From: N. Brouard Date: Sun, 12 May 2024 20:29:32 +0000 (+0000) Subject: Summary: Version 0.99s5 X-Git-Tag: imach-099s7~22 X-Git-Url: https://henry.ined.fr/git/?a=commitdiff_plain;h=43a21325101594e1c9f61e9a143d5e3965af3cf3;p=.git Summary: Version 0.99s5 * src/imach.c Version 0.99s5 In fact, the covariance of total life expectancy e.. with a partial life expectancy e.j is high, therefore the complete matrix of variance covariance has to be included in the formula of the standard error of the proportion of total life expectancy spent in a specific state: var(X/Y)=mu_x^2/mu_y^2*(sigma_x^2/mu_x^2 -2 sigma_xy/mu_x/mu_y+sigma^2/mu_y^2). Also an error with mle=-3 made the program core dump. It is fixed in this version. --- diff --git a/src/imach.c b/src/imach.c index c4a8439..3c02ae3 100644 --- a/src/imach.c +++ b/src/imach.c @@ -1,6 +1,9 @@ /* $Id$ $State$ $Log$ + Revision 1.360 2024/04/30 10:59:22 brouard + Summary: Version 0.99s4 and estimation of std of e.j/e.. + Revision 1.359 2024/04/24 21:21:17 brouard Summary: First IMaCh version using Brent Praxis software based on Buckhardt and Gegenfürtner C codes @@ -4411,14 +4414,14 @@ void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret #endif #ifdef POWELLORIGINAL if (t < 0.0) { /* Then we use it for new direction */ -#else +#else /* Not POWELLOriginal but Brouard's */ if (directest*t < 0.0) { /* Contradiction between both tests */ printf("directest= %.12lf (if <0 we include P0 Pn as new direction), t= %.12lf, f1= %.12lf,f2= %.12lf,f3= %.12lf, del= %.12lf\n",directest, t, fp,(*fret),fptt,del); printf("f1-2f2+f3= %.12lf, f1-f2-del= %.12lf, f1-f3= %.12lf\n",fp-2.0*(*fret)+fptt, fp -(*fret) -del, fp-fptt); fprintf(ficlog,"directest= %.12lf (if directest<0 or t<0 we include P0 Pn as new direction), t= %.12lf, f1= %.12lf,f2= %.12lf,f3= %.12lf, del= %.12lf\n",directest, t, fp,(*fret),fptt, del); fprintf(ficlog,"f1-2f2+f3= %.12lf, f1-f2-del= %.12lf, f1-f3= %.12lf\n",fp-2.0*(*fret)+fptt, fp -(*fret) -del, fp-fptt); } - if (directest < 0.0) { /* Then we use it for new direction */ + if (directest < 0.0) { /* Then we use (P0, Pn) for new direction Xi_n or Xi_iBig */ #endif #ifdef DEBUGLINMIN printf("Before linmin in direction P%d-P0\n",n); @@ -4452,6 +4455,21 @@ void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret xi[j][ibig]=xi[j][n]; /* Replace direction with biggest decrease by last direction n */ xi[j][n]=xit[j]; /* and this nth direction by the by the average p_0 p_n */ } + +/* #else */ +/* for (i=1;i<=n-1;i++) { */ +/* for (j=1;j<=n;j++) { */ +/* xi[j][i]=xi[j][i+1]; /\* Standard method of conjugate directions, not Powell who changes the nth direction by p0 pn . *\/ */ +/* } */ +/* } */ +/* for (j=1;j<=n;j++) { */ +/* xi[j][n]=xit[j]; /\* and this nth direction by the by the average p_0 p_n *\/ */ +/* } */ +/* /\* for (j=1;j<=n-1;j++) { *\/ */ +/* /\* xi[j][1]=xi[j][j+1]; /\\* Standard method of conjugate directions *\\/ *\/ */ +/* /\* xi[j][n]=xit[j]; /\\* and this nth direction by the by the average p_0 p_n *\\/ *\/ */ +/* /\* } *\/ */ +/* #endif */ #ifdef LINMINORIGINAL #else for (j=1, flatd=0;j<=n;j++) { @@ -4476,8 +4494,8 @@ void powell(double p[], double **xi, int n, double ftol, int *iter, double *fret free_vector(pt,1,n); return; #endif - } -#endif + } /* endif(flatd >0) */ +#endif /* LINMINORIGINAL */ printf("Gaining to use new