The data files can be downloaded from
http://rem.ph.ucla.edu/~rob/mld/data.html .
Table 6.1, page 149.
data small;
set smallmice;
cont_day = day;
cont_day2 = day**2;
run;
*Unstructured Covariance Matrix;
proc mixed data = small method = reml noitprint noclprint;
class id day;
model weight = cont_day cont_day2/ notest;
repeated day/ subject=id type = unstructured;
run;
The Mixed Procedure
Model Information
Data Set WORK.SMALL
Dependent Variable weight
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within
Dimensions
Covariance Parameters 28
Columns in X 3
Columns in Z 0
Subjects 14
Max Obs Per Subject 7
Number of Observations
Number of Observations Read 98
Number of Observations Used 98
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 909.07
UN(2,1) id 1313.72
UN(2,2) id 2248.87
UN(3,1) id 889.13
UN(3,2) id 2062.34
UN(3,3) id 3532.66
UN(4,1) id 941.45
UN(4,2) id 2470.39
UN(4,3) id 5346.10
UN(4,4) id 10600
UN(5,1) id 721.71
UN(5,2) id 2674.65
UN(5,3) id 6486.86
UN(5,4) id 12884
UN(5,5) id 17993
UN(6,1) id 943.31
UN(6,2) id 2662.18
UN(6,3) id 5989.36
UN(6,4) id 12463
UN(6,5) id 16892
UN(6,6) id 18053
UN(7,1) id 1266.36
UN(7,2) id 3030.37
UN(7,3) id 5799.41
UN(7,4) id 10739
UN(7,5) id 14324
UN(7,6) id 14866
UN(7,7) id 14492
Fit Statistics
-2 Res Log Likelihood 964.7
AIC (smaller is better) 1020.7
AICC (smaller is better) 1045.3
BIC (smaller is better) 1038.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
27 198.41 <.0001
*AR(1) Covariance Matrix;
proc mixed data = small method = reml noitprint noclprint;
class id day;
model weight = cont_day cont_day2/ notest;
repeated day/ subject=id type = ar(1);
run;
The Mixed Procedure
Model Information
Data Set WORK.SMALL
Dependent Variable weight
Covariance Structure Autoregressive
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within
Dimensions
Covariance Parameters 2
Columns in X 3
Columns in Z 0
Subjects 14
Max Obs Per Subject 7
Number of Observations
Number of Observations Read 98
Number of Observations Used 98
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
AR(1) id 0.8737
Residual 8796.77
Fit Statistics
-2 Res Log Likelihood 1035.3
AIC (smaller is better) 1039.3
AICC (smaller is better) 1039.4
BIC (smaller is better) 1040.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
1 127.83 <.0001
*RIAS Covariance Matrix;
proc mixed data = small method = reml noitprint noclprint;
class id day;
model weight = cont_day cont_day2/ notest;
random intercept cont_day/ subject=id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.SMALL
Dependent Variable weight
Covariance Structure Unstructured
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 4
Columns in X 3
Columns in Z Per Subject 2
Subjects 14
Max Obs Per Subject 7
Number of Observations
Number of Observations Read 98
Number of Observations Used 98
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 744.35
UN(2,1) id -49.8237
UN(2,2) id 55.5479
Residual 1399.56
Fit Statistics
-2 Res Log Likelihood 1038.6
AIC (smaller is better) 1046.6
AICC (smaller is better) 1047.0
BIC (smaller is better) 1049.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 124.48 <.0001
*CS Covariance Matrix;
proc mixed data = small method = reml noitprint noclprint;
class id day;
model weight = cont_day cont_day2/ notest;
random intercept/ subject=id;
run;
The Mixed Procedure
Model Information
Data Set WORK.SMALL
Dependent Variable weight
Covariance Structure Variance Components
Subject Effect id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 2
Columns in X 3
Columns in Z Per Subject 1
Subjects 14
Max Obs Per Subject 7
Number of Observations
Number of Observations Read 98
Number of Observations Used 98
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
Intercept id 6052.49
Residual 3618.76
Fit Statistics
-2 Res Log Likelihood 1105.3
AIC (smaller is better) 1109.3
AICC (smaller is better) 1109.4
BIC (smaller is better) 1110.6
proc mixed data = small method = reml noitprint noclprint;
class id day;
model weight = cont_day cont_day2/ notest;
repeated day / subject=id type = vc;
run;
The Mixed Procedure
Model Information
Data Set WORK.SMALL
Dependent Variable weight
Covariance Structure Variance Components
Subject Effect id
Estimation Method REML
Residual Variance Method Parameter
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within
Dimensions
Covariance Parameters 1
Columns in X 3
Columns in Z 0
Subjects 14
Max Obs Per Subject 7
Number of Observations
Number of Observations Read 98
Number of Observations Used 98
Number of Observations Not Used 0
Covariance Parameter
Estimates
Cov
Parm Subject Estimate
day id 9416.41
Fit Statistics
-2 Res Log Likelihood 1163.1
AIC (smaller is better) 1165.1
AICC (smaller is better) 1165.1
BIC (smaller is better) 1165.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
0 0.00 1.0000
Table 6.2, page 168.
Transformed estimates only.
data trans_pain;
set pain;
invsqrt = -paintol**(-.5);
run;
*Log2;
proc mixed data = trans_pain method= reml noitprint noclprint noinfo;
class id cs trial;
model l2paintol = cs / solution notest;
repeated trial/ subject = id type = unstructured;
run;
The Mixed Procedure
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 1.0065
UN(2,1) id 0.7482
UN(2,2) id 1.1281
UN(3,1) id 0.9522
UN(3,2) id 0.8736
UN(3,3) id 1.3423
UN(4,1) id 0.6725
UN(4,2) id 0.7908
UN(4,3) id 1.0022
UN(4,4) id 1.3071
Fit Statistics
-2 Res Log Likelihood 568.4
AIC (smaller is better) 588.4
AICC (smaller is better) 589.4
BIC (smaller is better) 610.0
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 170.12 <.0001
Solution for Fixed Effects
coping Standard
Effect style Estimate Error DF t Value Pr > |t|
Intercept 5.0770 0.1620 62 31.35 <.0001
cs attender -0.5054 0.2291 62 -2.21 0.0311
cs distracter 0 . . . .
*Negative inverse square root;
proc mixed data = trans_pain method= reml noitprint noclprint noinfo;
class id cs trial;
model invsqrt = cs / solution notest;
repeated trial/ subject = id type = unstructured;
run;
The Mixed Procedure
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 0.003276
UN(2,1) id 0.002723
UN(2,2) id 0.004548
UN(3,1) id 0.003166
UN(3,2) id 0.003089
UN(3,3) id 0.004971
UN(4,1) id 0.002611
UN(4,2) id 0.003206
UN(4,3) id 0.004182
UN(4,4) id 0.005695
Fit Statistics
-2 Res Log Likelihood -778.7
AIC (smaller is better) -758.7
AICC (smaller is better) -757.8
BIC (smaller is better) -737.1
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 164.19 <.0001
Solution for Fixed Effects
coping Standard
Effect style Estimate Error DF t Value Pr > |t|
Intercept -0.1831 0.009837 62 -18.62 <.0001
cs attender -0.02888 0.01389 62 -2.08 0.0418
cs distracter 0 . . . .