NEED TO ADD DATA TO SITE
data pain2;
infile 'i:atswebtextbookmlddatapain2.txt';
input id ses age_years age_months gender tmt0 cs0 helpful
easy tol11 tol12 rat11 rat12 tol13 tol14 rat13 rat14 senscat1 cpantic1 ;
run;
DATA pain2_long1 ;
set pain2;
array rat(4) rat11 rat12 rat13 rat14;
array tol(4) tol11 tol12 tol13 tol14;
do trial = 1 to 4;
if rat(trial) = -999 then rat(trial)=.;
if tol(trial) = -999 then tol(trial)=.;
rating = rat(trial);
tolerance = tol(trial);
log_tol = log2(tol(trial));
output;
end;
drop rat11 rat12 rat13 rat14 tol11 tol12 tol13 tol14;
RUN ;
Table 13.1, page 380.
proc sql;
create table pain2_long2 as
select *,
mean(rating) as mean_rating,
rating-mean(rating) as dev_rating,
count(rating) as freq_rating,
count(tolerance) as freq_tol,
(tmt0=1)*(trial = 4) as tmt1,
(tmt0=2)*(trial = 4) as tmt2,
(tmt0=3)*(trial = 4) as tmt3
from pain2_long1
group by id
order by id, trial;
quit;
*Model 1;
proc mixed data = pain2_long2 method = reml noclprint noitprint;
class trial id cs0;
model log_tol = rating cs0 tmt1 tmt2 tmt3 cs0*tmt1 cs0*tmt2 cs0*tmt3/solution notest;
repeated trial / subject = id type = un;
run;The Mixed Procedure
Model Information
Data Set WORK.PAIN2_LONG2
Dependent Variable log_tol
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 10
Columns in X 13
Columns in Z 0
Subjects 64
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 256
Number of Observations Used 245
Number of Observations Not Used 11
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 0.9556
UN(2,1) id 0.7248
UN(2,2) id 1.1155
UN(3,1) id 0.9023
UN(3,2) id 0.8619
UN(3,3) id 1.3036
UN(4,1) id 0.5477
UN(4,2) id 0.7351
UN(4,3) id 0.8760
UN(4,4) id 1.0821
Fit Statistics
-2 Res Log Likelihood 559.5
AIC (smaller is better) 579.5
AICC (smaller is better) 580.5
BIC (smaller is better) 601.1
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 163.83 <.0001
Solution for Fixed Effects
Standard
Effect cs0 Estimate Error DF t Value Pr > |t|
Intercept 5.3852 0.2158 62 24.96 <.0001
rating -0.05543 0.02450 62 -2.26 0.0272
cs0 1 -0.5127 0.2336 62 -2.19 0.0320
cs0 2 0 . . . .
tmt1 -0.08829 0.2161 62 -0.41 0.6842
tmt2 0.6980 0.2015 62 3.46 0.0010
tmt3 -0.4761 0.2172 62 -2.19 0.0321
tmt1*cs0 1 0.2591 0.2997 62 0.86 0.3908
tmt1*cs0 2 0 . . . .
tmt2*cs0 1 -0.5352 0.2937 62 -1.82 0.0732
tmt2*cs0 2 0 . . . .
tmt3*cs0 1 0.4578 0.3044 62 1.50 0.1377
tmt3*cs0 2 0 . . . .