average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig); fprintf(ficlog,"Gaining to use new average direction of P0 P%d instead of biggest increase direction %d :\n",n,ibig); @@ -8553,7 +8571,9 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc /************ Variance ******************/ void varevsij(char optionfilefiname[], double ***vareij, double **matcov, double x[], double delti[], int nlstate, int stepm, double bage, double fage, double **oldm, double **savm, double **prlim, double ftolpl, int *ncvyearp, int ij, int estepm, int cptcov, int cptcod, int popbased, int mobilav, char strstart[], int nres) { - /** Variance of health expectancies + /** Computes the matrix of variance covariance of health expectancies e.j= sum_i w_i e_ij where w_i depends of popbased, + * either cross-sectional or implied. + * return vareij[i][j][(int)age]=cov(e.i,e.j)=sum_h sum_k trgrad(h_p.i) V(theta) grad(k_p.k) Equation 20 * double **prevalim(double **prlim, int nlstate, double *xp, double age, double **oldm, double ** savm,double ftolpl); * double **newm; * int movingaverage(double ***probs, double bage,double fage, double ***mobaverage, int mobilav) @@ -8570,7 +8590,7 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc double ***gradg, ***trgradg; /**< for var eij */ double **gradgp, **trgradgp; /**< for var p point j */ double *gpp, *gmp; /**< for var p point j */ - double **varppt; /**< for var p point j nlstate to nlstate+ndeath */ + double **varppt; /**< for var e.. nlstate+1 to nlstate+ndeath */ double ***p3mat; double age,agelim, hf; /* double ***mobaverage; */ @@ -8638,7 +8658,7 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc fprintf(fichtm,"\n

  • Computing probabilities of dying over estepm months as a weighted average (i.e global mortality independent of initial healh state)

    • \n"); fprintf(fichtm,"\n
    %s
    \n",digitp); - varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath); + varppt = matrix(nlstate+1,nlstate+ndeath,nlstate+1,nlstate+ndeath); /* In fact, currently a double */ pstamp(ficresvij); fprintf(ficresvij,"# Variance and covariance of health expectancies e.j \n# (weighted average of eij where weights are "); if(popbased==1) @@ -8707,7 +8727,7 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc prlim[i][i]=mobaverage[(int)age][i][ij]; } } - /**< Computes the shifted transition matrix \f$ {}{h}_p^{ij}x\f$ at horizon h. + /**< Computes the shifted plus (gp) transition matrix \f$ {}{h}_p^{ij}x\f$ at horizon h. */ hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij,nres); /* Returns p3mat[i][j][h] for h=0 to nhstepm */ /**< And for each alive state j, sums over i \f$ w^i_x {}{h}_p^{ij}x\f$, which are the probability @@ -8716,14 +8736,14 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc for(j=1; j<= nlstate; j++){ for(h=0; h<=nhstepm; h++){ for(i=1, gp[h][j]=0.;i<=nlstate;i++) - gp[h][j] += prlim[i][i]*p3mat[i][j][h]; + gp[h][j] += prlim[i][i]*p3mat[i][j][h]; /* gp[h][j]= w_i h_pij */ } } /* Next for computing shifted+ probability of death (h=1 means computed over hstepm matrices product = hstepm*stepm months) as a weighted average of prlim(i) * p(i,j) p.3=w1*p13 + w2*p23 . */ - for(j=nlstate+1;j<=nlstate+ndeath;j++){ + for(j=nlstate+1;j<=nlstate+ndeath;j++){ /* Currently only once for theta plus p.3(age) Sum_i wi pi3*/ for(i=1,gpp[j]=0.; i<= nlstate; i++) gpp[j] += prlim[i][i]*p3mat[i][j][1]; } @@ -8745,9 +8765,9 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc } } - hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij,nres); + hpxij(p3mat,nhstepm,age,hstepm,xp,nlstate,stepm,oldm,savm, ij,nres); /* Still minus */ - for(j=1; j<= nlstate; j++){ /* Sum of wi * eij = e.j */ + for(j=1; j<= nlstate; j++){ /* gm[h][j]= Sum_i of wi * pij = h_p.j */ for(h=0; h<=nhstepm; h++){ for(i=1, gm[h][j]=0.;i<=nlstate;i++) gm[h][j] += prlim[i][i]*p3mat[i][j][h]; @@ -8755,37 +8775,39 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc } /* This for computing probability of death (h=1 means computed over hstepm matrices product = hstepm*stepm months) - as a weighted average of prlim. + as a weighted average of prlim. j is death. gmp[3]=sum_i w_i*p_i3=p.3 minus theta */ - for(j=nlstate+1;j<=nlstate+ndeath;j++){ + for(j=nlstate+1;j<=nlstate+ndeath;j++){ /* Currently only once theta_minus p.3=Sum_i wi pi3*/ for(i=1,gmp[j]=0.; i<= nlstate; i++) gmp[j] += prlim[i][i]*p3mat[i][j][1]; } /* end shifting computations */ - /**< Computing gradient matrix at horizon h + /**< Computing gradient of p.j matrix at horizon h and still for one parameter of vector theta + * equation 31 and 32 */ - for(j=1; j<= nlstate; j++) /* vareij */ + for(j=1; j<= nlstate; j++) /* computes grad p.j(x, over each h) where p.j is Sum_i w_i*pij(x over h) + * equation 24 */ for(h=0; h<=nhstepm; h++){ gradg[h][theta][j]= (gp[h][j]-gm[h][j])/2./delti[theta]; } - /**< Gradient of overall mortality p.3 (or p.j) + /**< Gradient of overall mortality p.3 (or p.death) */ - for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* var mu mortality from j */ + for(j=nlstate+1; j<= nlstate+ndeath; j++){ /* computes grad of p.3 from wi+pi3 grad p.3 (theta) */ gradgp[theta][j]= (gpp[j]-gmp[j])/2./delti[theta]; } } /* End theta */ - /* We got the gradient matrix for each theta and state j */ - trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); /* veij */ + /* We got the gradient matrix for each theta and each state j of gradg(h]theta][j)=grad(_hp.j(theta) */ + trgradg =ma3x(0,nhstepm,1,nlstate,1,npar); - for(h=0; h<=nhstepm; h++) /* veij */ + for(h=0; h<=nhstepm; h++) /* veij */ /* computes the transposed of grad (_hp.j(theta)*/ for(j=1; j<=nlstate;j++) for(theta=1; theta <=npar; theta++) trgradg[h][j][theta]=gradg[h][theta][j]; - for(j=nlstate+1; j<=nlstate+ndeath;j++) /* mu */ + for(j=nlstate+1; j<=nlstate+ndeath;j++) /* computes transposed of grad p.3 (theta)*/ for(theta=1; theta <=npar; theta++) trgradgp[j][theta]=gradgp[theta][j]; /**< as well as its transposed matrix @@ -8797,8 +8819,11 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc vareij[i][j][(int)age] =0.; /* Computing trgradg by matcov by gradg at age and summing over h - * and k (nhstepm) formula 15 of article - * Lievre-Brouard-Heathcote + * and k (nhstepm) formula 32 of article + * Lievre-Brouard-Heathcote so that for each j, computes the cov(e.j,e.k) (formula 31). + * for given h and k computes trgradg[h](i,j) matcov (theta) gradg(k)(i,j) into vareij[i][j] which is + cov(e.i,e.j) and sums on h and k + * including the covariances. */ for(h=0;h<=nhstepm;h++){ @@ -8807,20 +8832,21 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc matprod2(doldm,dnewm,1,nlstate,1,npar,1,nlstate,gradg[k]); for(i=1;i<=nlstate;i++) for(j=1;j<=nlstate;j++) - vareij[i][j][(int)age] += doldm[i][j]*hf*hf; + vareij[i][j][(int)age] += doldm[i][j]*hf*hf; /* This is vareij=sum_h sum_k trgrad(h_pij) V(theta) grad(k_pij) + including the covariances of e.j */ } } - /* pptj is p.3 or p.j = trgradgp by cov by gradgp, variance of - * p.j overall mortality formula 19 but computed directly because + /* Mortality: pptj is p.3 or p.death = trgradgp by cov by gradgp, variance of + * p.3=1-p..