/* Exercice 1 */

data h;
     input Trait Animal Y;
     datalines;
   1 1 6
   1 2 8
   1 3 7
   2 1 9
   2 2 5
   2 3 .
   ;
data g;
      input Row Col1-Col6;
      datalines;
   1  2  1  1  2   1  1
   2  1  2 .5  1   2  .5
   3  1 .5  2  1  .5  2
   4  2  1  1  3  1.5 1.5
   5  1  2 .5 1.5  3  .75
   6  1 .5  2 1.5 .75 3
   ;
proc mixed data=h mmeq mmeqsol;
      class Trait Animal;
      model Y = Trait / noint s outp=predicted;
      random Trait*Animal / type=un gdata=g g gi s;
      repeated / type=un sub=Animal r ri;
      parms (4) (1) (5) / noiter;
   run;


   proc print data=predicted;
   run;

data sp;
      input Block A B Y @@;
      datalines;
   1 1 1  56  1 1 2  41
   1 2 1  50  1 2 2  36
   1 3 1  39  1 3 2  35
   2 1 1  30  2 1 2  25
   2 2 1  36  2 2 2  28
   2 3 1  33  2 3 2  30
   3 1 1  32  3 1 2  24
   3 2 1  31  3 2 2  27
   3 3 1  15  3 3 2  19
   4 1 1  30  4 1 2  25
   4 2 1  35  4 2 2  30
   4 3 1  17  4 3 2  18
   ;

   proc mixed;
      class A B Block;
      model Y = A B A*B;
      random Block A*Block;
   run;