*Model 2;
proc mixed data = pain2_long2 method = reml noclprint noitprint;
where freq_tol = freq_rating =4;
class trial id cs0;
model log_tol = mean_rating cs0 tmt1 tmt2 tmt3 cs0*tmt1 cs0*tmt2 cs0*tmt3/solution notest;
repeated trial / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.PAIN2_LONG2
Dependent Variable log_tol
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 10
Columns in X 13
Columns in Z 0
Subjects 58
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 232
Number of Observations Used 232
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 1.0329
UN(2,1) id 0.7712
UN(2,2) id 1.1759
UN(3,1) id 0.9612
UN(3,2) id 0.8813
UN(3,3) id 1.3342
UN(4,1) id 0.5877
UN(4,2) id 0.7646
UN(4,3) id 0.8921
UN(4,4) id 1.1140
Fit Statistics
-2 Res Log Likelihood 533.9
AIC (smaller is better) 553.9
AICC (smaller is better) 554.9
BIC (smaller is better) 574.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 157.91 <.0001
Solution for Fixed Effects
Standard
Effect cs0 Estimate Error DF t Value Pr > |t|
Intercept 5.5215 0.4389 55 12.58 <.0001
mean_rating -0.07018 0.07229 55 -0.97 0.3359
cs0 1 -0.6438 0.2533 55 -2.54 0.0139
cs0 2 0 . . . .
tmt1 -0.2115 0.2154 55 -0.98 0.3304
tmt2 0.6754 0.2062 55 3.28 0.0018
tmt3 -0.4573 0.2395 55 -1.91 0.0615
tmt1*cs0 1 0.3509 0.3053 55 1.15 0.2554
tmt1*cs0 2 0 . . . .
tmt2*cs0 1 -0.5479 0.2992 55 -1.83 0.0725
tmt2*cs0 2 0 . . . .
tmt3*cs0 1 0.4156 0.3296 55 1.26 0.2126
tmt3*cs0 2 0 . . . .
*Model 3;
proc mixed data = pain2_long2 method = reml noclprint noitprint;
where freq_tol = freq_rating =4;
class trial id cs0;
model log_tol = dev_rating cs0 tmt1 tmt2 tmt3 cs0*tmt1 cs0*tmt2 cs0*tmt3/solution notest;
repeated trial / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.PAIN2_LONG2
Dependent Variable log_tol
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 10
Columns in X 13
Columns in Z 0
Subjects 58
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 232
Number of Observations Used 232
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 1.0140
UN(2,1) id 0.7635
UN(2,2) id 1.1538
UN(3,1) id 0.9728
UN(3,2) id 0.9151
UN(3,3) id 1.3898
UN(4,1) id 0.5985
UN(4,2) id 0.7645
UN(4,3) id 0.9463
UN(4,4) id 1.1417
Fit Statistics
-2 Res Log Likelihood 532.7
AIC (smaller is better) 552.7
AICC (smaller is better) 553.7
BIC (smaller is better) 573.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 162.64 <.0001
Solution for Fixed Effects
Standard
Effect cs0 Estimate Error DF t Value Pr > |t|
Intercept 5.1457 0.1775 56 29.00 <.0001
dev_rating -0.05545 0.02678 56 -2.07 0.0430
cs0 1 -0.6363 0.2510 56 -2.53 0.0141
cs0 2 0 . . . .
tmt1 -0.1115 0.2208 56 -0.50 0.6156
tmt2 0.6755 0.2051 56 3.29 0.0017
tmt3 -0.4158 0.2389 56 -1.74 0.0873
tmt1*cs0 1 0.3104 0.3047 56 1.02 0.3128
tmt1*cs0 2 0 . . . .
tmt2*cs0 1 -0.5125 0.2980 56 -1.72 0.0910
tmt2*cs0 2 0 . . . .
tmt3*cs0 1 0.3821 0.3282 56 1.16 0.2492
tmt3*cs0 2 0 . . . .
