double gennch(lua_RNG *o,double df,double xnonc)
/*
**********************************************************************
Generate random value of Noncentral CHIsquare variable
Function
Generates random deviate from the distribution of a noncentral
chisquare with DF degrees of freedom and noncentrality parameter
xnonc.
Arguments
df --> Degrees of freedom of the chisquare
(Must be > 1.0)
xnonc --> Noncentrality parameter of the chisquare
(Must be >= 0.0)
Method
Uses fact that noncentral chisquare is the sum of a chisquare
deviate with DF-1 degrees of freedom plus the square of a normal
deviate with mean XNONC and standard deviation 1.
**********************************************************************
*/
{
static double gennch;
if(!(df <= 1.0 || xnonc < 0.0)) goto S10;
fputs("DF <= 1 or XNONC < 0 in GENNCH - ABORT",stderr);
fprintf(stderr,"Value of DF: %16.6E Value of XNONC%16.6E\n",df,xnonc);
exit(1);
S10:
gennch = genchi(o,df-1.0)+pow(gennor(o,sqrt(xnonc),1.0),2.0);
return gennch;
}
static int rchisq_rng (lua_State *L) {
nl_RNG *r = getrng(L);
lua_Number df = luaL_checknumber(L, 1);
lua_Number xnonc = luaL_optnumber(L, 2, 0);
checknp(L, df);
checkneg(L, xnonc);
setdeviate(number,
(xnonc == 0) ? genchi(r, df) : gennch(r, df, xnonc), 3);
return 1;
}
double genf(lua_RNG *o,double dfn,double dfd)
/*
**********************************************************************
GENerate random deviate from the F distribution
Function
Generates a random deviate from the F (variance ratio)
distribution with DFN degrees of freedom in the numerator
and DFD degrees of freedom in the denominator.
Arguments
dfn --> Numerator degrees of freedom
(Must be positive)
dfd --> Denominator degrees of freedom
(Must be positive)
Method
Directly generates ratio of chisquare variates
**********************************************************************
*/
{
static double genf,xden,xnum;
if(!(dfn <= 0.0 || dfd <= 0.0)) goto S10;
fputs("Degrees of freedom nonpositive in GENF - abort!",stderr);
fprintf(stderr,"DFN value: %16.6EDFD value: %16.6E\n",dfn,dfd);
exit(1);
S10:
xnum = genchi(o,dfn)/dfn;
/*
GENF = ( GENCHI( DFN ) / DFN ) / ( GENCHI( DFD ) / DFD )
*/
xden = genchi(o,dfd)/dfd;
if(!(xden <= 9.999999999998E-39*xnum)) goto S20;
fputs(" GENF - generated numbers would cause overflow",stderr);
fprintf(stderr," Numerator %16.6E Denominator %16.6E\n",xnum,xden);
fputs(" GENF returning 1.0E38",stderr);
genf = 1.0E38;
goto S30;
S20:
genf = xnum/xden;
S30:
return genf;
}
double gennf(lua_RNG *o,double dfn,double dfd,double xnonc)
/*
**********************************************************************
GENerate random deviate from the Noncentral F distribution
Function
Generates a random deviate from the noncentral F (variance ratio)
distribution with DFN degrees of freedom in the numerator, and DFD
degrees of freedom in the denominator, and noncentrality parameter
XNONC.
Arguments
dfn --> Numerator degrees of freedom
(Must be >= 1.0)
dfd --> Denominator degrees of freedom
(Must be positive)
xnonc --> Noncentrality parameter
(Must be nonnegative)
Method
Directly generates ratio of noncentral numerator chisquare variate
to central denominator chisquare variate.
