Computing and drawing one step probabilities with their confidence intervals
Matrix of variance-covariance of one-step probabilities (drawings)
this page is important in order to visualize confidence intervals and especially correlation between disability and recovery, or more generally, way in and way back.\n\n
Matrix of variance-covariance of pairs of step probabilities
\n",optionfilehtmcov, optionfilehtmcov); - fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (pComputing and drawing one step probabilities with their confidence intervals
Matrix of variance-covariance of one-step probabilities (drawings)
this page is important in order to visualize confidence intervals and especially correlation between disability and recovery, or more generally, way in and way back.\n\n
Matrix of variance-covariance of pairs of step probabilities
\n",optionfilehtmcov, optionfilehtmcov); + fprintf(fichtmcov,"\nEllipsoids of confidence centered on point (p\n"); - fprintf(fichtmcov,"\n
Contour plot corresponding to x'cov-1x = 4 (where x is the column vector (pij,pkl)) are drawn. \ + fprintf(fichtmcov,"\n
Contour plot corresponding to x'cov-1x = 4 (where x is the column vector (pij,pkl)) are drawn. \ It can be understood this way: if pij and pkl where uncorrelated the (2x2) matrix of covariance \ would have been (1/(var pij), 0 , 0, 1/(var pkl)), and the confidence interval would be 2 \ standard deviations wide on each axis.
\ @@ -5248,252 +5251,252 @@ standard deviations wide on each axis. < and made the appropriate rotation to look at the uncorrelated principal directions.
\ To be simple, these graphs help to understand the significativity of each parameter in relation to a second other one.
\n"); - cov[1]=1; - /* tj=cptcoveff; */ - tj = (int) pow(2,cptcoveff); - if (cptcovn<1) {tj=1;ncodemax[1]=1;} - j1=0; - for(j1=1; j1<=tj;j1++){ /* For each valid combination of covariates */ - if (cptcovn>0) { - fprintf(ficresprob, "\n#********** Variable "); - for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); - fprintf(ficresprob, "**********\n#\n"); - fprintf(ficresprobcov, "\n#********** Variable "); - for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); - fprintf(ficresprobcov, "**********\n#\n"); + cov[1]=1; + /* tj=cptcoveff; */ + tj = (int) pow(2,cptcoveff); + if (cptcovn<1) {tj=1;ncodemax[1]=1;} + j1=0; + for(j1=1; j1<=tj;j1++){ /* For each valid combination of covariates */ + if (cptcovn>0) { + fprintf(ficresprob, "\n#********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprob, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); + fprintf(ficresprob, "**********\n#\n"); + fprintf(ficresprobcov, "\n#********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcov, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); + fprintf(ficresprobcov, "**********\n#\n"); - fprintf(ficgp, "\n#********** Variable "); - for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); - fprintf(ficgp, "**********\n#\n"); + fprintf(ficgp, "\n#********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(ficgp, " V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); + fprintf(ficgp, "**********\n#\n"); - fprintf(fichtmcov, "\n
********** Variable "); - for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); - fprintf(fichtmcov, "**********\n
"); + fprintf(fichtmcov, "\n
********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(fichtm, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); + fprintf(fichtmcov, "**********\n
"); - fprintf(ficresprobcor, "\n#********** Variable "); - for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); - fprintf(ficresprobcor, "**********\n#"); - if(invalidvarcomb[j1]){ - fprintf(ficgp,"\n#Combination (%d) ignored because no cases \n",j1); - fprintf(fichtmcov,"\n
Combination (%d) ignored because no cases