*Model 4;
proc mixed data = pain2_long2 method = reml noclprint noitprint;
where freq_tol = freq_rating =4;
class trial id cs0;
model log_tol = dev_rating mean_rating cs0 tmt1 tmt2 tmt3 cs0*tmt1 cs0*tmt2 cs0*tmt3/solution notest;
repeated trial / subject = id type = un;
estimate 'deviation - average' dev_rating 1 mean_rating -1;
run;
The Mixed Procedure
Model Information
Data Set WORK.PAIN2_LONG2
Dependent Variable log_tol
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 10
Columns in X 14
Columns in Z 0
Subjects 58
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 232
Number of Observations Used 232
Number of Observations Not Used 0
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 1.0041
UN(2,1) id 0.7675
UN(2,2) id 1.1717
UN(3,1) id 0.9490
UN(3,2) id 0.9051
UN(3,3) id 1.3521
UN(4,1) id 0.5856
UN(4,2) id 0.7659
UN(4,3) id 0.9202
UN(4,4) id 1.1269
Fit Statistics
-2 Res Log Likelihood 535.3
AIC (smaller is better) 555.3
AICC (smaller is better) 556.3
BIC (smaller is better) 575.9
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 159.50 <.0001
Solution for Fixed Effects
Standard
Effect cs0 Estimate Error DF t Value Pr > |t|
Intercept 5.5208 0.4345 55 12.71 <.0001
dev_rating -0.05527 0.02688 55 -2.06 0.0445
mean_rating -0.06863 0.07152 55 -0.96 0.3415
cs0 1 -0.6337 0.2515 55 -2.52 0.0147
cs0 2 0 . . . .
tmt1 -0.1071 0.2209 55 -0.49 0.6295
tmt2 0.6707 0.2053 55 3.27 0.0019
tmt3 -0.4139 0.2390 55 -1.73 0.0889
tmt1*cs0 1 0.2903 0.3053 55 0.95 0.3458
tmt1*cs0 2 0 . . . .
tmt2*cs0 1 -0.4906 0.2992 55 -1.64 0.1068
tmt2*cs0 2 0 . . . .
tmt3*cs0 1 0.3791 0.3282 55 1.16 0.2531
tmt3*cs0 2 0 . . . .
Estimates
Standard
Label Estimate Error DF t Value Pr > |t|
deviation - average 0.01335 0.07605 55 0.18 0.8612
Table 13.2, page 383.
data pain2_tol (rename=log_tol=response) pain2_rating (rename=rating=response);
set pain2_long2;
type = "t";
output pain2_tol;
type = "r";
output pain2_rating;
run;
data bi_pain2;
set pain2_tol pain2_rating;
drop rating tolerance log_tol;
run;
proc sort data = bi_pain2;
by id trial type;
run;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un;
repeated / subject = id(trial) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1317 0.5059 4.21 <.0001
UN(2,1) id -0.2740 0.2045 -1.34 0.1804
UN(2,2) id 0.7936 0.1598 4.97 <.0001
UN(1,1) id(trial) 2.3931 0.2557 9.36 <.0001
UN(2,1) id(trial) -0.1279 0.06916 -1.85 0.0645
UN(2,2) id(trial) 0.3432 0.03667 9.36 <.0001
Fit Statistics
-2 Res Log Likelihood 1568.8
AIC (smaller is better) 1580.8
AICC (smaller is better) 1581.0
BIC (smaller is better) 1593.8
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 310.59 <.0001
Table 13.3, page 384.
*Model 1;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest ;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un;
repeated / subject = id(trial) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1317 0.5059 4.21 <.0001
UN(2,1) id -0.2740 0.2045 -1.34 0.1804
UN(2,2) id 0.7936 0.1598 4.97 <.0001
UN(1,1) id(trial) 2.3931 0.2557 9.36 <.0001
UN(2,1) id(trial) -0.1279 0.06916 -1.85 0.0645
UN(2,2) id(trial) 0.3432 0.03667 9.36 <.0001
Fit Statistics
-2 Res Log Likelihood 1568.8
AIC (smaller is better) 1580.8
AICC (smaller is better) 1581.0
BIC (smaller is better) 1593.8
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 310.59 <.0001
*Model 2;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un;
repeated / subject = id(trial) type = un(1);
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1369 0.5068 4.22 <.0001
UN(2,1) id -0.3083 0.2039 -1.51 0.1306
UN(2,2) id 0.7955 0.1601 4.97 <.0001
UN(1,1) id(trial) 2.3916 0.2554 9.37 <.0001
UN(2,1) id(trial) 0 . . .
