Results: RepeatedNoise.sas

Noise data

The FREQ Procedure

The FREQ Procedure

Table 1 of age * noise

Cross-Tabular Freq Table

Frequency
Table 1 of age by noise
Controlling for sex=Male
age noise
1 2 3 4 5 Total
1
10
10
10
10
10
50
2
10
10
10
10
10
50
3
10
10
10
10
10
50
Total
30
30
30
30
30
150

Table 2 of age * noise

Cross-Tabular Freq Table

Frequency
Table 2 of age by noise
Controlling for sex=Female
age noise
1 2 3 4 5 Total
1
10
10
10
10
10
50
2
10
10
10
10
10
50
3
10
10
10
10
10
50
Total
30
30
30
30
30
150

Noise data

Classical mixed model repeated measures

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
ident 60 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
age 3 1 2 3
sex 2 Female Male
noise 5 1 2 3 4 5

Number of Observations

Number of Observations Read 300
Number of Observations Used 300

Noise data

Classical mixed model repeated measures

The GLM Procedure

Dependent Variable: discrim

Analysis of Variance

discrim

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 83 13902.14347 167.49570 4.13 <.0001
Error 216 8755.83320 40.53626    
Corrected Total 299 22657.97667      

Fit Statistics

R-Square Coeff Var Root MSE discrim Mean
0.613565 17.90609 6.366810 35.55667

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
age 2 1751.814067 875.907033 21.61 <.0001
sex 1 77.419200 77.419200 1.91 0.1684
age*sex 2 121.790600 60.895300 1.50 0.2249
noise 4 2289.314000 572.328500 14.12 <.0001
age*noise 8 334.429600 41.803700 1.03 0.4134
sex*noise 4 142.422800 35.605700 0.88 0.4777
age*sex*noise 8 345.664400 43.208050 1.07 0.3882
ident(age*sex) 54 8839.288800 163.690533 4.04 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
age 2 1751.814067 875.907033 21.61 <.0001
sex 1 77.419200 77.419200 1.91 0.1684
age*sex 2 121.790600 60.895300 1.50 0.2249
noise 4 2289.314000 572.328500 14.12 <.0001
age*noise 8 334.429600 41.803700 1.03 0.4134
sex*noise 4 142.422800 35.605700 0.88 0.4777
age*sex*noise 8 345.664400 43.208050 1.07 0.3882
ident(age*sex) 54 8839.288800 163.690533 4.04 <.0001

Noise data

Classical mixed model repeated measures

The GLM Procedure

Random Effects Analysis

Model Expected Mean Squares

Source Type III Expected Mean Square
age Var(Error) + 5 Var(ident(age*sex)) + Q(age,age*sex,age*noise,age*sex*noise)
sex Var(Error) + 5 Var(ident(age*sex)) + Q(sex,age*sex,sex*noise,age*sex*noise)
age*sex Var(Error) + 5 Var(ident(age*sex)) + Q(age*sex,age*sex*noise)
noise Var(Error) + Q(noise,age*noise,sex*noise,age*sex*noise)
age*noise Var(Error) + Q(age*noise,age*sex*noise)
sex*noise Var(Error) + Q(sex*noise,age*sex*noise)
age*sex*noise Var(Error) + Q(age*sex*noise)
ident(age*sex) Var(Error) + 5 Var(ident(age*sex))

Noise data

Classical mixed model repeated measures

The GLM Procedure

Tests of Hypotheses for Mixed Model Analysis of Variance

Dependent Variable: discrim

discrim

Type III Model ANOVA

  Source DF Type III SS Mean Square F Value Pr > F
Error: MS(ident(age*sex))
* This test assumes one or more other fixed effects are zero.
* age 2 1751.814067 875.907033 5.35 0.0076
* sex 1 77.419200 77.419200 0.47 0.4946
* age*sex 2 121.790600 60.895300 0.37 0.6911
  Error 54 8839.288800 163.690533    