\n",j1); - continue; - } - } - gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath)); - trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar); - gp=vector(1,(nlstate)*(nlstate+ndeath)); - gm=vector(1,(nlstate)*(nlstate+ndeath)); - for (age=bage; age<=fage; age ++){ - cov[2]=age; - if(nagesqr==1) - cov[3]= age*age; - for (k=1; k<=cptcovn;k++) { - cov[2+nagesqr+k]=nbcode[Tvar[k]][codtabm(j1,k)]; - /*cov[2+nagesqr+k]=nbcode[Tvar[k]][codtabm(j1,Tvar[k])];*//* j1 1 2 3 4 - * 1 1 1 1 1 - * 2 2 1 1 1 - * 3 1 2 1 1 - */ - /* nbcode[1][1]=0 nbcode[1][2]=1;*/ - } - /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */ - for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=nbcode[Tvar[Tage[k]]][codtabm(ij,k)]*cov[2]; - for (k=1; k<=cptcovprod;k++) - cov[2+nagesqr+Tprod[k]]=nbcode[Tvard[k][1]][codtabm(ij,k)]*nbcode[Tvard[k][2]][codtabm(ij,k)]; + fprintf(ficresprobcor, "\n#********** Variable "); + for (z1=1; z1<=cptcoveff; z1++) fprintf(ficresprobcor, "V%d=%d ",Tvaraff[z1],nbcode[Tvaraff[z1]][codtabm(j1,z1)]); + fprintf(ficresprobcor, "**********\n#"); + if(invalidvarcomb[j1]){ + fprintf(ficgp,"\n#Combination (%d) ignored because no cases \n",j1); + fprintf(fichtmcov,"\nCombination (%d) ignored because no cases
\n",j1); + continue; + } + } + gradg=matrix(1,npar,1,(nlstate)*(nlstate+ndeath)); + trgradg=matrix(1,(nlstate)*(nlstate+ndeath),1,npar); + gp=vector(1,(nlstate)*(nlstate+ndeath)); + gm=vector(1,(nlstate)*(nlstate+ndeath)); + for (age=bage; age<=fage; age ++){ + cov[2]=age; + if(nagesqr==1) + cov[3]= age*age; + for (k=1; k<=cptcovn;k++) { + cov[2+nagesqr+k]=nbcode[Tvar[k]][codtabm(j1,k)]; + /*cov[2+nagesqr+k]=nbcode[Tvar[k]][codtabm(j1,Tvar[k])];*//* j1 1 2 3 4 + * 1 1 1 1 1 + * 2 2 1 1 1 + * 3 1 2 1 1 + */ + /* nbcode[1][1]=0 nbcode[1][2]=1;*/ + } + /* for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=cov[2+Tage[k]]*cov[2]; */ + for (k=1; k<=cptcovage;k++) cov[2+Tage[k]]=nbcode[Tvar[Tage[k]]][codtabm(ij,k)]*cov[2]; + for (k=1; k<=cptcovprod;k++) + cov[2+nagesqr+Tprod[k]]=nbcode[Tvard[k][1]][codtabm(ij,k)]*nbcode[Tvard[k][2]][codtabm(ij,k)]; - for(theta=1; theta <=npar; theta++){ - for(i=1; i<=npar; i++) - xp[i] = x[i] + (i==theta ?delti[theta]:(double)0); + for(theta=1; theta <=npar; theta++){ + for(i=1; i<=npar; i++) + xp[i] = x[i] + (i==theta ?delti[theta]:(double)0); - pmij(pmmij,cov,ncovmodel,xp,nlstate); + pmij(pmmij,cov,ncovmodel,xp,nlstate); - k=0; - for(i=1; i<= (nlstate); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - gp[k]=pmmij[i][j]; - } - } + k=0; + for(i=1; i<= (nlstate); i++){ + for(j=1; j<=(nlstate+ndeath);j++){ + k=k+1; + gp[k]=pmmij[i][j]; + } + } - for(i=1; i<=npar; i++) - xp[i] = x[i] - (i==theta ?delti[theta]:(double)0); + for(i=1; i<=npar; i++) + xp[i] = x[i] - (i==theta ?delti[theta]:(double)0); - pmij(pmmij,cov,ncovmodel,xp,nlstate); - k=0; - for(i=1; i<=(nlstate); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - gm[k]=pmmij[i][j]; - } - } + pmij(pmmij,cov,ncovmodel,xp,nlstate); + k=0; + for(i=1; i<=(nlstate); i++){ + for(j=1; j<=(nlstate+ndeath);j++){ + k=k+1; + gm[k]=pmmij[i][j]; + } + } - for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) - gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta]; - } + for(i=1; i<= (nlstate)*(nlstate+ndeath); i++) + gradg[theta][i]=(gp[i]-gm[i])/(double)2./delti[theta]; + } - for(j=1; j<=(nlstate)*(nlstate+ndeath);j++) - for(theta=1; theta <=npar; theta++) - trgradg[j][theta]=gradg[theta][j]; + for(j=1; j<=(nlstate)*(nlstate+ndeath);j++) + for(theta=1; theta <=npar; theta++) + trgradg[j][theta]=gradg[theta][j]; - matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); - matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg); + matprod2(dnewm,trgradg,1,(nlstate)*(nlstate+ndeath),1,npar,1,npar,matcov); + matprod2(doldm,dnewm,1,(nlstate)*(nlstate+ndeath),1,npar,1,(nlstate)*(nlstate+ndeath),gradg); - pmij(pmmij,cov,ncovmodel,x,nlstate); + pmij(pmmij,cov,ncovmodel,x,nlstate); - k=0; - for(i=1; i<=(nlstate); i++){ - for(j=1; j<=(nlstate+ndeath);j++){ - k=k+1; - mu[k][(int) age]=pmmij[i][j]; - } - } - for(i=1;i<=(nlstate)*(nlstate+ndeath);i++) - for(j=1;j<=(nlstate)*(nlstate+ndeath);j++) - varpij[i][j][(int)age] = doldm[i][j]; + k=0; + for(i=1; i<=(nlstate); i++){ + for(j=1; j<=(nlstate+ndeath);j++){ + k=k+1; + mu[k][(int) age]=pmmij[i][j]; + } + } + for(i=1;i<=(nlstate)*(nlstate+ndeath);i++) + for(j=1;j<=(nlstate)*(nlstate+ndeath);j++) + varpij[i][j][(int)age] = doldm[i][j]; - /*printf("\n%d ",(int)age); - for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){ - printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i])); - fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i])); - }*/ + /*printf("\n%d ",(int)age); + for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){ + printf("%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i])); + fprintf(ficlog,"%e [%e ;%e] ",gm[i],gm[i]-2*sqrt(doldm[i][i]),gm[i]+2*sqrt(doldm[i][i])); + }*/ - fprintf(ficresprob,"\n%d ",(int)age); - fprintf(ficresprobcov,"\n%d ",(int)age); - fprintf(ficresprobcor,"\n%d ",(int)age); + fprintf(ficresprob,"\n%d ",(int)age); + fprintf(ficresprobcov,"\n%d ",(int)age); + fprintf(ficresprobcor,"\n%d ",(int)age); - for (i=1; i<=(nlstate)*(nlstate+ndeath);i++) - fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age])); - for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){ - fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]); - fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]); - } - i=0; - for (k=1; k<=(nlstate);k++){ - for (l=1; l<=(nlstate+ndeath);l++){ - i++; - fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l); - fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l); - for (j=1; j<=i;j++){ - /* printf(" k=%d l=%d i=%d j=%d\n",k,l,i,j);fflush(stdout); */ - fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]); - fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age])); - } - } - }/* end of loop for state */ - } /* end of loop for age */ - free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath)); - free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath)); - free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar); - free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar); - - /* Confidence intervalle of pij */ - /* - fprintf(ficgp,"\nunset parametric;unset label"); - fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\""); - fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65"); - fprintf(fichtm,"\nProbability with confidence intervals expressed in year-1 :pijgr%s.png, ",optionfilefiname,optionfilefiname); - fprintf(fichtm,"\n
![](\"pijgr%s.png\")
",optionfilefiname);
- fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
- fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
- */
-
- /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
- first1=1;first2=2;
- for (k2=1; k2<=(nlstate);k2++){
- for (l2=1; l2<=(nlstate+ndeath);l2++){
- if(l2==k2) continue;
- j=(k2-1)*(nlstate+ndeath)+l2;
- for (k1=1; k1<=(nlstate);k1++){
- for (l1=1; l1<=(nlstate+ndeath);l1++){
- if(l1==k1) continue;
- i=(k1-1)*(nlstate+ndeath)+l1;
- if(i<=j) continue;
- for (age=bage; age<=fage; age ++){
- if ((int)age %5==0){
- v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
- v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
- cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
- mu1=mu[i][(int) age]/stepm*YEARM ;
- mu2=mu[j][(int) age]/stepm*YEARM;
- c12=cv12/sqrt(v1*v2);
- /* Computing eigen value of matrix of covariance */
- lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
- lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
- if ((lc2 <0) || (lc1 <0) ){
- if(first2==1){
- first1=0;
- printf("Strange: j1=%d One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Probably WRONG RESULTS. See log file for details...\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
- }
- fprintf(ficlog,"Strange: j1=%d One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Probably WRONG RESULTS.\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);fflush(ficlog);
- /* lc1=fabs(lc1); */ /* If we want to have them positive */
- /* lc2=fabs(lc2); */
- }
+ for (i=1; i<=(nlstate)*(nlstate+ndeath);i++)
