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#include <string.h>
#include <stddef.h>
#include <stdio.h>
#include <math.h>
#include <Rmath.h>
#include <R.h>
#include "vector.h"
#include "subroutines.h"
#include "rand.h"
#include "bayes.h"
#include "sample.h"
/* Normal Parametric Model for 2x2 Tables */
void cBaseeco(
/*data input */
double *pdX, /* data (X, Y) */
int *pin_samp, /* sample size */
/*MCMC draws */
int *n_gen, /* number of gibbs draws */
int *burn_in, /* number of draws to be burned in */
int *pinth, /* keep every nth draw */
int *verbose, /* 1 for output monitoring */
/* prior specification*/
int *pinu0, /* prior df parameter for InvWish */
double *pdtau0, /* prior scale parameter for Sigma */
double *mu0, /* prior mean for mu */
double *pdS0, /* prior scale for Sigma */
double *mustart, /* starting values for mu */
double *Sigmastart, /* starting values for Sigma */
/* incorporating survey data */
int *survey, /*1 if survey data available (set of W_1, W_2)
0 not*/
int *sur_samp, /*sample size of survey data*/
double *sur_W, /*set of known W_1, W_2 */
/* incorporating homeogenous areas */
int *x1, /* 1 if X=1 type areas available
W_1 known, W_2 unknown */
int *sampx1, /* number X=1 type areas */
double *x1_W1, /* values of W_1 for X1 type areas */
int *x0, /* 1 if X=0 type areas available
W_2 known, W_1 unknown */
int *sampx0, /* number X=0 type areas */
double *x0_W2, /* values of W_2 for X0 type areas */
/* bounds of W1 */
double *minW1, double *maxW1,
/* flags */
int *parameter, /* 1 if save population parameter */
int *Grid, /* 1 if Grid algorithm is used; 0 for
Metropolis */
/* storage for Gibbs draws of mu/sigmat*/
double *pdSMu0, double *pdSMu1,
double *pdSSig00, double *pdSSig01, double *pdSSig11,
/* storage for Gibbs draws of W*/
double *pdSW1, double *pdSW2
){
/* some integers */
int n_samp = *pin_samp; /* sample size */
int s_samp = *sur_samp; /* sample size of survey data */
int x1_samp = *sampx1; /* sample size for X=1 */
int x0_samp = *sampx0; /* sample size for X=0 */
int t_samp = n_samp+s_samp+x1_samp+x0_samp; /* total sample size */
int nth = *pinth;
int n_dim = 2; /* dimension */
int n_step = 1000; /* 1/The default size of grid step */
/* prior parameters */
double tau0 = *pdtau0; /* prior scale */
int nu0 = *pinu0; /* prior degrees of freedom */
double **S0 = doubleMatrix(n_dim, n_dim); /* The prior S parameter for InvWish */
/* data */
double **X = doubleMatrix(n_samp, n_dim); /* The Y and covariates */
double **W = doubleMatrix(t_samp, n_dim); /* The W1 and W2 matrix */
double **Wstar = doubleMatrix(t_samp, n_dim); /* logit tranformed W */
double **S_W = doubleMatrix(s_samp, n_dim); /* The known W1 and W2 matrix*/
double **S_Wstar = doubleMatrix(s_samp, n_dim); /* logit transformed S_W*/
/* grids */
double **W1g = doubleMatrix(n_samp, n_step); /* grids for W1 */
double **W2g = doubleMatrix(n_samp, n_step); /* grids for W2 */
int *n_grid = intArray(n_samp); /* grid size */
/* model parameters */
double *mu = doubleArray(n_dim); /* The mean */
double **Sigma = doubleMatrix(n_dim, n_dim); /* The covariance matrix */
double **InvSigma = doubleMatrix(n_dim, n_dim); /* The inverse covariance matrix */
/* misc variables */
int i, j, k, main_loop; /* used for various loops */
int itemp, itempS, itempC, itempA;
int progress = 1, itempP = ftrunc((double) *n_gen/10);
double dtemp, dtemp1;
/* get random seed */
GetRNGstate();
/* read the priors */
itemp=0;
for(k=0;k<n_dim;k++)
for(j=0;j<n_dim;j++) S0[j][k]=pdS0[itemp++];
/* read the data */
itemp = 0;
for (j = 0; j < n_dim; j++)
for (i = 0; i < n_samp; i++)
X[i][j] = pdX[itemp++];
/* Initialize W, Wstar for n_samp */
for (i=0; i< n_samp; i++) {
if (X[i][1]!=0 && X[i][1]!=1) {
W[i][0]=runif(minW1[i], maxW1[i]);
W[i][1]=(X[i][1]-X[i][0]*W[i][0])/(1-X[i][0]);
}
if (X[i][1]==0)
for (j=0; j<n_dim; j++) W[i][j]=0.0001;
if (X[i][1]==1)