UN(2,2) id(trial) 0.3430 0.03662 9.37 <.0001
Fit Statistics
-2 Res Log Likelihood 1572.3
AIC (smaller is better) 1582.3
AICC (smaller is better) 1582.5
BIC (smaller is better) 1593.1
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 307.06 <.0001
*Model 3;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un(1);
repeated / subject = id(trial) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Banded
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.0976 0.5001 4.19 <.0001
UN(2,1) id 0 . . .
UN(2,2) id 0.7846 0.1582 4.96 <.0001
UN(1,1) id(trial) 2.4029 0.2576 9.33 <.0001
UN(2,1) id(trial) -0.1370 0.06961 -1.97 0.0491
UN(2,2) id(trial) 0.3444 0.03693 9.33 <.0001
Fit Statistics
-2 Res Log Likelihood 1570.7
AIC (smaller is better) 1580.7
AICC (smaller is better) 1580.8
BIC (smaller is better) 1591.5
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 308.67 <.0001
*Model 4;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un(1);
repeated / subject = id(trial) type = un(1);
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Banded
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1264 0.5050 4.21 <.0001
UN(2,1) id 0 . . .
UN(2,2) id 0.7938 0.1598 4.97 <.0001
UN(1,1) id(trial) 2.3947 0.2560 9.36 <.0001
UN(2,1) id(trial) 0 . . .
UN(2,2) id(trial) 0.3432 0.03667 9.36 <.0001
Fit Statistics
-2 Res Log Likelihood 1574.8
AIC (smaller is better) 1582.8
AICC (smaller is better) 1582.8
BIC (smaller is better) 1591.4
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 304.63 <.0001
Table 13.4, page 384.
data cog_arith (rename=arithmetic=response) cog_ravens (rename=ravens=response);
set cognitive;
type = "a";
output cog_arith;
type = "r";
output cog_ravens;
run;
data bi_cog;
set cog_arith cog_ravens;
drop arithmetic ravens;
newtmt = treatment;
if relyear<0 then newtmt = "control";
run;
proc sort data = bi_cog;
by id relmonth type;
run;
proc mixed data = bi_cog method = reml noclprint noitprint covtest;
class sex id treatment newtmt type rn;
model response = type*sex type*relyear type*newtmt*relyear/ notest;
random type /subject =id type = un;
repeated / subject = id(rn) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_COG
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(rn)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 15
Columns in Z Per Subject 2
Subjects 546
Max Obs Per Subject 10
Number of Observations
Number of Observations Read 5460
Number of Observations Used 5196
Number of Observations Not Used 264
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 1.4977 0.1083 13.83 <.0001
UN(2,1) id 1.1602 0.1231 9.42 <.0001
UN(2,2) id 2.4601 0.2284 10.77 <.0001
UN(1,1) id(rn) 1.2662 0.03960 31.97 <.0001
UN(2,1) id(rn) 0.3370 0.06053 5.57 <.0001
UN(2,2) id(rn) 5.8398 0.1824 32.02 <.0001
Fit Statistics
-2 Res Log Likelihood 21414.9
AIC (smaller is better) 21426.9
AICC (smaller is better) 21426.9
BIC (smaller is better) 21452.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 2221.59 <.0001
Table 13.5, page 386.
