One-Way Random-Effects Model

Apex Enterprises Example

Program Listing

DATA apex (DROP=rep);
 DO rep = 1 TO 4;
  DO officer = 'A','B','C','D','E';
    INPUT rating @@;
    OUTPUT;
   END;
  END;
 DATALINES;
76 59 49 74 66 65 75 63 71 84
85 81 61 85 80 74 67 46 89 79
;

OPTIONS LS=76 NONUMBER NOCENTER NODATE;

TITLE1 'One-Way Random-Effect Model';
TITLE2 'Apex Enterprises Data';
TITLE3 'Use Proc GLM';
PROC GLM DATA=apex;
 CLASS officer;
 MODEL rating = officer;
 RANDOM officer / TEST;
QUIT;

TITLE3 'Use Proc VARCOMP';
TITLE4 'Minimum InVariant Quadratic Unbiased Estimator';
PROC VARCOMP DATA=apex;
 CLASS officer;
 MODEL rating=officer;
RUN;

TITLE4 'REstricted Maximum Likelihood';
PROC VARCOMP DATA=apex METHOD=REML;
 CLASS officer;
 MODEL rating = officer;
RUN;

TITLE3 'Use Proc MIXED';
PROC MIXED DATA=apex;
 CLASS officer;
 MODEL rating=;
 RANDOM officer;
RUN;

Output Listing

One-Way Random-Effect Model
Apex Enterprises Data
Use Proc GLM

The GLM Procedure

     Class Level Information
Class         Levels    Values
officer            5    A B C D E


Number of Observations Read          20
Number of Observations Used          20



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc GLM

The GLM Procedure

Dependent Variable: rating

                            Sum of
Source            DF       Squares   Mean Square  F Value  Pr > F
Model              4   1579.700000    394.925000     5.39  0.0068
Error             15   1099.250000     73.283333
Corrected Total   19   2678.950000


R-Square     Coeff Var      Root MSE    rating Mean
0.589671      11.98120      8.560569       71.45000

Source          DF     Type I SS   Mean Square  F Value  Pr > F
officer          4   1579.700000    394.925000     5.39  0.0068

Source          DF   Type III SS   Mean Square  F Value  Pr > F
officer          4   1579.700000    394.925000     5.39  0.0068



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc GLM

The GLM Procedure

Source                  Type III Expected Mean Square
officer                 Var(Error) + 4 Var(officer)



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc GLM

The GLM Procedure
Tests of Hypotheses for Random Model Analysis of Variance

Dependent Variable: rating

Source            DF   Type III SS   Mean Square  F Value  Pr > F
officer            4   1579.700000    394.925000     5.39  0.0068
Error: MS(Error)  15   1099.250000     73.283333



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc VARCOMP
Minimum InVariant Quadratic Unbiased Estimator

Variance Components Estimation Procedure

     Class Level Information
Class         Levels    Values
officer            5    A B C D E


Number of Observations Read          20
Number of Observations Used          20


                    MIVQUE(0) SSQ Matrix

Source            officer             Error            rating
officer          64.00000          16.00000            6318.8
Error            16.00000          19.00000            2678.9


      MIVQUE(0) Estimates

Variance Component        rating
Var(officer)            80.41042
Var(Error)              73.28333



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc VARCOMP
REstricted Maximum Likelihood

Variance Components Estimation Procedure

     Class Level Information
Class         Levels    Values
officer            5    A B C D E


Number of Observations Read          20
Number of Observations Used          20


Dependent Variable:    rating

                         REML Iterations

Iteration         Objective      Var(officer)        Var(Error)
        0     88.3297815982     80.4104166667     73.2833333333
        1     88.3297815982     80.4104166667     73.2833333333

Convergence criteria met.


      REML Estimates
Variance
Component         Estimate
Var(officer)      80.41042
Var(Error)        73.28333


   Asymptotic Covariance Matrix of Estimates
                  Var(officer)        Var(Error)
Var(officer)            4918.7        -179.01490
Var(Error)          -179.01490         716.05959



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc MIXED

The Mixed Procedure

                  Model Information

Data Set                     WORK.APEX
Dependent Variable           rating
Covariance Structure         Variance Components
Estimation Method            REML
Residual Variance Method     Profile
Fixed Effects SE Method      Model-Based
Degrees of Freedom Method    Containment


              Class Level Information
Class      Levels    Values
officer         5    A B C D E


            Dimensions
Covariance Parameters             2
Columns in X                      1
Columns in Z                      5
Subjects                          1
Max Obs Per Subject              20


          Number of Observations
Number of Observations Read              20
Number of Observations Used              20
Number of Observations Not Used           0


                     Iteration History
Iteration    Evaluations    -2 Res Log Like       Criterion
        0              1       150.94147984
        1              1       145.24517813      0.00000000


                   Convergence criteria met.



One-Way Random-Effect Model
Apex Enterprises Data
Use Proc MIXED

The Mixed Procedure

Covariance Parameter
      Estimates
Cov Parm     Estimate
officer       80.4104
Residual      73.2833


           Fit Statistics
-2 Res Log Likelihood           145.2
AIC (smaller is better)         149.2
AICC (smaller is better)        150.0
BIC (smaller is better)         148.5