Chapter 5 Example: Means by Wave for outcome

The MEANS Procedure

Analysis Variable : outcome outcome: Test Score Outcome
N Obs Mean Std Dev Minimum Maximum
100 12.8496000 3.1384687 6.9600000 22.4100000

Analysis Variable : outcome outcome: Test Score Outcome
wave: Occasion (1-4) N Obs Mean Std Dev Minimum Maximum
1 25 10.4048000 1.5368152 6.9600000 13.7000000
2 25 11.8576000 2.2113255 7.5900000 15.4700000
3 25 13.5844000 2.4934248 9.1200000 17.8600000
4 25 15.5516000 3.4269042 8.6500000 22.4100000


Eq 5.1: Empty Means, Random Intercept Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structures Unstructured, Variance Components
Subject Effects PersonID, PersonID
Estimation Method REML
Residual Variance Method Parameter
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 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 512.01453007  
1 1 502.22381244 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 7.0554      
2   7.0554    
3     7.0554  
4       7.0554

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000      
2   1.0000    
3     1.0000  
4       1.0000

Estimated G Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1
1 Intercept 1 2.8819

Estimated G Correlation Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1
1 Intercept 1 1.0000

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 9.9373 2.8819 2.8819 2.8819
2 2.8819 9.9373 2.8819 2.8819
3 2.8819 2.8819 9.9373 2.8819
4 2.8819 2.8819 2.8819 9.9373

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.2900 0.2900 0.2900
2 0.2900 1.0000 0.2900 0.2900
3 0.2900 0.2900 1.0000 0.2900
4 0.2900 0.2900 0.2900 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 2.8819 1.3717 2.10 0.0178
wave PersonID 7.0554 1.1521 6.12 <.0001

Fit Statistics
-2 Res Log Likelihood 502.2
AIC (smaller is better) 506.2
AICC (smaller is better) 506.3
BIC (smaller is better) 508.7

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 9.79 0.0018

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
502.2 2 506.2 506.3 506.9 508.7 510.7

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 12.8496 0.4311 24 29.81 <.0001 0.05 11.9599 13.7393


Eq 5.3: Fixed Linear Time, Random Intercept Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structures Unstructured, Variance Components
Subject Effects PersonID, PersonID
Estimation Method REML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 2
Columns in X 2
Columns in Z Per Subject 1
Subjects 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 466.21530814  
1 1 415.09541603 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 2.1725      
2   2.1725    
3     2.1725  
4       2.1725

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000      
2   1.0000    
3     1.0000  
4       1.0000

Estimated G Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1
1 Intercept 1 4.1026

Estimated G Correlation Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1
1 Intercept 1 1.0000

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 6.2751 4.1026 4.1026 4.1026
2 4.1026 6.2751 4.1026 4.1026
3 4.1026 4.1026 6.2751 4.1026
4 4.1026 4.1026 4.1026 6.2751

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.6538 0.6538 0.6538
2 0.6538 1.0000 0.6538 0.6538
3 0.6538 0.6538 1.0000 0.6538
4 0.6538 0.6538 0.6538 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr > Z
UN(1,1) PersonID 4.1026 1.3441 3.05 0.0011
wave PersonID 2.1725 0.3572 6.08 <.0001

Fit Statistics
-2 Res Log Likelihood 415.1
AIC (smaller is better) 419.1
AICC (smaller is better) 419.2
BIC (smaller is better) 421.5

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 51.12 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
415.1 2 419.1 419.2 419.8 421.5 423.5

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.2745 0.4743 34.7 21.66 <.0001 0.05 9.3114 11.2377
time 1.7167 0.1318 74 13.02 <.0001 0.05 1.4540 1.9794

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 74 169.57 169.57 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Time=0 10.2745 0.4743 34.7 21.66 <.0001 0.05 9.3114 11.2377
Intercept at Time=1 11.9912 0.4361 25.1 27.50 <.0001 0.05 11.0933 12.8891
Intercept at Time=2 13.7080 0.4361 25.1 31.43 <.0001 0.05 12.8101 14.6059
Intercept at Time=3 15.4247 0.4743 34.7 32.52 <.0001 0.05 14.4615 16.3878