Type III Model ANOVA

  Source DF Type III SS Mean Square F Value Pr > F
* This test assumes one or more other fixed effects are zero.
* noise 4 2289.314000 572.328500 14.12 <.0001
* age*noise 8 334.429600 41.803700 1.03 0.4134
* sex*noise 4 142.422800 35.605700 0.88 0.4777
  age*sex*noise 8 345.664400 43.208050 1.07 0.3882
  ident(age*sex) 54 8839.288800 163.690533 4.04 <.0001
  Error: MS(Error) 216 8755.833200 40.536265    

Noise data

Classical mixed model repeated measures

Means

noise

discrim

Distribution of discrim by noise

Distribution of discrim by noise

Means

Level of
noise		 N discrim
Mean Std Dev
1 60 39.8216667 7.79326288
2 60 36.8300000 8.84743188
3 60 35.3016667 8.02074623
4 60 34.3850000 8.19035864
5 60 31.4450000 8.64900161

age

discrim

Distribution of discrim by age

Distribution of discrim by age

Means

Level of
age		 N discrim
Mean Std Dev
1 100 38.6610000 9.33913126
2 100 35.2420000 8.02510178
3 100 32.7670000 7.71697663

Noise data

Covariance structure (cs) with proc mixed

Replicate the classical tests

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.LOUD
Dependent Variable discrim
Covariance Structure Compound Symmetry
Subject Effect ident
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within

Class Level Information

Class Level Information
Class Levels Values
age 3 1 2 3
sex 2 Female Male
noise 5 1 2 3 4 5

Dimensions

Dimensions
Covariance Parameters 2
Columns in X 72
Columns in Z 0
Subjects 60
Max Obs per Subject 5

Number of Observations

Number of Observations
Number of Observations Read 300
Number of Observations Used 300
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 1963.08221734  
1 1 1910.26970621 0.00000000

Convergence Status

Convergence criteria met.

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Subject Estimate
CS ident 24.6309
Residual   40.5363

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 1910.3
AIC (Smaller is Better) 1914.3
AICC (Smaller is Better) 1914.3
BIC (Smaller is Better) 1918.5

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 52.81 <.0001

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
age 2 54 5.35 0.0076
sex 1 54 0.47 0.4946
age*sex 2 54 0.37 0.6911
noise 4 216 14.12 <.0001
age*noise 8 216 1.03 0.4134
sex*noise 4 216 0.88 0.4777
age*sex*noise 8 216 1.07 0.3882

Noise data

Include covariate, multiple comparisons, contrasts

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.LOUD
Dependent Variable discrim
Covariance Structure Compound Symmetry
Subject Effect ident
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within

Class Level Information

Class Level Information
Class Levels Values
age 3 1 2 3
sex 2 Female Male
noise 5 1 2 3 4 5

Dimensions

Dimensions
Covariance Parameters 2
Columns in X 73
Columns in Z 0
Subjects 60
Max Obs per Subject 5

Number of Observations

Number of Observations
Number of Observations Read 300
Number of Observations Used 300
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 1943.32710280  
1 1 1900.42320330 0.00000000

Convergence Status

Convergence criteria met.

Estimated R Matrix for Subject 1

Estimated R Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5
1 61.4286 20.8923 20.8923 20.8923 20.8923
2 20.8923 61.4286 20.8923 20.8923 20.8923
3 20.8923 20.8923 61.4286 20.8923 20.8923
4 20.8923 20.8923 20.8923 61.4286 20.8923
5 20.8923 20.8923 20.8923 20.8923 61.4286

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Subject Estimate
CS ident 20.8923
Residual   40.5363

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 1900.4
AIC (Smaller is Better) 1904.4
AICC (Smaller is Better) 1904.5
BIC (Smaller is Better) 1908.6