for (j=0; j<n_dim; j++) W[i][j]=0.9999;
for (j=0; j<n_dim; j++)
Wstar[i][j]=log(W[i][j])-log(1-W[i][j]);
}
/* read homeogenous areas information */
if (*x1==1)
for (i=0; i<x1_samp; i++) {
W[(n_samp+i)][0]=x1_W1[i];
if (W[(n_samp+i)][0]==0)
W[(n_samp+i)][0]=0.0001;
if (W[(n_samp+i)][0]==1)
W[(n_samp+i)][0]=0.9999;
Wstar[(n_samp+i)][0]=log(W[(n_samp+i)][0])-log(1-W[(n_samp+i)][0]);
}
if (*x0==1)
for (i=0; i<x0_samp; i++) {
W[(n_samp+x1_samp+i)][1]=x0_W2[i];
if (W[(n_samp+x1_samp+i)][1]==0)
W[(n_samp+x1_samp+i)][1]=0.0001;
if (W[(n_samp+x1_samp+i)][1]==1)
W[(n_samp+x1_samp+i)][1]=0.9999;
Wstar[(n_samp+x1_samp+i)][1]=log(W[(n_samp+x1_samp+i)][1])-log(1-W[(n_samp+x1_samp+i)][1]);
}
/* read the survey data */
if (*survey==1) {
itemp = 0;
for (j=0; j<n_dim; j++)
for (i=0; i<s_samp; i++) {
S_W[i][j]=sur_W[itemp++];
if (S_W[i][j]==0)
S_W[i][j]=0.0001;
if (S_W[i][j]==1)
S_W[i][j]=0.9999;
S_Wstar[i][j]=log(S_W[i][j])-log(1-S_W[i][j]);
W[(n_samp+x1_samp+x0_samp+i)][j]=S_W[i][j];
Wstar[(n_samp+x1_samp+x0_samp+i)][j]=S_Wstar[i][j];
}
}
/* counters */
itempA=0; /* for alpha */
itempS=0; /* for storage */
itempC=0; /* control nth draw */
/*** calculate grids ***/
if (*Grid)
GridPrep(W1g, W2g, X, maxW1, minW1, n_grid, n_samp, n_step);
/* starting vales of mu and Sigma */
itemp = 0;
for(j=0;j<n_dim;j++){
mu[j] = mustart[j];
for(k=0;k<n_dim;k++)
Sigma[j][k]=Sigmastart[itemp++];
}
dinv(Sigma, n_dim, InvSigma);
/*** Gibbs sampler! ***/
if (*verbose)
Rprintf("Starting Gibbs Sampler...\n");
for(main_loop=0; main_loop<*n_gen; main_loop++){
/** update W, Wstar given mu, Sigma in regular areas **/
for (i=0;i<n_samp;i++){
if ( X[i][1]!=0 && X[i][1]!=1 ) {
if (*Grid)
rGrid(W[i], W1g[i], W2g[i], n_grid[i], mu, InvSigma, n_dim);
else
rMH(W[i], X[i], minW1[i], maxW1[i], mu, InvSigma, n_dim);
}
/*3 compute Wsta_i from W_i*/
Wstar[i][0]=log(W[i][0])-log(1-W[i][0]);
Wstar[i][1]=log(W[i][1])-log(1-W[i][1]);
}
/* update W2 given W1, mu and Sigma in x1 homeogeneous areas */
if (*x1==1)
for (i=0; i<x1_samp; i++) {
dtemp=mu[1]+Sigma[0][1]/Sigma[0][0]*(Wstar[n_samp+i][0]-mu[0]);
dtemp1=Sigma[1][1]*(1-Sigma[0][1]*Sigma[0][1]/(Sigma[0][0]*Sigma[1][1]));
dtemp1=sqrt(dtemp1);
Wstar[n_samp+i][1]=rnorm(dtemp, dtemp1);
W[n_samp+i][1]=exp(Wstar[n_samp+i][1])/(1+exp(Wstar[n_samp+i][1]));
}
/* update W1 given W2, mu and Sigma in x0 homeogeneous areas */
if (*x0==1)
for (i=0; i<x0_samp; i++) {
dtemp=mu[0]+Sigma[0][1]/Sigma[1][1]*(Wstar[n_samp+x1_samp+i][1]-mu[1]);
dtemp1=Sigma[0][0]*(1-Sigma[0][1]*Sigma[0][1]/(Sigma[0][0]*Sigma[1][1]));
dtemp1=sqrt(dtemp1);
Wstar[n_samp+x1_samp+i][0]=rnorm(dtemp, dtemp1);
W[n_samp+x1_samp+i][0]=exp(Wstar[n_samp+x1_samp+i][0])/(1+exp(Wstar[n_samp+x1_samp+i][0]));
}
/* update mu, Sigma given wstar using effective sample of Wstar */
NIWupdate(Wstar, mu, Sigma, InvSigma, mu0, tau0, nu0, S0, t_samp, n_dim);
/*store Gibbs draw after burn-in and every nth draws */
if (main_loop>=*burn_in){
itempC++;
if (itempC==nth){
pdSMu0[itempA]=mu[0];
pdSMu1[itempA]=mu[1];
pdSSig00[itempA]=Sigma[0][0];
pdSSig01[itempA]=Sigma[0][1];
pdSSig11[itempA]=Sigma[1][1];
itempA++;
for(i=0; i<(n_samp+x1_samp+x0_samp); i++){
pdSW1[itempS]=W[i][0];
pdSW2[itempS]=W[i][1];
itempS++;
}
itempC=0;
}
}
if (*verbose)
if (itempP == main_loop) {
Rprintf("%3d percent done.\n", progress*10);
itempP+=ftrunc((double) *n_gen/10); progress++;
R_FlushConsole();
}
R_CheckUserInterrupt();
} /* end of Gibbs sampler */
if(*verbose)
Rprintf("100 percent done.\n");
/** write out the random seed **/
PutRNGstate();
/* Freeing the memory */
FreeMatrix(X, n_samp);
FreeMatrix(W, t_samp);
FreeMatrix(Wstar, t_samp);
FreeMatrix(S_W, s_samp);
FreeMatrix(S_Wstar, s_samp);
FreeMatrix(S0, n_dim);
FreeMatrix(W1g, n_samp);
FreeMatrix(W2g, n_samp);
free(n_grid);
free(mu);
FreeMatrix(Sigma,n_dim);
FreeMatrix(InvSigma, n_dim);
} /* main */
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