PsuedoR2 (% Reduction) for CovEmpty vs. CovFixLin

Name CovParm Subject Estimate StdErr ZValue ProbZ PseudoR2
CovEmpty UN(1,1) PersonID 2.8819 1.3717 2.10 0.0178 .
CovEmpty wave PersonID 7.0554 1.1521 6.12 <.0001 .
CovFixLin UN(1,1) PersonID 4.1026 1.3441 3.05 0.0011 -0.42359
CovFixLin wave PersonID 2.1725 0.3572 6.08 <.0001 0.69208


Eq 5.5: Random Linear Time Model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structures Unstructured, Variance Components
Subject Effects PersonID, PersonID
Estimation Method REML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 4
Columns in X 2
Columns in Z Per Subject 2
Subjects 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 466.21530814  
1 1 366.74150157 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 0.6986      
2   0.6986    
3     0.6986  
4       0.6986

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000      
2   1.0000    
3     1.0000  
4       1.0000

Estimated G Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 2.2624 0.05454
2 time 1 0.05454 0.9089

Estimated G Correlation Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 1.0000 0.03803
2 time 1 0.03803 1.0000

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 2.9611 2.3170 2.3715 2.4260
2 2.3170 3.9790 4.2438 5.2073
3 2.3715 4.2438 6.8148 7.9885
4 2.4260 5.2073 7.9885 11.4684

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.6750 0.5279 0.4163
2 0.6750 1.0000 0.8150 0.7709
3 0.5279 0.8150 1.0000 0.9036
4 0.4163 0.7709 0.9036 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 2.2624 0.8003 2.83 0.0023
UN(2,1) PersonID 0.05454 0.3507 0.16 0.8764
UN(2,2) PersonID 0.9089 0.3040 2.99 0.0014
wave PersonID 0.6986 0.1397 5.00 <.0001

Fit Statistics
-2 Res Log Likelihood 366.7
AIC (smaller is better) 374.7
AICC (smaller is better) 375.2
BIC (smaller is better) 379.6

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 99.47 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
366.7 4 374.7 375.2 376.1 379.6 383.6

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.2745 0.3318 24 30.97 <.0001 0.05 9.5898 10.9592
time 1.7167 0.2048 24 8.38 <.0001 0.05 1.2940 2.1394

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 24 70.26 70.26 <.0001 <.0001

Estimates
Label Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept at Time=0 10.2745 0.3318 24 30.97 <.0001 0.05 9.5898 10.9592
Intercept at Time=1 11.9912 0.3736 24 32.09 <.0001 0.05 11.2201 12.7624
Intercept at Time=2 13.7080 0.5030 24 27.25 <.0001 0.05 12.6698 14.7461
Intercept at Time=3 15.4247 0.6711 24 22.98 <.0001 0.05 14.0396 16.8097


Likelihood Ratio Test for FitFixLin vs. FitRandLin

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitFixLin 415.1 2 419.1 421.5 . . .
FitRandLin 366.7 4 374.7 379.6 48.3539 2 3.1629E-11


Ch 5: Saturated Means, Unstructured Variance Model
ANSWER KEY for both sides of the model

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structure Unstructured
Subject Effect PersonID
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite

Dimensions
Covariance Parameters 10
Columns in X 5
Columns in Z 0
Subjects 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 462.05245956  
1 1 353.75341815 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 2.3618 2.7867 1.9566 2.4204
2 2.7867 4.8900 4.0440 5.5525
3 1.9566 4.0440 6.2172 7.7994
4 2.4204 5.5525 7.7994 11.7437

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.8200 0.5106 0.4596
2 0.8200 1.0000 0.7334 0.7327
3 0.5106 0.7334 1.0000 0.9128
4 0.4596 0.7327 0.9128 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 2.3618 0.6818 3.46 0.0003
UN(2,1) PersonID 2.7867 0.8971 3.11 0.0019
UN(2,2) PersonID 4.8900 1.4116 3.46 0.0003
UN(3,1) PersonID 1.9566 0.8783 2.23 0.0259
UN(3,2) PersonID 4.0440 1.3958 2.90 0.0038
UN(3,3) PersonID 6.2172 1.7947 3.46 0.0003
UN(4,1) PersonID 2.4204 1.1831 2.05 0.0408
UN(4,2) PersonID 5.5525 1.9176 2.90 0.0038
UN(4,3) PersonID 7.7994 2.3615 3.30 0.0010
UN(4,4) PersonID 11.7437 3.3901 3.46 0.0003

