/*************  classicalmixed.sas *********************
Three levels of factor A, four levels of B
      Both fixed
      Both random
      A fixed, B random
      B nested within A
***************************************************/

data mixedup;
     infile '/folders/myfolders/mixedup.data.txt';
     input ID Y A B;

proc glm plots=none;
     title 'Default proc glm: Both Fixed';
     class A B ;
     model y = a | b;
     means a*b;

proc glm plots=none;
     title 'Both Random with proc glm';
     class A B ;
     model y = a | b;
     random a b a*b / test ; 
     /* Have to specify interaction random too, 
        and explicitly ask for tests */

proc glm plots=none;
     title 'A Fixed, B Random';
     class A B ;
     model y = a | b;
     random b a*b / test;

proc glm plots=none;
     title 'A fixed, B random and nested within A';
     class A B ;
     model y = a b(a);
     random b(a) / test;

proc mixed cl; /*Confidence Limits for variances (There are no tests) */
     title 'A fixed, B random and nested within A';
     title2 'Using proc mixed';
     title3 'Compare F for A = 7.32, F for B(A) = 3.11, p = 0.0126';
     class A B ;
     model y = a ;
     random b(a);

proc glm plots=none;
     title 'Both random, B nested within A';
     class A B ;
     model y = a b(a);
     random a b(a) / test;

proc sort; by A B; /* Data must be sorted in order of nesting*/
proc nested;
     title 'Nested random effects with proc nested';
     title2 'Compare F for A = 7.32, F for B(A) = 3.11';
     class A B;
     var Y;

proc mixed cl;
     title 'Pure nested with proc mixed';
     class A B ;
     model y =  ;
     random a b(a);

/****** What happens when the data are unbalanced? ******/

proc glm plots=none;
     title 'UNBALANCED: Both random, B nested within A';
     title2 'Using proc glm';
     title3 'Compare F for A = 7.32, F for B(A) = 3.11';
     where id ne 1; /* Throw out one case */
     class A B ;
     model y = a b(a);
     random a b(a) / test;

proc sort; by A B; /* Data must be sorted in order of nesting*/
proc nested;
     title 'UNBALANCED: Nested random effects with proc nested';
     title2 'Proc glm gave F for A = 7.38, F for B(A) = 2.77';
     where id ne 1; /* Throw out one case */
     class A B;
     var Y;

proc mixed cl;
     title 'UNBALANCED: Pure nested with proc mixed';
     title2 'Proc nested estimated Var[A]=14.39, Var[B(A)]=6.25';
     where id ne 1; /* Throw out one case */
     class A B ;
     model y =  ;
     random a b(a);

/* Conclusion: Proc glm tries to fix the problem, proc nested gives up 
               and proc mixed never cared in the first place. */