+ fprintf(ficresprob,"%11.3e (%11.3e) ",mu[i][(int) age],sqrt(varpij[i][i][(int)age]));
+ for (i=1; i<=(nlstate)*(nlstate+ndeath);i++){
+ fprintf(ficresprobcov,"%11.3e ",mu[i][(int) age]);
+ fprintf(ficresprobcor,"%11.3e ",mu[i][(int) age]);
+ }
+ i=0;
+ for (k=1; k<=(nlstate);k++){
+ for (l=1; l<=(nlstate+ndeath);l++){
+ i++;
+ fprintf(ficresprobcov,"\n%d %d-%d",(int)age,k,l);
+ fprintf(ficresprobcor,"\n%d %d-%d",(int)age,k,l);
+ for (j=1; j<=i;j++){
+ /* printf(" k=%d l=%d i=%d j=%d\n",k,l,i,j);fflush(stdout); */
+ fprintf(ficresprobcov," %11.3e",varpij[i][j][(int)age]);
+ fprintf(ficresprobcor," %11.3e",varpij[i][j][(int) age]/sqrt(varpij[i][i][(int) age])/sqrt(varpij[j][j][(int)age]));
+ }
+ }
+ }/* end of loop for state */
+ } /* end of loop for age */
+ free_vector(gp,1,(nlstate+ndeath)*(nlstate+ndeath));
+ free_vector(gm,1,(nlstate+ndeath)*(nlstate+ndeath));
+ free_matrix(trgradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
+ free_matrix(gradg,1,(nlstate+ndeath)*(nlstate+ndeath),1,npar);
+
+ /* Confidence intervalle of pij */
+ /*
+ fprintf(ficgp,"\nunset parametric;unset label");
+ fprintf(ficgp,"\nset log y;unset log x; set xlabel \"Age\";set ylabel \"probability (year-1)\"");
+ fprintf(ficgp,"\nset ter png small\nset size 0.65,0.65");
+ fprintf(fichtm,"\nProbability with confidence intervals expressed in year-1 :pijgr%s.png, ",optionfilefiname,optionfilefiname); + fprintf(fichtm,"\n
",optionfilefiname);
+ fprintf(ficgp,"\nset out \"pijgr%s.png\"",optionfilefiname);
+ fprintf(ficgp,"\nplot \"%s\" every :::%d::%d u 1:2 \"\%%lf",k1,k2,xfilevarprob);
+ */
+
+ /* Drawing ellipsoids of confidence of two variables p(k1-l1,k2-l2)*/
+ first1=1;first2=2;
+ for (k2=1; k2<=(nlstate);k2++){
+ for (l2=1; l2<=(nlstate+ndeath);l2++){
+ if(l2==k2) continue;
+ j=(k2-1)*(nlstate+ndeath)+l2;
+ for (k1=1; k1<=(nlstate);k1++){
+ for (l1=1; l1<=(nlstate+ndeath);l1++){
+ if(l1==k1) continue;
+ i=(k1-1)*(nlstate+ndeath)+l1;
+ if(i<=j) continue;
+ for (age=bage; age<=fage; age ++){
+ if ((int)age %5==0){
+ v1=varpij[i][i][(int)age]/stepm*YEARM/stepm*YEARM;
+ v2=varpij[j][j][(int)age]/stepm*YEARM/stepm*YEARM;
+ cv12=varpij[i][j][(int)age]/stepm*YEARM/stepm*YEARM;
+ mu1=mu[i][(int) age]/stepm*YEARM ;
+ mu2=mu[j][(int) age]/stepm*YEARM;
+ c12=cv12/sqrt(v1*v2);
+ /* Computing eigen value of matrix of covariance */
+ lc1=((v1+v2)+sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
+ lc2=((v1+v2)-sqrt((v1+v2)*(v1+v2) - 4*(v1*v2-cv12*cv12)))/2.;
+ if ((lc2 <0) || (lc1 <0) ){
+ if(first2==1){
+ first1=0;
+ printf("Strange: j1=%d One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Probably WRONG RESULTS. See log file for details...\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);
+ }
+ fprintf(ficlog,"Strange: j1=%d One eigen value of 2x2 matrix of covariance is negative, lc1=%11.3e, lc2=%11.3e, v1=%11.3e, v2=%11.3e, cv12=%11.3e.\n It means that the matrix was not well estimated (varpij), for i=%2d, j=%2d, age=%4d .\n See files %s and %s. Probably WRONG RESULTS.\n", j1, lc1, lc2, v1, v2, cv12, i, j, (int)age,fileresprobcov, fileresprobcor);fflush(ficlog);
+ /* lc1=fabs(lc1); */ /* If we want to have them positive */
+ /* lc2=fabs(lc2); */
+ }
- /* Eigen vectors */
- v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12));
- /*v21=sqrt(1.-v11*v11); *//* error */
- v21=(lc1-v1)/cv12*v11;
- v12=-v21;
- v22=v11;
- tnalp=v21/v11;
- if(first1==1){
- first1=0;
- printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
- }
- fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp);
- /*printf(fignu*/
- /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */
- /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */
- if(first==1){
- first=0;
- fprintf(ficgp,"\n# Ellipsoids of confidence\n#\n");
- fprintf(ficgp,"\nset parametric;unset label");
- fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2);
- fprintf(ficgp,"\nset ter svg size 640, 480");