proc mixed data = bi_cog method = reml noclprint noitprint covtest;
class sex id treatment newtmt type rn;
model response = type*sex type*relyear type*newtmt*relyear/ notest;
random type type*relyear /subject =id type = un;
repeated / subject = id(rn) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_COG
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(rn)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 13
Columns in X 15
Columns in Z Per Subject 4
Subjects 546
Max Obs Per Subject 10
Number of Observations
Number of Observations Read 5460
Number of Observations Used 5196
Number of Observations Not Used 264
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 1.5650 0.1250 12.52 <.0001
UN(2,1) id 1.1499 0.1423 8.08 <.0001
UN(2,2) id 2.2916 0.2792 8.21 <.0001
UN(3,1) id -0.08745 0.05491 -1.59 0.1112
UN(3,2) id -0.07814 0.07596 -1.03 0.3036
UN(3,3) id 0.1483 0.04283 3.46 0.0003
UN(4,1) id 0.04597 0.1115 0.41 0.6800
UN(4,2) id -0.03737 0.1807 -0.21 0.8362
UN(4,3) id 0.1099 0.06656 1.65 0.0986
UN(4,4) id 0.7748 0.2021 3.83 <.0001
UN(1,1) id(rn) 1.1756 0.04235 27.76 <.0001
UN(2,1) id(rn) 0.2697 0.06447 4.18 <.0001
UN(2,2) id(rn) 5.3625 0.1941 27.63 <.0001
Fit Statistics
-2 Res Log Likelihood 21370.9
AIC (smaller is better) 21396.9
AICC (smaller is better) 21396.9
BIC (smaller is better) 21452.8
Table 13.7, page 388.
proc sort data = bi_pain2;
by id type trial;
run;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
repeated / subject = id type = un rcorr;
run;The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
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 36
Columns in X 23
Columns in Z 0
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Estimated R Correlation Matrix for id 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8
1 1.0000 0.6372 0.4770 0.3226 -0.2843 -0.1466 -0.3092 -0.1942
2 0.6372 1.0000 0.4501 0.3414 -0.1433 -0.1321 -0.1906 -0.1650
3 0.4770 0.4501 1.0000 0.5349 -0.09852 0.09599 -0.1650 -0.01596
4 0.3226 0.3414 0.5349 1.0000 -0.06124 0.009164 -0.09867 -0.1009
5 -0.2843 -0.1433 -0.09852 -0.06124 1.0000 0.7041 0.8212 0.5543
6 -0.1466 -0.1321 0.09599 0.009164 0.7041 1.0000 0.7121 0.6774
7 -0.3092 -0.1906 -0.1650 -0.09867 0.8212 0.7121 1.0000 0.7378
8 -0.1942 -0.1650 -0.01596 -0.1009 0.5543 0.6774 0.7378 1.0000
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 4.7331 0.8639 5.48 <.0001
UN(2,1) id 3.0201 0.7255 4.16 <.0001
UN(2,2) id 4.7462 0.8579 5.53 <.0001
UN(3,1) id 2.2001 0.6563 3.35 0.0008
UN(3,2) id 2.0786 0.6736 3.09 0.0020
UN(3,3) id 4.4937 0.8517 5.28 <.0001
UN(4,1) id 1.4039 0.6264 2.24 0.0250
UN(4,2) id 1.4876 0.6127 2.43 0.0152
UN(4,3) id 2.2682 0.6467 3.51 0.0005
UN(4,4) id 4.0014 0.7625 5.25 <.0001
UN(5,1) id -0.6197 0.2908 -2.13 0.0331
UN(5,2) id -0.3128 0.2848 -1.10 0.2721
UN(5,3) id -0.2092 0.2805 -0.75 0.4557
UN(5,4) id -0.1227 0.2683 -0.46 0.6473
UN(5,5) id 1.0037 0.1807 5.55 <.0001
UN(6,1) id -0.3409 0.3029 -1.13 0.2603
UN(6,2) id -0.3077 0.3032 -1.01 0.3102
UN(6,3) id 0.2176 0.2988 0.73 0.4666
UN(6,4) id 0.01960 0.2834 0.07 0.9449
UN(6,5) id 0.7541 0.1683 4.48 <.0001
UN(6,6) id 1.1430 0.2100 5.44 <.0001
UN(7,1) id -0.7806 0.3402 -2.29 0.0218
UN(7,2) id -0.4817 0.3378 -1.43 0.1539
UN(7,3) id -0.4058 0.3282 -1.24 0.2164
UN(7,4) id -0.2290 0.3142 -0.73 0.4660
UN(7,5) id 0.9546 0.1927 4.95 <.0001
UN(7,6) id 0.8834 0.1981 4.46 <.0001
UN(7,7) id 1.3463 0.2472 5.45 <.0001
UN(8,1) id -0.4443 0.3124 -1.42 0.1550
UN(8,2) id -0.3781 0.3076 -1.23 0.2190
UN(8,3) id -0.03559 0.2982 -0.12 0.9050
UN(8,4) id -0.2123 0.2854 -0.74 0.4570
UN(8,5) id 0.5841 0.1577 3.70 0.0002
UN(8,6) id 0.7619 0.1788 4.26 <.0001
UN(8,7) id 0.9005 0.2005 4.49 <.0001
UN(8,8) id 1.1066 0.2101 5.27 <.0001
Fit Statistics
-2 Res Log Likelihood 1524.4
AIC (smaller is better) 1596.4
AICC (smaller is better) 1602.5
BIC (smaller is better) 1674.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
35 354.96 <.0001
Table 13.8, page 389.