**********************************************************************
*/
{
static double gennf,xden,xnum;
static long qcond;
qcond = dfn <= 1.0 || dfd <= 0.0 || xnonc < 0.0;
if(!qcond) goto S10;
fputs("In GENNF - Either (1) Numerator DF <= 1.0 or",stderr);
fputs("(2) Denominator DF < 0.0 or ",stderr);
fputs("(3) Noncentrality parameter < 0.0",stderr);
fprintf(stderr,
"DFN value: %16.6EDFD value: %16.6EXNONC value: \n%16.6E\n",dfn,dfd,
xnonc);
exit(1);
S10:
xnum = gennch(o,dfn,xnonc)/dfn;
/*
GENNF = ( GENNCH( DFN, XNONC ) / DFN ) / ( GENCHI( DFD ) / DFD )
*/
xden = genchi(o,dfd)/dfd;
if(!(xden <= 9.999999999998E-39*xnum)) goto S20;
fputs(" GENNF - generated numbers would cause overflow",stderr);
fprintf(stderr," Numerator %16.6E Denominator %16.6E\n",xnum,xden);
fputs(" GENNF returning 1.0E38",stderr);
gennf = 1.0E38;
goto S30;
S20:
gennf = xnum/xden;
S30:
return gennf;
}
void semip_gc(
//Output Arguments
double *bdraw, // draws for beta (ndraw - nomit,k) matrix
double *adraw, // draws for regional effects, a, (m,1) vector
double *pdraw, // draws for rho (ndraw - nomit,1) vector
double *sdraw, // draws for sige (ndraw - nomit,1) vector
double *rdraw, // draws for rval (ndraw - nomit,1) vector (if mm != 0)
double *vmean, // mean of vi draws (n,1) vector
double *amean, // mean of a-draws (m,1) vector
double *zmean, // mean of latent z-draws (n,1) vector
double *yhat, // mean of posterior predicted y (n,1) vector
//Input Arguments
double *y, // (n,1) lhs vector with 0,1 values
double *x, // (n,k) matrix of explanatory variables
double *W, // (m,m) weight matrix
int ndraw, // # of draws
int nomit, // # of burn-in draws to omit
int nsave, // # of draws saved (= ndraw - nomit)
int n, // # of observations
int k, // # of explanatory variables
int m, // # of regions
int *mobs, // (m,1) vector of obs numbers in each region
double *a, // (m,1) vector of regional effects
double nu, // prior parameter for sige
double d0, // prior parameter for sige
double rval, // hyperparameter r
double mm, // prior parameter for rval
double kk, // prior parameter for rval
double *detval, // (ngrid,2) matrix with [rho , log det values]
int ngrid, // # of values in detval (rows)
double *TI, // prior var-cov for beta (inverted in matlab)
double *TIc) // prior var-cov * prior mean
{
// Local Variables
int i,j,l,iter,invt,accept,rcount,cobs,obsi,zflag;
double rmin,rmax,sige,chi,ee,ratio,p,rho,rho_new;
double junk,aBBa,vsqrt,ru,rhox,rhoy,phi,awi,aw2i,bi,di;
double *z,*tvec,*e,*e0,*xb,*mn,*ys,*limit1,*limit2,*zmt;
double *bhat,*b0,*b0tmp,*v,*vv,*b1,*b1tmp,*Bpa,*rdet,*ldet,*w1;
double **xs,**xst,**xsxs,**A0,**A1,**Bpt,**Bp,**xmat,**W2;