- fprintf(fichtmcov,"\nEllipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year-1\ + /* Eigen vectors */ + v11=(1./sqrt(1+(v1-lc1)*(v1-lc1)/cv12/cv12)); + /*v21=sqrt(1.-v11*v11); *//* error */ + v21=(lc1-v1)/cv12*v11; + v12=-v21; + v22=v11; + tnalp=v21/v11; + if(first1==1){ + first1=0; + printf("%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tang %.3f\nOthers in log...\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp); + } + fprintf(ficlog,"%d %d%d-%d%d mu %.4e %.4e Var %.4e %.4e cor %.3f cov %.4e Eig %.3e %.3e 1stv %.3f %.3f tan %.3f\n",(int) age,k1,l1,k2,l2,mu1,mu2,v1,v2,c12,cv12,lc1,lc2,v11,v21,tnalp); + /*printf(fignu*/ + /* mu1+ v11*lc1*cost + v12*lc2*sin(t) */ + /* mu2+ v21*lc1*cost + v22*lc2*sin(t) */ + if(first==1){ + first=0; + fprintf(ficgp,"\n# Ellipsoids of confidence\n#\n"); + fprintf(ficgp,"\nset parametric;unset label"); + fprintf(ficgp,"\nset log y;set log x; set xlabel \"p%1d%1d (year-1)\";set ylabel \"p%1d%1d (year-1)\"",k1,l1,k2,l2); + fprintf(ficgp,"\nset ter svg size 640, 480"); + fprintf(fichtmcov,"\n
Ellipsoids of confidence cov(p%1d%1d,p%1d%1d) expressed in year-1\ : \ %s_%d%1d%1d-%1d%1d.svg, ",k1,l1,k2,l2,\ - subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2, \ - subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); - fprintf(fichtmcov,"\n
![](\"%s_%d%1d%1d-%1d%1d.svg\")
",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2);
- fprintf(fichtmcov,"\nCorrelation at age %d (%.3f),",(int) age, c12); - fprintf(ficgp,"\nset out \"%s_%d%1d%1d-%1d%1d.svg\"",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); - fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2); - fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2); - fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not", \ - mu1,std,v11,sqrt(lc1),v12,sqrt(lc2), \ - mu2,std,v21,sqrt(lc1),v22,sqrt(lc2)); - }else{ - first=0; - fprintf(fichtmcov," %d (%.3f),",(int) age, c12); - fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2); - fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2); - fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not", \ - mu1,std,v11,sqrt(lc1),v12,sqrt(lc2), \ - mu2,std,v21,sqrt(lc1),v22,sqrt(lc2)); - }/* if first */ - } /* age mod 5 */ - } /* end loop age */ - fprintf(ficgp,"\nset out;\nset out \"%s_%d%1d%1d-%1d%1d.svg\";replot;set out;",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); - first=1; - } /*l12 */ - } /* k12 */ - } /*l1 */ - }/* k1 */ - } /* loop on combination of covariates j1 */ - free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage); - free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage); - free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath)); - free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar); - free_vector(xp,1,npar); - fclose(ficresprob); - fclose(ficresprobcov); - fclose(ficresprobcor); - fflush(ficgp); - fflush(fichtmcov); -} + subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2, \ + subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); + fprintf(fichtmcov,"\n
",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2);
+ fprintf(fichtmcov,"\nCorrelation at age %d (%.3f),",(int) age, c12); + fprintf(ficgp,"\nset out \"%s_%d%1d%1d-%1d%1d.svg\"",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); + fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2); + fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2); + fprintf(ficgp,"\nplot [-pi:pi] %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not", \ + mu1,std,v11,sqrt(lc1),v12,sqrt(lc2), \ + mu2,std,v21,sqrt(lc1),v22,sqrt(lc2)); + }else{ + first=0; + fprintf(fichtmcov," %d (%.3f),",(int) age, c12); + fprintf(ficgp,"\n# Age %d, p%1d%1d - p%1d%1d",(int) age, k1,l1,k2,l2); + fprintf(ficgp,"\nset label \"%d\" at %11.3e,%11.3e center",(int) age, mu1,mu2); + fprintf(ficgp,"\nreplot %11.3e+ %.