*Bivar RI;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un;
repeated / subject = id(trial) type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1317 0.5059 4.21 <.0001
UN(2,1) id -0.2740 0.2045 -1.34 0.1804
UN(2,2) id 0.7936 0.1598 4.97 <.0001
UN(1,1) id(trial) 2.3931 0.2557 9.36 <.0001
UN(2,1) id(trial) -0.1279 0.06916 -1.85 0.0645
UN(2,2) id(trial) 0.3432 0.03667 9.36 <.0001
Fit Statistics
-2 Res Log Likelihood 1568.8
AIC (smaller is better) 1580.8
AICC (smaller is better) 1581.0
BIC (smaller is better) 1593.8
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
5 310.59 <.0001
*Ind RI;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
random type /subject =id type = un(1);
repeated / subject = id(trial) type = un(1);
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Banded
Subject Effects id, id(trial)
Estimation Method REML
Residual Variance Method None
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 6
Columns in X 23
Columns in Z Per Subject 2
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 2.1264 0.5050 4.21 <.0001
UN(2,1) id 0 . . .
UN(2,2) id 0.7938 0.1598 4.97 <.0001
UN(1,1) id(trial) 2.3947 0.2560 9.36 <.0001
UN(2,1) id(trial) 0 . . .
UN(2,2) id(trial) 0.3432 0.03667 9.36 <.0001
Fit Statistics
-2 Res Log Likelihood 1574.8
AIC (smaller is better) 1582.8
AICC (smaller is better) 1582.8
BIC (smaller is better) 1591.4
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 304.63 <.0001
*PCUN:
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ noint notest;
repeated trial type/ subject = id type = un@un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured @
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 13
Columns in X 22
Columns in Z 0
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
trial UN(1,1) id 5.2498 0.7804 6.73 <.0001
UN(2,1) id 3.6753 0.6647 5.53 <.0001
UN(2,2) id 5.7007 0.8563 6.66 <.0001
UN(3,1) id 3.8333 0.7274 5.27 <.0001
UN(3,2) id 3.6546 0.7317 4.99 <.0001
UN(3,3) id 6.2221 0.9756 6.38 <.0001
UN(4,1) id 2.3249 0.5826 3.99 <.0001
UN(4,2) id 2.9566 0.6463 4.57 <.0001
UN(4,3) id 3.7839 0.7365 5.14 <.0001
UN(4,4) id 5.2698 0.8302 6.35 <.0001
type UN(1,1) id 1.0000 0 . .
