The data files can be downloaded from
http://rem.ph.ucla.edu/~rob/mld/data.html .
Table 9.1, page 314.
data bsi;
set bsitotal;
knot18 = (true_month - 18)*(true_month >= 18);
knot36 = (true_month - 36)*(true_month >= 36);
spring = (season = "spring (3-6)");
summer = (season = "summer (7-10)");
l2bsi_gsi = log(bsi_gsi + 1/53)/log(2);
run;
proc mixed data = bsi method = reml noitprint noclprint covtest;
class pid rounded3_true_month gender drug_status;
model l2bsi_gsi = true_month knot18 knot36 spring summer gender parent_alcohol parent_marijuana drug_status/
notest;
repeated rounded3_true_month / subject = pid type = arma(1,1);
run;
The Mixed Procedure
Model Information
Data Set WORK.BSI
Dependent Variable l2bsi_gsi
Covariance Structure Autoregressive
Moving Average
Subject Effect pid
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Between-Within
Dimensions
Covariance Parameters 3
Columns in X 13
Columns in Z 0
Subjects 329
Max Obs Per Subject 13
Number of Observations
Number of Observations Read 4857
Number of Observations Used 1907
Number of Observations Not Used 2950
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Rho pid 0.9415 0.01068 88.19 <.0001
Gamma pid 0.5855 0.02435 24.05 <.0001
Residual 4.0431 0.1954 20.69 <.0001
Fit Statistics
-2 Res Log Likelihood 7367.7
AIC (smaller is better) 7373.7
AICC (smaller is better) 7373.7
BIC (smaller is better) 7385.1
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
2 761.23 <.0001
proc mixed data = bsi method = reml noitprint noclprint covtest;
class pid rounded3_true_month gender drug_status parent;
model l2bsi_gsi = true_month knot18 knot36 spring summer gender parent_alcohol parent_marijuana drug_status/
notest;
repeated rounded3_true_month / subject = pid(parent) type = arma(1,1);
random intercept / subject = parent type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.BSI
Dependent Variable l2bsi_gsi
Covariance Structures Unstructured,
Autoregressive
Moving Average
Subject Effects parent, pid(parent)
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 13
Columns in Z Per Subject 1
Subjects 220
Max Obs Per Subject 44
Number of Observations
Number of Observations Read 4857
Number of Observations Used 1907
Number of Observations Not Used 2950
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
UN(1,1) parent 0.7199 0.2348 3.07 0.0011
Rho pid(parent) 0.9047 0.02247 40.25 <.0001
Gamma pid(parent) 0.5036 0.03542 14.22 <.0001
Residual 3.3345 0.2248 14.83 <.0001
Fit Statistics
-2 Res Log Likelihood 7357.2
AIC (smaller is better) 7365.2
AICC (smaller is better) 7365.2
BIC (smaller is better) 7378.8
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 771.70 <.0001
Table 9.2, page 315.
data weight2_1;
set weight2;
d1 = day;
d2 = day*day/100;
run;
*Model 1;
proc mixed data = weight2_1 method = reml noitprint noclprint;
class id ;
model weight = d1 d2 / solution notest;
random intercept d1 / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.WEIGHT2
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 38
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 304
Number of Observations Used 265
Number of Observations Not Used 39
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 666.30
UN(2,1) id -0.6606
UN(2,2) id 0.01148
Residual 4.5231
Fit Statistics
-2 Res Log Likelihood 1474.1
AIC (smaller is better) 1482.1
AICC (smaller is better) 1482.3
BIC (smaller is better) 1488.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 986.16 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 193.72 4.1976 37 46.15 <.0001
d1 -0.2653 0.03428 37 -7.74 <.0001
d2 0.2079 0.06208 188 3.35 0.0010
*Model 2;
proc mixed data = weight2_1 method = reml noitprint noclprint;
class id;
model weight = d1 d2 visit/ solution notest;
random intercept d1 / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.WEIGHT2
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 4
Columns in Z Per Subject 2
Subjects 38
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 304
Number of Observations Used 265
Number of Observations Not Used 39
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 666.06
UN(2,1) id -0.6833
UN(2,2) id 0.01179
Residual 3.4397
Fit Statistics
-2 Res Log Likelihood 1420.7
AIC (smaller is better) 1428.7
AICC (smaller is better) 1428.9
BIC (smaller is better) 1435.3
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
3 1034.39 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 193.46 4.1945 37 46.12 <.0001
d1 -0.1732 0.03337 37 -5.19 <.0001
d2 0.1104 0.05577 187 1.98 0.0492
visit -2.3782 0.3025 187 -7.86 <.0001
*Model 3;
proc mixed data = weight2_1 method = reml noitprint noclprint;
class id;
model weight = d1 d2 visit/ solution notest;
random intercept d1 / subject = id type = un;
random visit /subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.WEIGHT2
Dependent Variable weight
Covariance Structure Unstructured
Subject Effects id, id
Estimation Method REML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Containment
Dimensions
Covariance Parameters 5
Columns in X 4
Columns in Z Per Subject 3
Subjects 38
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 304
Number of Observations Used 265
Number of Observations Not Used 39
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 667.10
UN(2,1) id -0.5547
UN(2,2) id 0.01195
UN(1,1) id 4.0915
Residual 2.5165
Fit Statistics
-2 Res Log Likelihood 1399.4
AIC (smaller is better) 1409.4
AICC (smaller is better) 1409.6
BIC (smaller is better) 1417.6
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
4 1055.75 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 193.45 4.1957 37 46.11 <.0001
d1 -0.1715 0.03021 37 -5.68 <.0001
d2 0.1081 0.04824 150 2.24 0.0266
visit -2.3786 0.4219 37 -5.64 <.0001
*Model 4;
proc mixed data = weight2_1 method = reml noitprint noclprint;
class id ;
model weight = d1 d2 visit/ solution notest;
random intercept d1 visit / subject = id type = un;
run;
The Mixed Procedure
Model Information
Data Set WORK.WEIGHT2
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 7
Columns in X 4
Columns in Z Per Subject 3
Subjects 38
Max Obs Per Subject 8
Number of Observations
Number of Observations Read 304
Number of Observations Used 265
Number of Observations Not Used 39
Covariance Parameter Estimates
Cov Parm Subject Estimate
UN(1,1) id 667.00
UN(2,1) id -0.4385
UN(2,2) id 0.01223
UN(3,1) id -13.5255
UN(3,2) id -0.02733
UN(3,3) id 4.3062
Residual 2.5039
Fit Statistics
-2 Res Log Likelihood 1397.3
AIC (smaller is better) 1411.3
AICC (smaller is better) 1411.7
BIC (smaller is better) 1422.7
Null Model Likelihood Ratio Test
DF Chi-Square Pr > ChiSq
6 1057.86 <.0001
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 193.45 4.1954 37 46.11 <.0001
d1 -0.1721 0.03028 37 -5.69 <.0001
d2 0.1091 0.04810 150 2.27 0.0248
visit -2.3724 0.4285 37 -5.54 <.0001