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)), %11.3e +%.3f*(%11.3e*%11.3e*cos(t)+%11.3e*%11.3e*sin(t)) not", \ + mu1,std,v11,sqrt(lc1),v12,sqrt(lc2), \ + mu2,std,v21,sqrt(lc1),v22,sqrt(lc2)); + }/* if first */ + } /* age mod 5 */ + } /* end loop age */ + fprintf(ficgp,"\nset out;\nset out \"%s_%d%1d%1d-%1d%1d.svg\";replot;set out;",subdirf2(optionfilefiname,"VARPIJGR_"), j1,k1,l1,k2,l2); + first=1; + } /*l12 */ + } /* k12 */ + } /*l1 */ + }/* k1 */ + } /* loop on combination of covariates j1 */ + free_ma3x(varpij,1,nlstate,1,nlstate+ndeath,(int) bage, (int)fage); + free_matrix(mu,1,(nlstate+ndeath)*(nlstate+ndeath),(int) bage, (int)fage); + free_matrix(doldm,1,(nlstate)*(nlstate+ndeath),1,(nlstate)*(nlstate+ndeath)); + free_matrix(dnewm,1,(nlstate)*(nlstate+ndeath),1,npar); + free_vector(xp,1,npar); + fclose(ficresprob); + fclose(ficresprobcov); + fclose(ficresprobcor); + fflush(ficgp); + fflush(fichtmcov); + } /******************* Printing html file ***********/ @@ -5536,81 +5539,81 @@ void printinghtml(char fileresu[], char %s
\n", subdirf2(fileresu,"F_"),subdirf2(fileresu,"F_")); } -fprintf(fichtm," \n
- Graphs
- Graphs
"); + fprintf(fichtm," \n
"); - m=pow(2,cptcoveff); - if (cptcovn < 1) {m=1;ncodemax[1]=1;} + m=pow(2,cptcoveff); + if (cptcovn < 1) {m=1;ncodemax[1]=1;} - jj1=0; - for(k1=1; k1<=m;k1++){ + jj1=0; + for(k1=1; k1<=m;k1++){ - /* for(i1=1; i1<=ncodemax[k1];i1++){ */ - jj1++; - if (cptcovn > 0) { - fprintf(fichtm,"
************ Results for covariates"); - for (cpt=1; cpt<=cptcoveff;cpt++){ - fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]); - printf(" V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]);fflush(stdout); - } - fprintf(fichtm," ************\n
"); - if(invalidvarcomb[k1]){ - fprintf(fichtm,"\n
Combination (%d) ignored because no cases
\n",k1); - printf("\nCombination (%d) ignored because no cases \n",k1); - continue; - } - } - /* aij, bij */ - fprintf(fichtm,"- Logit model (yours is: 1+age+%s), for example: logit(pij)=log(pij/pii)= aij+ bij age + V1 age + etc. as a function of age: %s_%d-1.svg
\ + /* for(i1=1; i1<=ncodemax[k1];i1++){ */ + jj1++; + if (cptcovn > 0) { + fprintf(fichtm,"
************ Results for covariates"); + for (cpt=1; cpt<=cptcoveff;cpt++){ + fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]); + printf(" V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]);fflush(stdout); + } + fprintf(fichtm," ************\n
"); + if(invalidvarcomb[k1]){ + fprintf(fichtm,"\n
Combination (%d) ignored because no cases
\n",k1); + printf("\nCombination (%d) ignored because no cases \n",k1); + continue; + } + } + /* aij, bij */ + fprintf(fichtm,"- Logit model (yours is: 1+age+%s), for example: logit(pij)=log(pij/pii)= aij+ bij age + V1 age + etc. as a function of age: %s_%d-1.svg
\
![](\"%s_%d-1.svg\")
",model,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1);
- /* Pij */
- fprintf(fichtm,"\n- Pij or conditional probabilities to be observed in state j being in state i, %d (stepm) months before: %s_%d-2.svg
\ + /* Pij */ + fprintf(fichtm,"
\n- Pij or conditional probabilities to be observed in state j being in state i, %d (stepm) months before: %s_%d-2.svg
\
![](\"%s_%d-2.svg\")
",stepm,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1);
- /* Quasi-incidences */
- fprintf(fichtm,"\n- Iij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\ + /* Quasi-incidences */ + fprintf(fichtm,"
\n- Iij or Conditional probabilities to be observed in state j being in state i %d (stepm) months\ before but expressed in per year i.e. quasi incidences if stepm is small and probabilities too, \ incidence (rates) are the limit when h tends to zero of the ratio of the probability hPij \ divided by h: hPij/h : %s_%d-3.svg
\
![](\"%s_%d-3.svg\")
",stepm,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1,subdirf2(optionfilefiname,"PE_"),jj1);
- /* Survival functions (period) in state j */
- for(cpt=1; cpt<=nlstate;cpt++){
- fprintf(fichtm,"\n- Survival functions in state %d. Or probability to survive in state %d being in state (1 to %d) at different ages. %s%d_%d.svg
![%s%d_%d.svg](\"%s%d_%d.svg\"){kind=link}
\ + /* Survival functions (period) in state j */ + for(cpt=1; cpt<=nlstate;cpt++){ + fprintf(fichtm,"