Fit Statistics
-2 Res Log Likelihood 353.8
AIC (smaller is better) 373.8
AICC (smaller is better) 376.3
BIC (smaller is better) 385.9

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 108.30 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
353.8 10 373.8 376.3 377.1 385.9 395.9

Solution for Fixed Effects
Effect wave:
Occasion
(1-4)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept   15.5516 0.6854 24 22.69 <.0001 0.05 14.1370 16.9662
wave 1 -5.1468 0.6088 24 -8.45 <.0001 0.05 -6.4032 -3.8904
wave 2 -3.6940 0.4703 24 -7.86 <.0001 0.05 -4.6646 -2.7234
wave 3 -1.9672 0.3074 24 -6.40 <.0001 0.05 -2.6016 -1.3328
wave 4 0 . . . . . . .

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
wave 3 24 71.58 23.86 <.0001 <.0001

Least Squares Means
Effect wave:
Occasion
(1-4)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
wave 1 10.4048 0.3074 24 33.85 <.0001 0.05 9.7704 11.0392
wave 2 11.8576 0.4423 24 26.81 <.0001 0.05 10.9448 12.7704
wave 3 13.5844 0.4987 24 27.24 <.0001 0.05 12.5552 14.6136
wave 4 15.5516 0.6854 24 22.69 <.0001 0.05 14.1370 16.9662

Differences of Least Squares Means
Effect wave:
Occasion
(1-4)		 wave:
Occasion
(1-4)		 Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
wave 1 2 -1.4528 0.2591 24 -5.61 <.0001 0.05 -1.9876 -0.9180
wave 1 3 -3.1796 0.4320 24 -7.36 <.0001 0.05 -4.0712 -2.2880
wave 1 4 -5.1468 0.6088 24 -8.45 <.0001 0.05 -6.4032 -3.8904
wave 2 3 -1.7268 0.3475 24 -4.97 <.0001 0.05 -2.4440 -1.0096
wave 2 4 -3.6940 0.4703 24 -7.86 <.0001 0.05 -4.6646 -2.7234
wave 3 4 -1.9672 0.3074 24 -6.40 <.0001 0.05 -2.6016 -1.3328


Ch 5: Random Linear Time Model with AR1 R Matrix

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structures Unstructured, Autoregressive
Subject Effects PersonID, PersonID
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 2
Columns in Z Per Subject 2
Subjects 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 466.21530814  
1 2 366.79889430 0.00054788
2 2 366.74220275 0.00002897
3 1 366.73940527 0.00000012
4 1 366.73939441 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 0.7193 0.01841 0.000471 0.000012
2 0.01841 0.7193 0.01841 0.000471
3 0.000471 0.01841 0.7193 0.01841
4 0.000012 0.000471 0.01841 0.7193

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.02560 0.000655 0.000017
2 0.02560 1.0000 0.02560 0.000655
3 0.000655 0.02560 1.0000 0.02560
4 0.000017 0.000655 0.02560 1.0000

Estimated G Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 2.2216 0.06949
2 time 1 0.06949 0.9015

Estimated G Correlation Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 1.0000 0.04910
2 time 1 0.04910 1.0000

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 2.9409 2.3095 2.3610 2.4301
2 2.3095 3.9814 4.2516 5.2046
3 2.3610 4.2516 6.8250 7.9967
4 2.4301 5.2046 7.9967 11.4717

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.6749 0.5270 0.4184
2 0.6749 1.0000 0.8156 0.7701
3 0.5270 0.8156 1.0000 0.9037
4 0.4184 0.7701 0.9037 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 2.2216 1.2181 1.82 0.0341
UN(2,1) PersonID 0.06949 0.4842 0.14 0.8859
UN(2,2) PersonID 0.9015 0.3459 2.61 0.0046
AR(1) PersonID 0.02560 0.5688 0.05 0.9641
Residual   0.7193 0.4969 1.45 0.0739