double *Wa, **Wmat;
double c0, c1,c2;
// Allocate Matrices and Vectors
xs = dmatrix(0,n-1,0,k-1);
xst = dmatrix(0,k-1,0,n-1);
xsxs = dmatrix(0,k-1,0,k-1);
A0 = dmatrix(0,k-1,0,k-1);
A1 = dmatrix(0,m-1,0,m-1);
Bp = dmatrix(0,m-1,0,m-1);
Bpt = dmatrix(0,m-1,0,m-1);
xmat = dmatrix(0,n-1,0,k-1);
W2 = dmatrix(0,m-1,0,m-1);
Wmat = dmatrix(0,m-1,0,m-1);
z = dvector(0,n-1);
tvec = dvector(0,n-1);
e = dvector(0,n-1);
e0 = dvector(0,n-1);
xb = dvector(0,n-1);
mn = dvector(0,n-1);
ys = dvector(0,n-1);
limit1 = dvector(0,n-1);
limit2 = dvector(0,n-1);
zmt = dvector(0,n-1);
vv = dvector(0,n-1);
bhat = dvector(0,k-1);
b0 = dvector(0,k-1);
b0tmp = dvector(0,k-1);
v = dvector(0,m-1);
b1 = dvector(0,m-1);
b1tmp = dvector(0,m-1);
Bpa = dvector(0,m-1);
w1 = dvector(0,m-1);
rdet = dvector(0,ngrid-1);
ldet = dvector(0,ngrid-1);
Wa = dvector(0,m-1);
// Initializations
junk = 0.0; // Placeholder for mean in meanvar()
rho = 0.5;
sige = 1.0;
zflag = 0; // a flag for 0,1 y-values
// Initialize (z,vv,limits,tvec)
for(i=0; i<n; i++){
z[i] = y[i];
vv[i] = 1.0;
tvec[i] = 1.0;
if (y[i] == 0.0){
limit1[i] = -10000;
limit2[i] = 0.0;
zflag = 1; // we have 0,1 y-values so sample z
}else{
limit1[i] = 0.0;
limit2[i] = 10000;
}
}
// Initialize v, b1tmp, Bp
for(i=0; i<m; i++){
v[i] = 1.0;
b1tmp[i] = 1.0;
for(j=0; j<m; j++){
if (j == i){
Bp[i][j] = 1 - rho*W[i + j*m];
}else{
Bp[i][j] = - rho*W[i + j*m];
}
Wmat[i][j] = W[i + j*m];
}
}
// Parse detval into rdet and ldet vectors
// and define (rmin,rmax)
for(i=0; i<ngrid; i++){
j=0;
rdet[i] = detval[i + j*ngrid];
j=1;
ldet[i] = detval[i + j*ngrid];
}
rmin = rdet[0];
rmax = rdet[ngrid-1];
// Put x into xmat
for(i=0; i<n; i++){
for(j=0; j<k; j++)
xmat[i][j] = x[i + j*n];
}
// Compute matrices to be used for updating a-vector
if(m > 100){ // Used only for large m
for(i=0; i<m; i++){
w1[i] = 0.0; // Form w1[i]
for(j=0;j<m;j++){
w1[i] = w1[i] + (W[j + i*m]*W[j + i*m]);
}
for(j=0;j<m;j++){ // Form W2[i][*]
W2[i][j] = 0.0;
if(j != i){
for(l=0;l<m;l++){
W2[i][j] = W2[i][j] + W[l + i*m]*W[l + j*m];
}
} // Note that W2[i][i] = 0.0 by construction
}
}
} // End if(m > 10)
// ======================================
// Start the Sampler
// ======================================
for(iter=0; iter<ndraw; iter++){
// UPDATE: beta
// (1) Apply stnd devs (vsqrt) to x, z, z - tvec
for(i=0; i<n; i++){
vsqrt = sqrt(vv[i]);
zmt[i] = (z[i] - tvec[i])/vsqrt;
for(j=0; j<k; j++)
xs[i][j] = x[i + j*n]/vsqrt;
}
// (2) Construct A0 matrix
transpose(xs,n,k,xst); // form xs'
matmat(xst,k,n,xs,k,xsxs); // form xs'*xs
for(i=0; i<k; i++){ // form xs'*xs + TI
for(j=0; j<k; j++)
A0[i][j] = xsxs[i][j] + TI[i + j*k];