\n- Survival functions in state %d. Or probability to survive in state %d being in state (1 to %d) at different ages. %s%d_%d.svg
\
![](\"%s_%d-%d.svg\")
", cpt, cpt, nlstate, subdirf2(optionfilefiname,"LIJ_"),cpt,jj1,subdirf2(optionfilefiname,"LIJ_"),cpt,jj1,subdirf2(optionfilefiname,"LIJ_"),cpt,jj1);
- }
- /* State specific survival functions (period) */
- for(cpt=1; cpt<=nlstate;cpt++){
- fprintf(fichtm,"\n- Survival functions from state %d in each live state and total.\ + } + /* State specific survival functions (period) */ + for(cpt=1; cpt<=nlstate;cpt++){ + fprintf(fichtm,"
\n- Survival functions from state %d in each live state and total.\ Or probability to survive in various states (1 to %d) being in state %d at different ages. \ %s%d_%d.svg
", cpt, nlstate, cpt, subdirf2(optionfilefiname,"LIJT_"),cpt,jj1,subdirf2(optionfilefiname,"LIJT_"),cpt,jj1,subdirf2(optionfilefiname,"LIJT_"),cpt,jj1);
- }
- /* Period (stable) prevalence in each health state */
- for(cpt=1; cpt<=nlstate;cpt++){
- fprintf(fichtm,"\n- Convergence to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s_%d-%d.svg
\ -
", cpt, cpt, nlstate, subdirf2(optionfilefiname,"P_"),cpt,jj1,subdirf2(optionfilefiname,"P_"),cpt,jj1,subdirf2(optionfilefiname,"P_"),cpt,jj1);
- }
- if(backcast==1){
- /* Period (stable) back prevalence in each health state */
+ }
+ /* Period (stable) prevalence in each health state */
for(cpt=1; cpt<=nlstate;cpt++){
- fprintf(fichtm,"\n- Convergence to period (stable) back prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s_%d-%d.svg
\ + fprintf(fichtm,"
\n- Convergence to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s_%d-%d.svg
\ +
", cpt, cpt, nlstate, subdirf2(optionfilefiname,"P_"),cpt,jj1,subdirf2(optionfilefiname,"P_"),cpt,jj1,subdirf2(optionfilefiname,"P_"),cpt,jj1);
+ }
+ if(backcast==1){
+ /* Period (stable) back prevalence in each health state */
+ for(cpt=1; cpt<=nlstate;cpt++){
+ fprintf(fichtm,"\n- Convergence to period (stable) back prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s_%d-%d.svg
\
", cpt, cpt, nlstate, subdirf2(optionfilefiname,"PB_"),cpt,jj1,subdirf2(optionfilefiname,"PB_"),cpt,jj1,subdirf2(optionfilefiname,"PB_"),cpt,jj1);
+ }
}
- }
- if(prevfcast==1){
- /* Projection of prevalence up to period (stable) prevalence in each health state */
- for(cpt=1; cpt<=nlstate;cpt++){
- fprintf(fichtm,"\n- Projection of cross-sectional prevalence (estimated with cases observed from %.1f to %.1f) up to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s%d_%d.svg
\ + if(prevfcast==1){ + /* Projection of prevalence up to period (stable) prevalence in each health state */ + for(cpt=1; cpt<=nlstate;cpt++){ + fprintf(fichtm,"
\n- Projection of cross-sectional prevalence (estimated with cases observed from %.1f to %.1f) up to period (stable) prevalence in state %d. Or probability to be in state %d being in state (1 to %d) at different ages. %s%d_%d.svg
\
", dateprev1, dateprev2, cpt, cpt, nlstate, subdirf2(optionfilefiname,"PROJ_"),cpt,jj1,subdirf2(optionfilefiname,"PROJ_"),cpt,jj1,subdirf2(optionfilefiname,"PROJ_"),cpt,jj1);
- }
- }
+ }
+ }
- for(cpt=1; cpt<=nlstate;cpt++) {
- fprintf(fichtm,"\n- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies in each alive state (1 to %d) (or area under each survival functions): %s_%d%d.svg
\ + for(cpt=1; cpt<=nlstate;cpt++) { + fprintf(fichtm,"\n
- Life expectancy by health state (%d) at initial age and its decomposition into health expectancies in each alive state (1 to %d) (or area under each survival functions): %s_%d%d.svg
\
![](\"%s_%d%d.svg\")
",cpt,nlstate,subdirf2(optionfilefiname,"EXP_"),cpt,jj1,subdirf2(optionfilefiname,"EXP_"),cpt,jj1,subdirf2(optionfilefiname,"EXP_"),cpt,jj1);
- }
- /* } /\* end i1 *\/ */
- }/* End k1 */
- fprintf(fichtm,"Result files (second order: variances)
\n\ - Parameter file with estimated parameters and covariance matrix: %s\ - 95%% confidence intervals and Wald tests of the estimated parameters are in the log file if optimization has been done (mle != 0).