UN(2,1) id -0.06394 0.02678 -2.39 0.0170
UN(2,2) id 0.1688 0.02253 7.50 <.0001
Fit Statistics
-2 Res Log Likelihood 1553.4
AIC (smaller is better) 1577.4
AICC (smaller is better) 1578.0
BIC (smaller is better) 1603.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
11 326.04 <.0001
*INDUN;
proc sort data = bi_pain2;
by type id trial;
run;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
by type;
class id trial type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
repeated / subject = id type = un;
run;
type=r
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
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 10
Columns in X 12
Columns in Z 0
Subjects 64
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 256
Number of Observations Used 245
Number of Observations Not Used 11
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 4.7499 0.8688 5.47 <.0001
UN(2,1) id 3.0182 0.7255 4.16 <.0001
UN(2,2) id 4.7280 0.8528 5.54 <.0001
UN(3,1) id 2.2391 0.6631 3.38 0.0007
UN(3,2) id 2.0756 0.6736 3.08 0.0021
UN(3,3) id 4.5148 0.8583 5.26 <.0001
UN(4,1) id 1.4049 0.6278 2.24 0.0252
UN(4,2) id 1.4891 0.6093 2.44 0.0145
UN(4,3) id 2.2617 0.6485 3.49 0.0005
UN(4,4) id 4.0015 0.7625 5.25 <.0001
Fit Statistics
-2 Res Log Likelihood 981.7
AIC (smaller is better) 1001.7
AICC (smaller is better) 1002.7
BIC (smaller is better) 1023.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 68.77 <.0001
type=t
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
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 10
Columns in X 12
Columns in Z 0
Subjects 64
Max Obs Per Subject 4
Number of Observations
Number of Observations Read 256
Number of Observations Used 245
Number of Observations Not Used 11
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 1.0088 0.1825 5.53 <.0001
UN(2,1) id 0.7478 0.1663 4.50 <.0001
UN(2,2) id 1.1262 0.2046 5.50 <.0001
UN(3,1) id 0.9500 0.1915 4.96 <.0001
UN(3,2) id 0.8660 0.1932 4.48 <.0001
UN(3,3) id 1.3317 0.2429 5.48 <.0001
UN(4,1) id 0.5752 0.1556 3.70 0.0002
UN(4,2) id 0.7448 0.1733 4.30 <.0001
UN(4,3) id 0.8820 0.1954 4.51 <.0001
UN(4,4) id 1.0885 0.2040 5.33 <.0001
Fit Statistics
-2 Res Log Likelihood 558.8
AIC (smaller is better) 578.8
AICC (smaller is better) 579.8
BIC (smaller is better) 600.4
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
9 166.04 <.0001
*UN;
proc sort data = bi_pain2;
by id trial type;
run;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ notest;
repeated / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
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 36
Columns in X 23
Columns in Z 0
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) id 4.7331 0.8639 5.48 <.0001
UN(2,1) id -0.6197 0.2908 -2.13 0.0331
UN(2,2) id 1.0037 0.1807 5.55 <.0001
UN(3,1) id 3.0201 0.7255 4.16 <.0001
UN(3,2) id -0.3128 0.2848 -1.10 0.2721
UN(3,3) id 4.7462 0.8579 5.53 <.0001
UN(4,1) id -0.3409 0.3029 -1.13 0.2603
UN(4,2) id 0.7541 0.1683 4.48 <.0001
UN(4,3) id -0.3077 0.3032 -1.01 0.3102
UN(4,4) id 1.1430 0.2100 5.44 <.0001
UN(5,1) id 2.2001 0.6563 3.35 0.0008
UN(5,2) id -0.2092 0.2805 -0.75 0.4557
UN(5,3) id 2.0786 0.6736 3.09 0.0020
UN(5,4) id 0.2176 0.2988 0.73 0.4666
UN(5,5) id 4.4937 0.8517 5.28 <.0001
UN(6,1) id -0.7806 0.3402 -2.29 0.0218
UN(6,2) id 0.9546 0.1927 4.95 <.0001
UN(6,3) id -0.4817 0.3378 -1.43 0.1539
UN(6,4) id 0.8834 0.1981 4.46 <.0001
UN(6,5) id -0.4058 0.3282 -1.24 0.2164
UN(6,6) id 1.3463 0.2472 5.45 <.0001
UN(7,1) id 1.4039 0.6264 2.24 0.0250
UN(7,2) id -0.1227 0.2683 -0.46 0.6473
UN(7,3) id 1.4876 0.6127 2.43 0.0152
UN(7,4) id 0.01960 0.2834 0.07 0.9449
UN(7,5) id 2.2682 0.6467 3.51 0.0005
UN(7,6) id -0.2290 0.3142 -0.73 0.4660
UN(7,7) id 4.0014 0.7625 5.25 <.0001
UN(8,1) id -0.4443 0.3124 -1.42 0.1550
UN(8,2) id 0.5841 0.1577 3.70 0.0002
UN(8,3) id -0.3781 0.3076 -1.23 0.2190
UN(8,4) id 0.7619 0.1788 4.26 <.0001
UN(8,5) id -0.03559 0.2982 -0.12 0.9050
UN(8,6) id 0.9005 0.2005 4.49 <.0001
UN(8,7) id -0.2123 0.2854 -0.74 0.4570
UN(8,8) id 1.1066 0.2101 5.27 <.0001
Fit Statistics
-2 Res Log Likelihood 1524.4
AIC (smaller is better) 1596.4
AICC (smaller is better) 1602.5
BIC (smaller is better) 1674.2
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
35 354.96 <.0001
Table 13.9, page 391.
