Table 7.1 using data set https://stats.idre.ucla.edu/wp-content/uploads/2016/02/pupcross.sas7bdat.
Part 1: Intercept only.
proc mixed data =pupcross covtest noclprint method=ml; class pupil pschool sschool; model achiev = / solution ddfm =satterth; random intercept / subject=sschool; random intercept / subject=pschool; run;
The Mixed Procedure
Model Information
Data Set WORK.PUPCROSS Dependent Variable ACHIEV Covariance Structure Variance Components Subject Effects SSCHOOL, PSCHOOL Estimation Method ML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite
Dimensions
Covariance Parameters 3 Columns in X 1 Columns in Z Per Subject 80 Subjects 1 Max Obs Per Subject 1000
Convergence criteria met.
Covariance Parameter Estimates
Standard Z Cov Parm Subject Estimate Error Value Pr Z
Intercept SSCHOOL 0.06540 0.02131 3.07 0.0011 Intercept PSCHOOL 0.1693 0.03931 4.31 <.0001 Residual 0.5132 0.02390 21.47 <.0001
Fit Statistics
-2 Log Likelihood 2317.8
AIC (smaller is better) 2325.8
AICC (smaller is better) 2325.9
BIC (smaller is better) 2317.8
Solution for Fixed Effects
Standard Effect Estimate Error DF t Value Pr > |t|
Intercept 6.3487 0.07831 66.7 81.07 <.0001
Part 2: intercept plus pupil level variables.
proc mixed data =pupcross covtest noclprint method=ml; class pupil pschool sschool; model achiev = pupsex pupses / solution ddfm =satterth; random intercept / subject=sschool; random intercept / subject=pschool; run;
The Mixed Procedure Model Information Data Set WORK.PUPCROSS Dependent Variable ACHIEV Covariance Structure Variance Components Subject Effects SSCHOOL, PSCHOOL Estimation Method ML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite Dimensions Covariance Parameters 3 Columns in X 3 Columns in Z Per Subject 80 Subjects 1 Max Obs Per Subject 1000 Convergence criteria met. Covariance Parameter Estimates Standard Z Cov Parm Subject Estimate Error Value Pr Z Intercept SSCHOOL 0.06361 0.02059 3.09 0.0010 Intercept PSCHOOL 0.1690 0.03878 4.36 <.0001 Residual 0.4743 0.02209 21.47 <.0001 Fit Statistics -2 Log Likelihood 2243.5 AIC (smaller is better) 2255.5 AICC (smaller is better) 2255.6 BIC (smaller is better) 2243.5 Solution for Fixed Effects Standard Effect Estimate Error DF t Value Pr > |t| Intercept 5.7555 0.1053 214 54.67 <.0001 PUPSEX 0.2613 0.04564 949 5.73 <.0001 PUPSES 0.1141 0.01610 943 7.09 <.0001 Type 3 Tests of Fixed Effects Num Den Effect DF DF F Value Pr > F PUPSEX 1 949 32.79 <.0001 PUPSES 1 943 50.21 <.0001
Part 3: primary by secondary School crossed with pupil and school variables.