=1-sum i p.i overall mortality computed directly because * we compute the grad (wix pijx) instead of grad (pijx),even if - * wix is independent of theta. + * wix is independent of theta. */ matprod2(dnewmp,trgradgp,nlstate+1,nlstate+ndeath,1,npar,1,npar,matcov); matprod2(doldmp,dnewmp,nlstate+1,nlstate+ndeath,1,npar,nlstate+1,nlstate+ndeath,gradgp); for(j=nlstate+1;j<=nlstate+ndeath;j++) for(i=nlstate+1;i<=nlstate+ndeath;i++) - varppt[j][i]=doldmp[j][i]; + varppt[j][i]=doldmp[j][i]; /* This is the variance of p.3 */ /* end ppptj */ /* x centered again */ @@ -8843,15 +8869,15 @@ void concatwav(int wav[], int **dh, int **bh, int **mw, int **s, double *agedc hpxij(p3mat,nhstepm,age,hstepm,x,nlstate,stepm,oldm,savm, ij, nres); for(j=nlstate+1;j<=nlstate+ndeath;j++){ for(i=1,gmp[j]=0.;i<= nlstate; i++) - gmp[j] += prlim[i][i]*p3mat[i][j][1]; + gmp[j] += prlim[i][i]*p3mat[i][j][1]; /* gmp[j] is p.3 */ } /* end probability of death */ fprintf(ficresprobmorprev,"%3d %d ",(int) age, ij); for(j=nlstate+1; j<=(nlstate+ndeath);j++){ - fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j])); + fprintf(ficresprobmorprev," %11.3e %11.3e",gmp[j], sqrt(varppt[j][j]));/* p.3 (STD p.3) */ for(i=1; i<=nlstate;i++){ - fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]); + fprintf(ficresprobmorprev," %11.3e %11.3e ",prlim[i][i],p3mat[i][j][1]); /* wi, pi3 */ } } fprintf(ficresprobmorprev,"\n"); @@ -14602,6 +14628,7 @@ int main(int argc, char *argv[]) double ageminpar=AGEOVERFLOW,agemin=AGEOVERFLOW, agemaxpar=-AGEOVERFLOW, agemax=-AGEOVERFLOW; double ageminout=-AGEOVERFLOW,agemaxout=AGEOVERFLOW; /* Smaller Age range redefined after movingaverage */ + double stdpercent; /* for computing the std error of percent e.i: e.i/e.. */ double fret; double dum=0.; /* Dummy variable */ /* double*** p3mat;*/ @@ -15798,9 +15825,19 @@ Interval (in months) between two waves: Min=%d Max=%d Mean=%.2lf
    \n",\ gsl_multimin_fminimizer_free (sfm); /* p *(sfm.x.data) et p *(sfm.x.data+1) */ #endif #ifdef POWELL +#ifdef LINMINORIGINAL +#else /* LINMINORIGINAL */ + + flatdir=ivector(1,npar); + for (j=1;j<=npar;j++) flatdir[j]=0; +#endif /*LINMINORIGINAL */ powell(p,ximort,NDIM,ftol,&iter,&fret,gompertz); #endif fclose(ficrespow); +#ifdef LINMINORIGINAL +#else + free_ivector(flatdir,1,npar); +#endif /* LINMINORIGINAL*/ hesscov(matcov, hess, p, NDIM, delti, 1e-4, gompertz); @@ -16775,6 +16812,8 @@ Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpa cptcod= 0; /* To be deleted */ printf("varevsij vpopbased=%d popbased=%d \n",vpopbased,popbased); fprintf(ficlog, "varevsij vpopbased=%d popbased=%d \n",vpopbased,popbased); + /* Call to varevsij to get cov(e.i, e.j)= vareij[i][j][(int)age]=sum_h sum_k trgrad(h_p.i) V(theta) grad(k_p.k) Equation 20 */ + /* Depending of popbased which changes the prevalences, either cross-sectional or period */ varevsij(optionfilefiname, vareij, matcov, p, delti, nlstate, stepm, (int) bage, (int) fage, oldm, savm, prlim, ftolpl, &ncvyear, k, estepm, cptcov,cptcod,vpopbased,mobilav, strstart, nres); /* cptcod not initialized Intel */ fprintf(ficrest,"# Total life expectancy with std error and decomposition into time to be expected in each state\n\ # (these are weighted average of eij where weights are "); @@ -16811,26 +16850,35 @@ Please run with mle=-1 to get a correct covariance matrix.