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 42.90 <.0001

Solution for Fixed Effects

Solution for Fixed Effects
Effect age sex noise Estimate Standard
Error		 DF t Value Pr > |t|
Intercept       16.5108 4.2580 53 3.88 0.0003
interest       3.5524 1.2590 53 2.82 0.0067
age 1     8.7702 3.5241 53 2.49 0.0160
age 2     8.2846 3.6022 53 2.30 0.0254
age 3     0 . . . .
sex   Female   0.5413 3.5268 53 0.15 0.8786
sex   Male   0 . . . .
age*sex 1 Female   3.2374 4.9662 53 0.65 0.5173
age*sex 1 Male   0 . . . .
age*sex 2 Female   -1.1957 5.0303 53 -0.24 0.8130
age*sex 2 Male   0 . . . .
age*sex 3 Female   0 . . . .
age*sex 3 Male   0 . . . .
noise     1 11.9300 2.8473 216 4.19 <.0001
noise     2 9.5000 2.8473 216 3.34 0.0010
noise     3 7.7600 2.8473 216 2.73 0.0069
noise     4 4.4000 2.8473 216 1.55 0.1237
noise     5 0 . . . .
age*noise 1   1 -3.7400 4.0267 216 -0.93 0.3540
age*noise 1   2 -4.3800 4.0267 216 -1.09 0.2779
age*noise 1   3 -2.4100 4.0267 216 -0.60 0.5501
age*noise 1   4 -2.0100 4.0267 216 -0.50 0.6182
age*noise 1   5 0 . . . .
age*noise 2   1 -4.3600 4.0267 216 -1.08 0.2801
age*noise 2   2 -8.0300 4.0267 216 -1.99 0.0474
age*noise 2   3 -7.1100 4.0267 216 -1.77 0.0789
age*noise 2   4 -5.6000 4.0267 216 -1.39 0.1657
age*noise 2   5 0 . . . .
age*noise 3   1 0 . . . .
age*noise 3   2 0 . . . .
age*noise 3   3 0 . . . .
age*noise 3   4 0 . . . .
age*noise 3   5 0 . . . .
sex*noise   Female 1 -0.6900 4.0267 216 -0.17 0.8641
sex*noise   Female 2 -1.2000 4.0267 216 -0.30 0.7660
sex*noise   Female 3 -2.4400 4.0267 216 -0.61 0.5452
sex*noise   Female 4 4.8200 4.0267 216 1.20 0.2326
sex*noise   Female 5 0 . . . .
sex*noise   Male 1 0 . . . .
sex*noise   Male 2 0 . . . .
sex*noise   Male 3 0 . . . .
sex*noise   Male 4 0 . . . .
sex*noise   Male 5 0 . . . .
age*sex*noise 1 Female 1 -1.4200 5.6946 216 -0.25 0.8033
age*sex*noise 1 Female 2 -0.1600 5.6946 216 -0.03 0.9776
age*sex*noise 1 Female 3 -4.5400 5.6946 216 -0.80 0.4262
age*sex*noise 1 Female 4 -7.7100 5.6946 216 -1.35 0.1772
age*sex*noise 1 Female 5 0 . . . .
age*sex*noise 1 Male 1 0 . . . .
age*sex*noise 1 Male 2 0 . . . .
age*sex*noise 1 Male 3 0 . . . .
age*sex*noise 1 Male 4 0 . . . .
age*sex*noise 1 Male 5 0 . . . .
age*sex*noise 2 Female 1 -1.6300 5.6946 216 -0.29 0.7750
age*sex*noise 2 Female 2 3.8900 5.6946 216 0.68 0.4953
age*sex*noise 2 Female 3 7.4800 5.6946 216 1.31 0.1904
age*sex*noise 2 Female 4 -0.2900 5.6946 216 -0.05 0.9594
age*sex*noise 2 Female 5 0 . . . .
age*sex*noise 2 Male 1 0 . . . .
age*sex*noise 2 Male 2 0 . . . .
age*sex*noise 2 Male 3 0 . . . .
age*sex*noise 2 Male 4 0 . . . .
age*sex*noise 2 Male 5 0 . . . .
age*sex*noise 3 Female 1 0 . . . .
age*sex*noise 3 Female 2 0 . . . .
age*sex*noise 3 Female 3 0 . . . .
age*sex*noise 3 Female 4 0 . . . .
age*sex*noise 3 Female 5 0 . . . .
age*sex*noise 3 Male 1 0 . . . .
age*sex*noise 3 Male 2 0 . . . .
age*sex*noise 3 Male 3 0 . . . .
age*sex*noise 3 Male 4 0 . . . .
age*sex*noise 3 Male 5 0 . . . .