}
invt = inverse(A0, k); // replace A0 = inv(A0)
if (invt != 1)
mexPrintf("semip_gc: Inversion error in beta conditional \n");
// (3) Construct b0 vector
matvec(xst,k,n,zmt,b0tmp); //form xs'*zmt
for(i=0; i<k; i++){
b0tmp[i] = b0tmp[i] + TIc[i]; //form b0tmp = xs'*zmt + TIc
}
matvec(A0,k,k,b0tmp,b0); //form b0 = A0*b0tmp
// (4) Do multivariate normal draw from N(b0,A0)
normal_rndc(A0, k, bhat); // generate N(0,A0) vector
for(i=0; i<k; i++){
bhat[i] = bhat[i] + b0[i]; // add mean vector, b0
}
// (5) Now update related values:
matvec(xmat,n,k,bhat,xb); // form xb = xmat*bhat
for(i=0; i<n; i++){ // form e0 = z - x*bhat
e0[i] = z[i] - xb[i];
}
cobs = 0;
for(i=0; i<m; i++){ // form b1tmp = e0i/v[i]
obsi = mobs[i];
b1tmp[i] = 0.0;
for(j=cobs; j<cobs + obsi; j++){
b1tmp[i] = b1tmp[i] + (e0[j]/v[i]);
}
cobs = cobs + obsi;
}
// UPDATE: a
if(m <= 100){ // For small m use straight inverse
// (1) Define A1 and b1
transpose(Bp,m,m,Bpt); // form Bp'
matmat(Bpt,m,m,Bp,m,A1); // form Bp'*Bp
for(i=0; i<m; i++){ // form A1 = (1/sige)*Bp'Bp + diag(mobs/v)
for(j=0; j<m; j++){
if (j == i){
A1[i][j] = (1/sige)*A1[i][j] + ((double)mobs[i])/v[i];
}else{
A1[i][j] = (1/sige)*A1[i][j];
}
}
}
inverse(A1,m); // set A1 = inv(A1)
matvec(A1,m,m,b1tmp,b1); // form b1
// (2) Do multivariate normal draw from N(b1,A1)
normal_rndc(A1,m,a); // generate N(0,A1) vector
for(i=0; i<m; i++){
a[i] = a[i] + b1[i]; // add mean vector, b1
}
}else{ // For large m use marginal distributions
cobs = 0;
for(i=0;i<m;i++){
obsi = mobs[i];
phi = 0.0;
for(j=cobs;j<cobs+obsi;j++){
phi = phi + ((z[j] - xb[j])/v[i]); // form phi
}
awi = 0.0;
aw2i = 0.0;
for(j=0;j<m;j++){ // form awi and aw2i
aw2i = aw2i + W2[i][j]*a[j]; // (W2[i][i] = 0)
if(j != i){
awi = awi + (W[i + j*m] + W[j + i*m])*a[j];
}
}
bi = phi + (rho/sige)*awi - ((rho*rho)/sige)*aw2i;
di = (1/sige) + ((rho*rho)/sige)*w1[i] + (obsi/v[i]);
a[i] = (bi/di) + sqrt(1/di)*snorm(); // Form a[i]
cobs = cobs + obsi;
}
} // End update of a
// Compute tvec = del*a
cobs = 0;
for(i=0; i<m; i++){
obsi = mobs[i];
for(j=cobs; j<cobs + obsi; j++){
tvec[j] = a[i];
}
cobs = cobs + obsi;
}
//UPDATE: sige
matvec(Bp,m,m,a,Bpa); //form Bp*a
aBBa = 0.0; //form aBBa = a'*Bp'*Bp*a
for(i=0; i<m; i++){
aBBa = aBBa + Bpa[i]*Bpa[i];
}
chi = genchi(m + 2.0*nu);
sige = (aBBa + 2.0*d0)/chi;
//UPDATE: v (and vv = del*v)
for(i=0; i<n; i++){
e[i] = e0[i] - tvec[i]; //form e = z - x*bhat - tvec
}
cobs = 0;
for(i=0; i<m; i++){
obsi = mobs[i];
chi = genchi(rval + obsi);
ee = 0.0;
for(j=cobs; j<cobs + obsi; j++){ // form ee
ee = ee + e[j]*e[j];
}
v[i] = (ee + rval)/chi; // form v
for(j=cobs; j<cobs + obsi; j++){