\n",ageminpar,agemaxpa /*ZZZ printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]);*/ /* printf("%lf %lf ", prlim[i][i] ,eij[i][j][(int)age]); */ } - epj[nlstate+1] +=epj[j]; + epj[nlstate+1] +=epj[j]; /* epp=sum_j epj = sum_j sum_i w_i e_ij */ } /* printf(" age %4.0f \n",age); */ - for(i=1, vepp=0.;i <=nlstate;i++) + for(i=1, vepp=0.;i <=nlstate;i++) /* Variance of total life expectancy e.. */ for(j=1;j <=nlstate;j++) - vepp += vareij[i][j][(int)age]; + vepp += vareij[i][j][(int)age]; /* sum_i sum_j cov(e.i, e.j) = var(e..) */ fprintf(ficrest," %7.3f (%7.3f)", epj[nlstate+1],sqrt(vepp)); - /* vareij[j][i] is the variance of epj */ + /* vareij[i][j] is the covariance cov(e.i, e.j) and vareij[j][j] is the variance of e.j */ for(j=1;j <=nlstate;j++){ fprintf(ficrest," %7.3f (%7.3f)", epj[j],sqrt(vareij[j][j][(int)age])); } /* And proportion of time spent in state j */ /* $$ E[r(X,Y)-E(r(X,Y))]^2=[\frac{1}{\mu_y} -\frac{\mu_x}{{\mu_y}^2}]' Var(X,Y)[\frac{1}{\mu_y} -\frac{\mu_x}{{\mu_y}^2}]$$ */ - /* \sigma^2_x/\mu_y^2 +\sigma^2_y \mu^2x/\mu_y^4 */ - /*\mu_x = epj[j], \sigma^2_x = vareij[j][j][(int)age] and \mu_y=epj[nlstate+1], \sigma^2_y=vepp */ - /* vareij[j][j][(int)age]/epj[nlstate+1]^2 + vepp/epj[nlstata+1]^4 */ + /* \frac{\mu_x^2}{\mu_y^2} ( \frac{\sigma^2_x}{\mu_x^2}-2\frac{\sigma_{xy}}{\mu_x\mu_y} +\frac{\sigma^2_y}{\mu_y^2}) */ + /* \frac{e_{.i}^2}{e_{..}^2} ( \frac{\Var e_{.i}}{e_{.i}^2}-2\frac{\Var e_{.i} + \sum_{j\ne i} \Cov e_{.j},e_{.i}}{e_{.i}e_{..}} +\frac{\Var e_{..}}{e_{..}^2})*/ + /*\mu_x = epj[j], \sigma^2_x = vareij[j][j][(int)age] and \mu_y=epj[nlstate+1], \sigma^2_y=vepp \sigmaxy= */ + /* vareij[j][j][(int)age]/epj[nlstate+1]^2 + vepp/epj[nlstate+1]^4 */ for(j=1;j <=nlstate;j++){ /* fprintf(ficrest," %7.3f (%7.3f)", epj[j]/epj[nlstate+1], sqrt( vareij[j][j][(int)age]/epj[j]/epj[j] + vepp/epj[j]/epj[j]/epj[j]/epj[j] )); */ - fprintf(ficrest," %7.3f (%7.3f)", epj[j]/epj[nlstate+1], sqrt( vareij[j][j][(int)age]/epj[nlstate+1]/epj[nlstate+1] + vepp/epj[nlstate+1]/epj[nlstate+1]/epj[nlstate+1]/epj[nlstate+1] )); + /* fprintf(ficrest," %7.3f (%7.3f)", epj[j]/epj[nlstate+1], sqrt( vareij[j][j][(int)age]/epj[j]/epj[j] + vepp/epj[j]/epj[j]/epj[j]/epj[j] )); */ + + for(i=1,stdpercent=0.;i<=nlstate;i++){ /* Computing cov(e..,e.j)=cov(sum_i e.i,e.j)=sum_i cov(e.i, e.j) */ + stdpercent += vareij[i][j][(int)age]; + } + stdpercent= epj[j]*epj[j]/epj[nlstate+1]/epj[nlstate+1]* (vareij[j][j][(int)age]/epj[j]/epj[j]-2.*stdpercent/epj[j]/epj[nlstate+1]+ vepp/epj[nlstate+1]/epj[nlstate+1]); + /* stdpercent= epj[j]*epj[j]/epj[nlstate+1]/epj[nlstate+1]*(vareij[j][j][(int)age]/epj[j]/epj[j] + vepp/epj[nlstate+1]/epj[nlstate+1]); */ /* Without covariance */ + /* fprintf(ficrest," %7.3f (%7.3f)", epj[j]/epj[nlstate+1], sqrt( vareij[j][j][(int)age]/epj[nlstate+1]/epj[nlstate+1] + epj[j]*epj[j]*vepp/epj[nlstate+1]/epj[nlstate+1]/epj[nlstate+1]/epj[nlstate+1] )); */ + fprintf(ficrest," %7.3f (%7.3f)", epj[j]/epj[nlstate+1], sqrt(stdpercent)); } fprintf(ficrest,"\n"); }