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
interest 1 53 7.96 0.0067
age 2 53 7.18 0.0017
sex 1 53 0.55 0.4630
age*sex 2 53 0.02 0.9797
noise 4 216 14.12 <.0001
age*noise 8 216 1.03 0.4134
sex*noise 4 216 0.88 0.4777
age*sex*noise 8 216 1.07 0.3882

Contrasts

Contrasts
Label Num DF Den DF F Value Pr > F
Noise Linear 3 216 0.64 0.5899

Least Squares Means

Least Squares Means
Effect age noise Estimate Standard
Error		 DF t Value Pr > |t|
age 1   38.6847 1.2042 53 32.13 <.0001
age 2   35.7985 1.2202 53 29.34 <.0001
age 3   32.1868 1.2216 53 26.35 <.0001
noise   1 39.8217 1.0118 216 39.36 <.0001
noise   2 36.8300 1.0118 216 36.40 <.0001
noise   3 35.3017 1.0118 216 34.89 <.0001
noise   4 34.3850 1.0118 216 33.98 <.0001
noise   5 31.4450 1.0118 216 31.08 <.0001

Differences of Least Squares Means

Differences of Least Squares Means
Effect age noise _age _noise Estimate Standard
Error		 DF t Value Pr > |t| Adjustment Adj P
age 1   2   2.8861 1.7134 53 1.68 0.0980 Bonferroni 0.2939
age 1   3   6.4979 1.7163 53 3.79 0.0004 Bonferroni 0.0012
age 2   3   3.6118 1.7499 53 2.06 0.0439 Bonferroni 0.1318
noise   1   2 2.9917 1.1624 216 2.57 0.0107 Bonferroni 0.1073
noise   1   3 4.5200 1.1624 216 3.89 0.0001 Bonferroni 0.0013
noise   1   4 5.4367 1.1624 216 4.68 <.0001 Bonferroni <.0001
noise   1   5 8.3767 1.1624 216 7.21 <.0001 Bonferroni <.0001
noise   2   3 1.5283 1.1624 216 1.31 0.1900 Bonferroni 1.0000
noise   2   4 2.4450 1.1624 216 2.10 0.0366 Bonferroni 0.3659
noise   2   5 5.3850 1.1624 216 4.63 <.0001 Bonferroni <.0001
noise   3   4 0.9167 1.1624 216 0.79 0.4312 Bonferroni 1.0000
noise   3   5 3.8567 1.1624 216 3.32 0.0011 Bonferroni 0.0106
noise   4   5 2.9400 1.1624 216 2.53 0.0121 Bonferroni 0.1215

Noise data

Unknown covariance structure

The Mixed Procedure

The MIXED Procedure

Model Information

Model Information
Data Set WORK.LOUD
Dependent Variable discrim
Covariance Structure Unstructured
Subject Effect ident
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within

Class Level Information

Class Level Information
Class Levels Values
age 3 1 2 3
sex 2 Female Male
noise 5 1 2 3 4 5

Dimensions

Dimensions
Covariance Parameters 15
Columns in X 73
Columns in Z 0
Subjects 60
Max Obs per Subject 5

Number of Observations

Number of Observations
Number of Observations Read 300
Number of Observations Used 300
Number of Observations Not Used 0

Iteration History

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 1943.32710280  
1 2 1891.88847746 0.00000000

Convergence Status

Convergence criteria met.

Estimated R Matrix for Subject 1

Estimated R Matrix for Subject 1
Row Col1 Col2 Col3 Col4 Col5
1 54.2083 11.6057 22.4781 13.7302 23.6770
2 11.6057 68.4473 14.5203 25.6457 19.3361
3 22.4781 14.5203 63.7287 26.3737 24.6320
4 13.7302 25.6457 26.3737 59.4281 27.0529
5 23.6770 19.3361 24.6320 27.0529 61.3852