/* Exercice 3*/
/* Modele nonlineaire */
   data nl;
    data theoph;
      input subject time conc dose wt;
      datalines; 
   1  0.00  0.74 4.02 79.6
   1  0.25  2.84 4.02 79.6
   1  0.57  6.57 4.02 79.6
   1  1.12 10.50 4.02 79.6
   1  2.02  9.66 4.02 79.6
   1  3.82  8.58 4.02 79.6
   1  5.10  8.36 4.02 79.6
   1  7.03  7.47 4.02 79.6
   1  9.05  6.89 4.02 79.6
   1 12.12  5.94 4.02 79.6
   1 24.37  3.28 4.02 79.6
   2  0.00  0.00 4.40 72.4
   2  0.27  1.72 4.40 72.4
   2  0.52  7.91 4.40 72.4
   2  1.00  8.31 4.40 72.4
   2  1.92  8.33 4.40 72.4
   2  3.50  6.85 4.40 72.4
   2  5.02  6.08 4.40 72.4
   2  7.03  5.40 4.40 72.4
   2  9.00  4.55 4.40 72.4
   2 12.00  3.01 4.40 72.4
   2 24.30  0.90 4.40 72.4
   3  0.00  0.00 4.53 70.5
   3  0.27  4.40 4.53 70.5
   3  0.58  6.90 4.53 70.5
   3  1.02  8.20 4.53 70.5
   3  2.02  7.80 4.53 70.5
   3  3.62  7.50 4.53 70.5
   3  5.08  6.20 4.53 70.5
   3  7.07  5.30 4.53 70.5
   3  9.00  4.90 4.53 70.5
   3 12.15  3.70 4.53 70.5
   3 24.17  1.05 4.53 70.5
   4  0.00  0.00 4.40 72.7
   4  0.35  1.89 4.40 72.7
   4  0.60  4.60 4.40 72.7
   4  1.07  8.60 4.40 72.7
   4  2.13  8.38 4.40 72.7
   4  3.50  7.54 4.40 72.7
   4  5.02  6.88 4.40 72.7
   4  7.02  5.78 4.40 72.7
   4  9.02  5.33 4.40 72.7
   4 11.98  4.19 4.40 72.7
   4 24.65  1.15 4.40 72.7
   5  0.00  0.00 5.86 54.6
   5  0.30  2.02 5.86 54.6
   5  0.52  5.63 5.86 54.6
   5  1.00 11.40 5.86 54.6
   5  2.02  9.33 5.86 54.6
   5  3.50  8.74 5.86 54.6
   5  5.02  7.56 5.86 54.6
   5  7.02  7.09 5.86 54.6
   5  9.10  5.90 5.86 54.6
   5 12.00  4.37 5.86 54.6
   5 24.35  1.57 5.86 54.6
   6  0.00  0.00 4.00 80.0
   6  0.27  1.29 4.00 80.0
   6  0.58  3.08 4.00 80.0
   6  1.15  6.44 4.00 80.0
   6  2.03  6.32 4.00 80.0
   6  3.57  5.53 4.00 80.0
   6  5.00  4.94 4.00 80.0
   6  7.00  4.02 4.00 80.0
   6  9.22  3.46 4.00 80.0
   6 12.10  2.78 4.00 80.0
   6 23.85  0.92 4.00 80.0
   7  0.00  0.15 4.95 64.6
   7  0.25  0.85 4.95 64.6
   7  0.50  2.35 4.95 64.6
   7  1.02  5.02 4.95 64.6
   7  2.02  6.58 4.95 64.6
   7  3.48  7.09 4.95 64.6
   7  5.00  6.66 4.95 64.6
   7  6.98  5.25 4.95 64.6
   7  9.00  4.39 4.95 64.6
   7 12.05  3.53 4.95 64.6
   7 24.22  1.15 4.95 64.6
   8  0.00  0.00 4.53 70.5
   8  0.25  3.05 4.53 70.5
   8  0.52  3.05 4.53 70.5
   8  0.98  7.31 4.53 70.5
   8  2.02  7.56 4.53 70.5
   8  3.53  6.59 4.53 70.5
   8  5.05  5.88 4.53 70.5
   8  7.15  4.73 4.53 70.5
   8  9.07  4.57 4.53 70.5
   8 12.10  3.00 4.53 70.5
   8 24.12  1.25 4.53 70.5
   9  0.00  0.00 3.10 86.4
   9  0.30  7.37 3.10 86.4
   9  0.63  9.03 3.10 86.4
   9  1.05  7.14 3.10 86.4
   9  2.02  6.33 3.10 86.4
   9  3.53  5.66 3.10 86.4
   9  5.02  5.67 3.10 86.4
   9  7.17  4.24 3.10 86.4
   9  8.80  4.11 3.10 86.4
   9 11.60  3.16 3.10 86.4
   9 24.43  1.12 3.10 86.4
  10  0.00  0.24 5.50 58.2
  10  0.37  2.89 5.50 58.2
  10  0.77  5.22 5.50 58.2
  10  1.02  6.41 5.50 58.2
  10  2.05  7.83 5.50 58.2
  10  3.55 10.21 5.50 58.2
  10  5.05  9.18 5.50 58.2
  10  7.08  8.02 5.50 58.2
  10  9.38  7.14 5.50 58.2
  10 12.10  5.68 5.50 58.2
  10 23.70  2.42 5.50 58.2
  11  0.00  0.00 4.92 65.0
  11  0.25  4.86 4.92 65.0
  11  0.50  7.24 4.92 65.0
  11  0.98  8.00 4.92 65.0
  11  1.98  6.81 4.92 65.0
  11  3.60  5.87 4.92 65.0
  11  5.02  5.22 4.92 65.0
  11  7.03  4.45 4.92 65.0
  11  9.03  3.62 4.92 65.0
  11 12.12  2.69 4.92 65.0
  11 24.08  0.86 4.92 65.0
  12  0.00  0.00 5.30 60.5
  12  0.25  1.25 5.30 60.5
  12  0.50  3.96 5.30 60.5
  12  1.00  7.82 5.30 60.5
  12  2.00  9.72 5.30 60.5
  12  3.52  9.75 5.30 60.5
  12  5.07  8.57 5.30 60.5
  12  7.07  6.59 5.30 60.5
  12  9.03  6.11 5.30 60.5
  12 12.05  4.57 5.30 60.5
  12 24.15  1.17 5.30 60.5
  run;
proc nlmixed data=theoph;
      parms beta1=-3.22 beta2=0.47 beta3=-2.45 
         s2b1=0.03 cb12=0 s2b2=0.4 s2=0.5;
      cl = exp(beta1 + b1);
      ka = exp(beta2 + b2);
      ke = exp(beta3);
      pred = dose*ke*ka*(exp(-ke*time)-exp(-ka*time))/cl/(ka-ke);
      model conc ~ normal(pred,s2);
      random b1 b2 ~ normal([0,0],[s2b1,cb12,s2b2]) subject=subject;
   run;