vv[j] = v[i]; // form vv
}
cobs = cobs + obsi;
}
//UPDATE: rval (if necessary)
if (mm != 0.0){
rval = gengam(mm,kk);
}
//UPDATE: rho (using univariate integration)
matvec(Wmat,m,m,a,Wa); // form Wa vector
c0 = 0.0; // form a'*a
c1 = 0.0; // form a'*Wa
c2 = 0.0; // form (Wa)'*Wa
for(i=0; i<m; i++){
c0 = c0 + a[i]*a[i];
c1 = c1 + a[i]*Wa[i];
c2 = c2 + Wa[i]*Wa[i];
}
rho = draw_rho(rdet,ldet,c0,c1,c2,sige,ngrid,m,k,rho);
// (4) Update Bp matrix using new rho
for(i=0; i<m; i++){
for(j=0; j<m; j++){
if (j == i){
Bp[i][j] = 1 - rho*W[i + j*m];
}else{
Bp[i][j] = - rho*W[i + j*m];
}
}
}
//UPDATE: z
if (zflag == 1){ // skip this for continuous y-values
// (1) Generate vector of means
cobs = 0;
for(i=0; i<m; i++){
obsi = mobs[i];
for(j=cobs; j<cobs + obsi; j++){
mn[j] = xb[j] + a[i];
}
cobs = cobs + obsi;
}
// (2) Sample truncated normal for latent z values
normal_truncc(n,mn,vv,limit1,limit2,z);
// (3) Compute associated sample y vector: ys
for(i=0; i<n; i++){
if(z[i]<0){
ys[i] = 0.0;
}else{
ys[i] = 1.0;
}
}
} // end of if zflag == 1
// ===================
// Save sample draws
// ===================
if (iter > nomit-1){
pdraw[iter - nomit] = rho; //save rho-draws
sdraw[iter - nomit] = sige; //save sige-draws
if(mm != 0.0)
rdraw[iter - nomit] = rval; //save r-draws (if necessary)
for(j=0; j<k; j++)
bdraw[(iter - nomit) + j*nsave] = bhat[j]; //save beta-draws
for(i=0; i<m; i++){
vmean[i] = vmean[i] + v[i]/((double) (nsave)); //save mean v-draws
adraw[(iter - nomit) + i*nsave] = a[i]; //save a-draws
amean[i] = amean[i] + a[i]/((double) (nsave)); //save mean a-draws
}
for(i=0; i<n; i++){
zmean[i] = zmean[i] + z[i]/((double) (nsave)); //save mean z-draws
yhat[i] = yhat[i] + mn[i]/((double) (nsave)); //save mean y-values
}
}
} // End iteration loop
// ===============================
// END SAMPLER
// ===============================
// Free up allocated vectors
free_dmatrix(xs,0,n-1,0);
free_dmatrix(xst,0,k-1,0);
free_dmatrix(xsxs,0,k-1,0);
free_dmatrix(A0,0,k-1,0);
free_dmatrix(A1,0,m-1,0);
free_dmatrix(Bp,0,m-1,0);
free_dmatrix(Bpt,0,m-1,0);
free_dmatrix(W2,0,m-1,0);
free_dmatrix(xmat,0,n-1,0);
free_dmatrix(Wmat,0,m-1,0);
free_dvector(z,0);
free_dvector(tvec,0);
free_dvector(e,0);
free_dvector(e0,0);
free_dvector(xb,0);
free_dvector(mn,0);
free_dvector(ys,0);
free_dvector(limit1,0);
free_dvector(limit2,0);
free_dvector(zmt,0);
free_dvector(vv,0);
free_dvector(bhat,0);
free_dvector(b0,0);
free_dvector(b0tmp,0);
free_dvector(v,0);
free_dvector(b1,0);
free_dvector(b1tmp,0);
free_dvector(Bpa,0);
free_dvector(rdet,0);
free_dvector(ldet,0);
free_dvector(w1,0);
free_dvector(Wa,0);
} // End of semip_gc
