup 1 3Current 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
age85 1 541 7.80 7.80 0.0052 0.0054
grip9 1 541 17.41 17.41 <.0001 <.0001
sexMW 1 541 19.45 19.45 <.0001 <.0001
demgroup 2 541 129.24 64.62 <.0001 <.0001
age85*grip9 1 541 9.16 9.16 0.0025 0.0026
sexMW*demgroup 2 541 6.98 3.49 0.0304 0.0311

Least Squares Means
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
sexMW*demgroup 0 1None 0.00 0.00 29.0701 0.7485 541 38.84 <.0001 0.05 27.5998 30.5405
sexMW*demgroup 0 2Future 0.00 0.00 23.0142 1.4928 541 15.42 <.0001 0.05 20.0819 25.9466
sexMW*demgroup 0 3Current 0.00 0.00 17.0994 2.1402 541 7.99 <.0001 0.05 12.8953 21.3036
sexMW*demgroup 1 1None 0.00 0.00 26.1946 0.6388 541 41.00 <.0001 0.05 24.9397 27.4495
sexMW*demgroup 1 2Future 0.00 0.00 20.3029 1.1186 541 18.15 <.0001 0.05 18.1055 22.5003
sexMW*demgroup 1 3Current 0.00 0.00 6.3487 1.9479 541 3.26 0.0012 0.05 2.5224 10.1751

Differences of Least Squares Means
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
sexMW*demgroup 0 1None 0 2Future 0.00 0.00 6.0559 1.6351 541 3.70 0.0002 0.05 2.8439 9.2679
sexMW*demgroup 0 1None 0 3Current 0.00 0.00 11.9707 2.2450 541 5.33 <.0001 0.05 7.5608 16.3806
sexMW*demgroup 0 1None 1 1None 0.00 0.00 2.8756 1.0112 541 2.84 0.0046 0.05 0.8892 4.8620
sexMW*demgroup 0 1None 1 2Future 0.00 0.00 8.7672 1.3522 541 6.48 <.0001 0.05 6.1109 11.4235
sexMW*demgroup 0 1None 1 3Current 0.00 0.00 22.7214 2.0981 541 10.83 <.0001 0.05 18.6000 26.8429
sexMW*demgroup 0 2Future 0 3Current 0.00 0.00 5.9148 2.5868 541 2.29 0.0226 0.05 0.8335 10.9962
sexMW*demgroup 0 2Future 1 1None 0.00 0.00 -3.1803 1.6509 541 -1.93 0.0546 0.05 -6.4233 0.06273
sexMW*demgroup 0 2Future 1 2Future 0.00 0.00 2.7113 1.8741 541 1.45 0.1485 0.05 -0.9700 6.3927
sexMW*demgroup 0 2Future 1 3Current 0.00 0.00 16.6655 2.4724 541 6.74 <.0001 0.05 11.8088 21.5222
sexMW*demgroup 0 3Current 1 1None 0.00 0.00 -9.0951 2.2436 541 -4.05 <.0001 0.05 -13.5024 -4.6879
sexMW*demgroup 0 3Current 1 2Future 0.00 0.00 -3.2035 2.4179 541 -1.32 0.1858 0.05 -7.9531 1.5461
sexMW*demgroup 0 3Current 1 3Current 0.00 0.00 10.7507 2.8993 541 3.71 0.0002 0.05 5.0554 16.4460
sexMW*demgroup 1 1None 1 2Future 0.00 0.00 5.8916 1.2778 541 4.61 <.0001 0.05 3.3817 8.4016
sexMW*demgroup 1 1None 1 3Current 0.00 0.00 19.8458 2.0286 541 9.78 <.0001 0.05 15.8610 23.8307
sexMW*demgroup 1 2Future 1 3Current 0.00 0.00 13.9542 2.2389 541 6.23 <.0001 0.05 9.5562 18.3522

Tests of Effect Slices
Effect sexMW:
Sex (0=Men,
1=Women)		 demgroup: Dementia
Diagnosis (1=None,
2=Future, 3=Current)		 age85 grip9 Num DF Den DF F Value Pr > F
sexMW*demgroup   1None 0.00 0.00 1 541 8.09 0.0046
sexMW*demgroup   2Future 0.00 0.00 1 541 2.09 0.1485
sexMW*demgroup   3Current 0.00 0.00 1 541 13.75 0.0002
sexMW*demgroup 0   0.00 0.00 2 541 18.69 <.0001
sexMW*demgroup 1   0.00 0.00 2 541 53.16 <.0001