\ @@ -5622,32 +5625,32 @@ variances but at the covariance matrix. covariance matrix of the one-step probabilities. \ See page 'Matrix of variance-covariance of one-step probabilities' below. \n", rfileres,rfileres); - fprintf(fichtm," - Standard deviation of one-step probabilities: %s
\n", - subdirf2(fileresu,"PROB_"),subdirf2(fileresu,"PROB_")); - fprintf(fichtm,"\ + fprintf(fichtm," - Standard deviation of one-step probabilities: %s
\n", + subdirf2(fileresu,"PROB_"),subdirf2(fileresu,"PROB_")); + fprintf(fichtm,"\ - Variance-covariance of one-step probabilities: %s
\n", - subdirf2(fileresu,"PROBCOV_"),subdirf2(fileresu,"PROBCOV_")); + subdirf2(fileresu,"PROBCOV_"),subdirf2(fileresu,"PROBCOV_")); - fprintf(fichtm,"\ + fprintf(fichtm,"\ - Correlation matrix of one-step probabilities: %s
\n", - subdirf2(fileresu,"PROBCOR_"),subdirf2(fileresu,"PROBCOR_")); - fprintf(fichtm,"\ + subdirf2(fileresu,"PROBCOR_"),subdirf2(fileresu,"PROBCOR_")); + fprintf(fichtm,"\ - Variances and covariances of health expectancies by age and initial health status (cov(eij,ekl)(estepm=%2d months): \ %s
\n
\n", estepm,subdirf2(fileresu,"STDE_"),subdirf2(fileresu,"STDE_")); - fprintf(fichtm,"\ + fprintf(fichtm,"\ - Variances and covariances of health expectancies by age. Status (i) based health expectancies (in state j), eij are weighted by the period prevalences in each state i (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): %s
\n", - estepm, subdirf2(fileresu,"V_"),subdirf2(fileresu,"V_")); - fprintf(fichtm,"\ + estepm, subdirf2(fileresu,"V_"),subdirf2(fileresu,"V_")); + fprintf(fichtm,"\ - Total life expectancy and total health expectancies to be spent in each health state e.j with their standard errors (if popbased=1, an additional computation is done using the cross-sectional prevalences, i.e population based) (estepm=%d months): %s
\n", - estepm, subdirf2(fileresu,"T_"),subdirf2(fileresu,"T_")); - fprintf(fichtm,"\ + estepm, subdirf2(fileresu,"T_"),subdirf2(fileresu,"T_")); + fprintf(fichtm,"\ - Standard deviation of period (stable) prevalences: %s
\n",\ - subdirf2(fileresu,"VPL_"),subdirf2(fileresu,"VPL_")); + subdirf2(fileresu,"VPL_"),subdirf2(fileresu,"VPL_")); /* if(popforecast==1) fprintf(fichtm,"\n */ /* - Prevalences forecasting: f%s
\n */ @@ -5655,26 +5658,26 @@ See page 'Matrix of variance-covariance /*
",fileres,fileres,fileres,fileres); */ /* else */ /* fprintf(fichtm,"\n No population forecast: popforecast = %d (instead of 1) or stepm = %d (instead of 1) or model=%s (instead of .)
\n",popforecast, stepm, model); */ - fflush(fichtm); - fprintf(fichtm,"
- Graphs
- Graphs
"); + fflush(fichtm); + fprintf(fichtm,"
"); - m=pow(2,cptcoveff); - if (cptcovn < 1) {m=1;ncodemax[1]=1;} + m=pow(2,cptcoveff); + if (cptcovn < 1) {m=1;ncodemax[1]=1;} - jj1=0; - for(k1=1; k1<=m;k1++){ - /* for(i1=1; i1<=ncodemax[k1];i1++){ */ - jj1++; + jj1=0; + for(k1=1; k1<=m;k1++){ + /* for(i1=1; i1<=ncodemax[k1];i1++){ */ + jj1++; if (cptcovn > 0) { fprintf(fichtm,"
************ Results for covariates"); for (cpt=1; cpt<=cptcoveff;cpt++) - fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]); + fprintf(fichtm," V%d=%d ",Tvaraff[cpt],nbcode[Tvaraff[cpt]][codtabm(jj1,cpt)]); fprintf(fichtm," ************\n
"); - if(invalidvarcomb[k1]){ - fprintf(fichtm,"\n
Combination (%d) ignored because no cases
\n",k1); - continue; - } + if(invalidvarcomb[k1]){ + fprintf(fichtm,"\nCombination (%d) ignored because no cases
\n",k1); + continue; + } } for(cpt=1; cpt<=nlstate;cpt++) { fprintf(fichtm,"\n- Observed (cross-sectional) and period (incidence based) \ @@ -5687,10 +5690,10 @@ true period expectancies (those weighted drawn in addition to the population based expectancies computed using\ observed and cahotic prevalences: %s_%d.svg\n
\
![](\"%s_%d.svg\")
",subdirf2(optionfilefiname,"E_"),jj1,subdirf2(optionfilefiname,"E_"),jj1,subdirf2(optionfilefiname,"E_"),jj1);
- /* } /\* end i1 *\/ */
- }/* End k1 */
- fprintf(fichtm,"