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CODE FINAL
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CODE FINAL
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proc iml;
sigma=i(50); *identité;
null=j(50,1,0);
mvn=randnormal(50,null,sigma); **pour faire tordre le modèle on change ça + changer la sk;
/* DGP 1: hyptohèses de base vérifiées */
eps=normal(j(nrow(mvn),1,0))*0.1; **0 = seed;
Y=0.7*mvn[,1]+0.6*mvn[,2]+0.5*mvn[,3]+0.4*mvn[,4]+0.3*mvn[,5]+eps;
total=y||mvn;
nom='y'||('X1':'X50');
create total from total[colname=nom];
append from total;
close total;
submit;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=forward(select=AICC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=forward(select=BIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=forward(select=SBC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=forward(select=PRESS) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=backward(select=AICC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=backward(select=AIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=backward(select=BIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=backward(select=SBC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=backward(select=PRESS) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lasso(select=AICC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lasso(select=AIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lasso(select=BIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lasso(select=SBC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lasso(select=PRESS) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lars(select=AICC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lars(select=AIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lars(select=BIC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lars(select=SBC) ;
run;
proc glmselect data=total plots=all;
model y=x1-x50 / selection=lars(select=PRESS) ;
run;
endsubmit;
**********************************************************************************************************;
proc iml;
sigma=i(50); *identité;
null=j(50,1,0);
mvn=randnormal(50,null,sigma); **pour faire tordre le modèle on change ça + changer la sk;
/* DGP 2 : on ajoute de l'autocorrélation entre les variables explicatives */
T = toeplitz({1 0.75 0.5 0.45 0.2});
*print T;
start ImanConoverTransform(X, C);
N = nrow(X);
S = J(N, ncol(X));
/* T1: Create normal scores of each column */
do i = 1 to ncol(X);
ranks = ranktie(X[,i], "mean"); /* tied ranks */
S[,i] = quantile("Normal", ranks/(N+1)); /* van der Waerden scores */
end;
/* T2: apply two linear transformations to the scores */
CS = corr(S); /* correlation of scores */
Q = root(CS); /* Cholesky root of correlation of scores */
P = root(C); /* Cholesky root of target correlation */
T = solve(Q,P); /* same as T = inv(Q) * P; */
Y = S*T; /* transform scores: Y has rank corr close to target C */
/* T3: Permute or reorder data in the columns of X to have the same ranks as Y */
W = X;
do i = 1 to ncol(Y);
rank = rank(Y[,i]); /* use ranks as subscripts, so no tied ranks */
tmp = W[,i]; call sort(tmp); /* sort column by ranks */
W[,i] = tmp[rank]; /* reorder the column of X by the ranks of M */
end;
return( W );
finish;
store module=(ImanConoverTransform);
W = ImanConoverTransform(mvn[,1:5], T);
mvn2 = W||mvn[,6:50];
eps2=normal(j(nrow(mvn2),1,0))*0.1;
Y=0.7*mvn2[,1]+0.6*mvn2[,2]+0.5*mvn2[,3]+0.4*mvn2[,4]+0.3*mvn2[,5]+eps2;
total2=y||mvn2;
nom='y'||('X1':'X50');
create total2 from total2[colname=nom];
append from total2;
close total2;
submit;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=forward(select=AICC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=forward(select=BIC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=forward(select=SBC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=forward(select=PRESS) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=backward(select=AICC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=backward(select=BIC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=backward(select=SBC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=backward(select=PRESS) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lasso(select=AICC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lasso(select=BIC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lasso(select=SBC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lasso(select=PRESS) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lars(select=AICC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lars(select=BIC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lars(select=SBC) ;
run;
proc glmselect data=total2 plots=all;
model y=x1-x50 / selection=lars(select=PRESS) ;
run;
endsubmit;
**********************************************************************************************************;
proc iml;
sigma=i(50);
null=j(50,1,0);
mvn=randnormal(50,null,sigma);
/* DGP 3: corrélation + valeurs extrêmes */
mu= {-6, 3, 8, -4, 5};
sigma={0.5, 0.6, 2.5, 1.2, 1.9};
do t=1 to 50;
call randgen(u, "Uniform", 1, 6);
i=floor(u);
x1=x1//normal(0)*sigma[i]+mu[i];
x2=x2//normal(0)*sigma[i]+mu[i];
x3=x3//normal(0)*sigma[i]+mu[i];
x4=x4//normal(0)*sigma[i]+mu[i];
x5=x5//normal(0)*sigma[i]+mu[i];
x = x1||x2||x3||x4||x5;
end;
mvn2 = x||mvn[,6:50];
T = toeplitz({1 0.75 0.5 0.45 0.2});
start ImanConoverTransform(X, C);
N = nrow(X);
S = J(N, ncol(X));
/* T1: Create normal scores of each column */
do i = 1 to ncol(X);
ranks = ranktie(X[,i], "mean"); /* tied ranks */
S[,i] = quantile("Normal", ranks/(N+1)); /* van der Waerden scores */
end;
/* T2: apply two linear transformations to the scores */
CS = corr(S); /* correlation of scores */
Q = root(CS); /* Cholesky root of correlation of scores */
P = root(C); /* Cholesky root of target correlation */
T = solve(Q,P); /* same as T = inv(Q) * P; */
Y = S*T; /* transform scores: Y has rank corr close to target C */
/* T3: Permute or reorder data in the columns of X to have the same ranks as Y */
W = X;
do i = 1 to ncol(Y);
rank = rank(Y[,i]); /* use ranks as subscripts, so no tied ranks */
tmp = W[,i]; call sort(tmp); /* sort column by ranks */
W[,i] = tmp[rank]; /* reorder the column of X by the ranks of M */
end;
return( W );
finish;
store module=(ImanConoverTransform);
W = ImanConoverTransform(mvn2[,1:5], T);
mvn3 = W||mvn2[,6:50];
eps3=normal(j(nrow(mvn3),1,0))*0.1;
Y=0.7*mvn3[,1]+0.6*mvn3[,2]+0.5*mvn3[,3]+0.4*mvn3[,4]+0.3*mvn3[,5]+eps3;
total3=y||mvn3;
nom='y'||('X1':'X50');
create total3 from total3[colname=nom];
append from total3;
close total3;
submit;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=forward(select=AICC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=forward(select=BIC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=forward(select=SBC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=forward(select=PRESS) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=backward(select=AICC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=backward(select=BIC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=backward(select=SBC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=backward(select=PRESS) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lasso(select=AICC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lasso(select=BIC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lasso(select=SBC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lasso(select=PRESS) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lars(select=AICC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lars(select=BIC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lars(select=SBC) ;
run;
proc glmselect data=total3 plots=all;
model y=x1-x50 / selection=lars(select=PRESS) ;
run;
endsubmit;
quit;