Fit Statistics
-2 Res Log Likelihood 366.7
AIC (smaller is better) 376.7
AICC (smaller is better) 377.4
BIC (smaller is better) 382.8

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 99.48 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
366.7 5 376.7 377.4 378.4 382.8 387.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.2763 0.3308 20.2 31.06 <.0001 0.05 9.5867 10.9658
time 1.7167 0.2047 23.7 8.39 <.0001 0.05 1.2940 2.1393

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 23.7 70.36 70.36 <.0001 <.0001


Likelihood Ratio Test for FitRandLin vs. FitRandLinAR1

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitRandLin 366.7 4 374.7 379.6 . . .
FitRandLinAR1 366.7 5 376.7 382.8 .002107160 1 0.96339


Ch 5: Random Linear Time Model with TOEP2 R Matrix

The Mixed Procedure

Model Information
Data Set WORK.CHAPTER5
Dependent Variable outcome
Covariance Structures Unstructured, Banded Toeplitz
Subject Effects PersonID, PersonID
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 2
Columns in Z Per Subject 2
Subjects 25
Max Obs Per Subject 4

Number of Observations
Number of Observations Read 100
Number of Observations Used 100
Number of Observations Not Used 0

Iteration History
Iteration Evaluations -2 Res Log Like Criterion
0 1 466.21530814  
1 2 366.75664905 0.00015976
2 1 366.74037556 0.00000383
3 1 366.74001231 0.00000000

Convergence criteria met.

Estimated R Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 0.7127 0.01259    
2 0.01259 0.7127 0.01259  
3   0.01259 0.7127 0.01259
4     0.01259 0.7127

Estimated R Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.01766    
2 0.01766 1.0000 0.01766  
3   0.01766 1.0000 0.01766
4     0.01766 1.0000

Estimated G Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 2.2342 0.06496
2 time 1 0.06496 0.9038

Estimated G Correlation Matrix
Row Effect PersonID:
Person
Identification
Number		 Col1 Col2
1 Intercept 1 1.0000 0.04571
2 time 1 0.04571 1.0000

Estimated V Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 2.9470 2.3118 2.3641 2.4291
2 2.3118 3.9807 4.2493 5.2055
3 2.3641 4.2493 6.8220 7.9944
4 2.4291 5.2055 7.9944 11.4709

Estimated V Correlation Matrix for PersonID 1
Row Col1 Col2 Col3 Col4
1 1.0000 0.6750 0.5273 0.4178
2 0.6750 1.0000 0.8154 0.7703
3 0.5273 0.8154 1.0000 0.9037
4 0.4178 0.7703 0.9037 1.0000

Covariance Parameter Estimates
Cov Parm Subject Estimate Standard Error Z Value Pr Z
UN(1,1) PersonID 2.2342 1.0786 2.07 0.0192
UN(2,1) PersonID 0.06496 0.4407 0.15 0.8828
UN(2,2) PersonID 0.9038 0.3309 2.73 0.0032
TOEP(2) PersonID 0.01259 0.3232 0.04 0.9689
Residual   0.7127 0.3908 1.82 0.0341

Fit Statistics
-2 Res Log Likelihood 366.7
AIC (smaller is better) 376.7
AICC (smaller is better) 377.4
BIC (smaller is better) 382.8

Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 99.48 <.0001

Information Criteria
Neg2LogLike Parms AIC AICC HQIC BIC CAIC
366.7 5 376.7 377.4 378.4 382.8 387.8

Solution for Fixed Effects
Effect Estimate Standard Error DF t Value Pr > |t| Alpha Lower Upper
Intercept 10.2757 0.3311 21.3 31.04 <.0001 0.05 9.5878 10.9636
time 1.7167 0.2047 23.8 8.39 <.0001 0.05 1.2940 2.1394

Type 3 Tests of Fixed Effects
Effect Num DF Den DF Chi-Square F Value Pr > ChiSq Pr > F
time 1 23.8 70.33 70.33 <.0001 <.0001


Likelihood Ratio Test for FitRandLin vs. FitRandLinTOEP2

Name Neg2LogLike Parms AIC BIC DevDiff DFdiff Pvalue
FitRandLin 366.7 4 374.7 379.6 . . .
FitRandLinTOEP2 366.7 5 376.7 382.8 .001489262 1 0.96922