proc sort data = bi_pain2;
by id type trial;
run;
proc mixed data = bi_pain2 method = reml noclprint noitprint covtest;
class trial id type cs0;
model response = type*cs0 type*tmt1 type*tmt2 type*tmt3 type*cs0*tmt1 type*cs0*tmt2 type*cs0*tmt3/ noint notest;
repeated trial type/ subject = id type = un@un rcorr;
run;
The Mixed Procedure
Model Information
Data Set WORK.BI_PAIN2
Dependent Variable response
Covariance Structure Unstructured @
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 13
Columns in X 22
Columns in Z 0
Subjects 64
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 512
Number of Observations Used 490
Number of Observations Not Used 22
Estimated R Correlation Matrix for id 1
Row Col1 Col2 Col3 Col4 Col5 Col6 Col7 Col8
1 1.0000 0.6718 0.6707 0.4420 -0.1556 -0.1045 -0.1044 -0.06878
2 0.6718 1.0000 0.6136 0.5394 -0.1045 -0.1556 -0.09548 -0.08393
3 0.6707 0.6136 1.0000 0.6608 -0.1044 -0.09548 -0.1556 -0.1028
4 0.4420 0.5394 0.6608 1.0000 -0.06878 -0.08393 -0.1028 -0.1556
5 -0.1556 -0.1045 -0.1044 -0.06878 1.0000 0.6718 0.6707 0.4420
6 -0.1045 -0.1556 -0.09548 -0.08393 0.6718 1.0000 0.6136 0.5394
7 -0.1044 -0.09548 -0.1556 -0.1028 0.6707 0.6136 1.0000 0.6608
8 -0.06878 -0.08393 -0.1028 -0.1556 0.4420 0.5394 0.6608 1.0000
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
trial UN(1,1) id 5.2498 0.7804 6.73 <.0001
UN(2,1) id 3.6753 0.6647 5.53 <.0001
UN(2,2) id 5.7007 0.8563 6.66 <.0001
UN(3,1) id 3.8333 0.7274 5.27 <.0001
UN(3,2) id 3.6546 0.7317 4.99 <.0001
UN(3,3) id 6.2221 0.9756 6.38 <.0001
UN(4,1) id 2.3249 0.5826 3.99 <.0001
UN(4,2) id 2.9566 0.6463 4.57 <.0001
UN(4,3) id 3.7839 0.7365 5.14 <.0001
UN(4,4) id 5.2698 0.8302 6.35 <.0001
type UN(1,1) id 1.0000 0 . .
UN(2,1) id -0.06394 0.02678 -2.39 0.0170
UN(2,2) id 0.1688 0.02253 7.50 <.0001
Fit Statistics
-2 Res Log Likelihood 1553.4
AIC (smaller is better) 1577.4
AICC (smaller is better) 1578.0
BIC (smaller is better) 1603.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
11 326.04 <.0001