Covariance Parameter Estimates

Covariance Parameter Estimates
Cov Parm Subject Estimate Alpha Lower Upper
UN(1,1) ident 54.2083 0.05 38.3771 82.3908
UN(2,1) ident 11.6057 0.05 -5.1092 28.3206
UN(2,2) ident 68.4473 0.05 48.3893 104.25
UN(3,1) ident 22.4781 0.05 5.4927 39.4635
UN(3,2) ident 14.5203 0.05 -3.6107 32.6513
UN(3,3) ident 63.7287 0.05 44.8071 97.8508
UN(4,1) ident 13.7302 0.05 -1.9529 29.4132
UN(4,2) ident 25.6457 0.05 7.1307 44.1607
UN(4,3) ident 26.3737 0.05 8.3497 44.3978
UN(4,4) ident 59.4281 0.05 42.0687 90.3363
UN(5,1) ident 23.6770 0.05 6.9632 40.3909
UN(5,2) ident 19.3361 0.05 1.2359 37.4362
UN(5,3) ident 24.6320 0.05 6.2233 43.0407
UN(5,4) ident 27.0529 0.05 9.3318 44.7739
UN(5,5) ident 61.3852 0.05 43.3968 93.4925

Fit Statistics

Fit Statistics
-2 Res Log Likelihood 1891.9
AIC (Smaller is Better) 1921.9
AICC (Smaller is Better) 1923.8
BIC (Smaller is Better) 1953.3

Null Model Likelihood Ratio Test

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
14 51.44 <.0001

Type 3 Tests of Fixed Effects

Type 3 Tests of Fixed Effects
Effect Num DF Den DF F Value Pr > F
interest 1 53 9.57 0.0032
age 2 53 7.30 0.0016
sex 1 53 0.55 0.4627
age*sex 2 53 0.01 0.9888
noise 4 53 16.26 <.0001
age*noise 8 53 1.20 0.3145
sex*noise 4 53 0.89 0.4765
age*sex*noise 8 53 1.17 0.3352

Contrasts

Contrasts
Label Num DF Den DF F Value Pr > F
Noise Linear 3 53 0.86 0.4701

Least Squares Means

Least Squares Means
Effect age noise Estimate Standard
Error		 DF t Value Pr > |t|
age 1   38.6867 1.2044 53 32.12 <.0001
age 2   35.8452 1.2201 53 29.38 <.0001
age 3   32.1381 1.2214 53 26.31 <.0001
noise   1 39.8217 0.9505 53 41.89 <.0001
noise   2 36.8300 1.0681 53 34.48 <.0001
noise   3 35.3017 1.0306 53 34.25 <.0001
noise   4 34.3850 0.9952 53 34.55 <.0001
noise   5 31.4450 1.0115 53 31.09 <.0001

Differences of Least Squares Means

Differences of Least Squares Means
Effect age noise _age _noise Estimate Standard
Error		 DF t Value Pr > |t| Adjustment Adj P
age 1   2   2.8414 1.7135 53 1.66 0.1032 Bonferroni 0.3095
age 1   3   6.5486 1.7164 53 3.82 0.0004 Bonferroni 0.0011
age 2   3   3.7071 1.7492 53 2.12 0.0388 Bonferroni 0.1163
noise   1   2 2.9917 1.2874 53 2.32 0.0240 Bonferroni 0.2400
noise   1   3 4.5200 1.1029 53 4.10 0.0001 Bonferroni 0.0014
noise   1   4 5.4367 1.1984 53 4.54 <.0001 Bonferroni 0.0003
noise   1   5 8.3767 1.0665 53 7.85 <.0001 Bonferroni <.0001
noise   2   3 1.5283 1.3111 53 1.17 0.2490 Bonferroni 1.0000
noise   2   4 2.4450 1.1298 53 2.16 0.0350 Bonferroni 0.3498
noise   2   5 5.3850 1.2326 53 4.37 <.0001 Bonferroni 0.0006
noise   3   4 0.9167 1.0833 53 0.85 0.4012 Bonferroni 1.0000
noise   3   5 3.8567 1.1244 53 3.43 0.0012 Bonferroni 0.0118
noise   4   5 2.9400 1.0544 53 2.79 0.0073 Bonferroni 0.0734

Noise data

Test for difference between covariance structures

Compound symmetry versus unknown

The IML Procedure

ChiSquared_df_pvalue

ChiSquared df pvalue
8.54 13 0.8067304