proc mixed data =pupcross covtest noclprint method=ml; class pupil pschool sschool; model achiev = pupsex pupses pdenom sdenom/ solution ddfm =satterth; random intercept / subject=sschool; random intercept / subject=pschool; run;
The Mixed Procedure
Model Information
Data Set WORK.PUPCROSS Dependent Variable ACHIEV Covariance Structure Variance Components Subject Effects SSCHOOL, PSCHOOL Estimation Method ML Residual Variance Method Profile Fixed Effects SE Method Model-Based Degrees of Freedom Method Satterthwaite
Dimensions
Covariance Parameters 3
Columns in X 5
Columns in Z Per Subject 80
Subjects 1
Max Obs Per Subject 1000
Covariance Parameter Estimates
Standard Z Cov Parm Subject Estimate Error Value Pr Z
Intercept SSCHOOL 0.05542 0.01852 2.99 0.0014 Intercept PSCHOOL 0.1594 0.03686 4.33 <.0001 Residual 0.4741 0.02208 21.47 <.0001
Fit Statistics
-2 Log Likelihood 2237.5
AIC (smaller is better) 2253.5
AICC (smaller is better) 2253.6
BIC (smaller is better) 2237.5
Solution for Fixed Effects
Standard Effect Estimate Error DF t Value Pr > |t|
Intercept 5.5185 0.1408 145 39.20 <.0001 PUPSEX 0.2631 0.04561 950 5.77 <.0001 PUPSES 0.1136 0.01609 945 7.06 <.0001 PDENOM 0.2041 0.1241 50.2 1.64 0.1063 SDENOM 0.1762 0.09466 48.1 1.86 0.0689
Type 3 Tests of Fixed Effects
Num Den Effect DF DF F Value Pr > F
PUPSEX 1 950 33.27 <.0001 PUPSES 1 945 49.79 <.0001 PDENOM 1 50.2 2.71 0.1063 SDENOM 1 48.1 3.46 0.0689
Part 4: primary by secondary School crossed with pupil and school variables with variable pupses being modeled as a random effect.
proc mixed data =pupcross covtest noclprint method=ml; class pupil pschool sschool; model achiev = pupsex pupses pdenom sdenom/ solution ddfm =satterth; random intercept / subject=sschool; random intercept pupses / subject=pschool type=un; run;
The Mixed Procedure
Model Information
Data Set WORK.PUPCROSS
Dependent Variable ACHIEV
Covariance Structures Variance Components,
Unstructured
Subject Effects SSCHOOL, PSCHOOL
Estimation Method ML
Residual Variance Method Profile
Fixed Effects SE Method Model-Based
Degrees of Freedom Method Satterthwaite
Dimensions
Covariance Parameters 5
Columns in X 5
Columns in Z Per Subject 130
Subjects 1
Max Obs Per Subject 1000
Number of Observations
Number of Observations Read 1000
Number of Observations Used 1000
Number of Observations Not Used 0
Iteration History
Iteration Evaluations -2 Log Like Criterion
0 1 2474.36462150
1 3 2224.66280358 0.00088577
2 1 2224.47834515 0.00001539
3 1 2224.47532928 0.00000001
Convergence criteria met.
Covariance Parameter Estimates
Standard Z
Cov Parm Subject Estimate Error Value Pr Z
Intercept SSCHOOL 0.05373 0.01801 2.98 0.0014
UN(1,1) PSCHOOL 0.1486 0.07521 1.98 0.0241
UN(2,1) PSCHOOL -0.01560 0.01500 -1.04 0.2983
UN(2,2) PSCHOOL 0.008014 0.003882 2.06 0.0195
Residual 0.4584 0.02185 20.98 <.0001
Fit Statistics
-2 Log Likelihood 2224.5
AIC (smaller is better) 2244.5
AICC (smaller is better) 2244.7
BIC (smaller is better) 2224.5
Solution for Fixed Effects
Standard
Effect Estimate Error DF t Value Pr > |t|
Intercept 5.5324 0.1375 104 40.25 <.0001
PUPSEX 0.2532 0.04530 949 5.59 <.0001
PUPSES 0.1142 0.02047 54.3 5.58 <.0001
PDENOM 0.1999 0.1176 49.2 1.70 0.0956
SDENOM 0.1646 0.09344 47.7 1.76 0.0846
Type 3 Tests of Fixed Effects
Num Den
Effect DF DF F Value Pr > F
PUPSEX 1 949 31.23 <.0001
PUPSES 1 54.3 31.15 <.0001
PDENOM 1 49.2 2.89 0.0956
SDENOM 1 47.7 3.10 0.0846
Table 7.2 using data set https://stats.idre.ucla.edu/wp-content/uploads/2016/02/socsflat.sas7bdat. We will skip this example for the time being.