static void
irt_rpf_mdim_drm_prob(const double *spec,
const double *param, const double *th,
double *out)
{
int numDims = spec[RPF_ISpecDims];
double dprod = dotprod(param, th, numDims);
double diff = param[numDims];
double athb = -(dprod + diff);
if (athb < -EXP_STABLE_DOMAIN) athb = -EXP_STABLE_DOMAIN;
else if (athb > EXP_STABLE_DOMAIN) athb = EXP_STABLE_DOMAIN;
double tmp;
if (numDims == 0) {
tmp = 1/(1+exp(athb));
} else {
const double gg = antilogit(param[numDims+1]);
const double uu = antilogit(param[numDims+2]);
const double width = uu-gg;
if (width < 0) tmp = nan("I");
else {
tmp = gg + width / (1 + exp(athb));
}
}
out[0] = 1-tmp;
out[1] = tmp;
}
static void
irt_rpf_mdim_drm_prob2(const double *spec,
const double *param, const double *th,
double *out1, double *out2)
{
int numDims = spec[RPF_ISpecDims];
double dprod = dotprod(param, th, numDims);
double diff = param[numDims];
double athb = -(dprod + diff);
if (athb < -EXP_STABLE_DOMAIN) athb = -EXP_STABLE_DOMAIN;
else if (athb > EXP_STABLE_DOMAIN) athb = EXP_STABLE_DOMAIN;
double tmp = 1 / (1 + exp(athb));
out1[0] = 1-tmp;
out1[1] = tmp;
if (numDims) {
const double gg = antilogit(param[numDims+1]);
const double uu = antilogit(param[numDims+2]);
tmp = gg + (uu-gg) * tmp;
}
out2[0] = 1-tmp;
out2[1] = tmp;
}
void P_dich(vector<double> &P, const vector<double> &par, const NumericMatrix &Theta,
const NumericVector &ot, const int &N, const int &nfact)
{
const int len = par.size();
const double utmp = par[len-1];
const double gtmp = par[len-2];
const double g = antilogit(>mp);
const double u = antilogit(&utmp);
const double d = par[len-3];
const int USEOT = ot.size() > 1;
for (int i = 0; i < N; ++i){
double z = d;
for (int j = 0; j < nfact; ++j)
z += par[j] * Theta(i,j);
if(USEOT) z += ot[i];
if(z > ABS_MAX_Z) z = ABS_MAX_Z;
else if(z < -ABS_MAX_Z) z = -ABS_MAX_Z;
P[i+N] = g + (u - g) /(1.0 + exp(-z));
P[i] = 1.0 - P[i + N];
}
}
static void
irt_rpf_mdim_drm_dTheta(const double *spec, const double *param,
const double *where, const double *dir,
double *grad, double *hess)
{
int numDims = spec[RPF_ISpecDims];
double PQ[2];
double PQstar[2];
irt_rpf_mdim_drm_prob2(spec, param, where, PQstar, PQ);
double Pstar = PQstar[0];
double Qstar = PQstar[1];
const double *aa = param;
const double guess = antilogit(param[numDims + 1]);
const double upper = antilogit(param[numDims + 2]);
for (int ax=0; ax < numDims; ax++) {
double piece = dir[ax] * (upper-guess) * aa[ax] * (Pstar * Qstar);
grad[1] += piece;
grad[0] -= piece;
piece = dir[ax] * (2 * (upper - guess) * aa[ax]*aa[ax] * (Qstar * Qstar * Pstar) -
(upper - guess) * aa[ax]*aa[ax] * (Pstar * Qstar));
hess[1] -= piece;
hess[0] += piece;
}
}
void P_comp(vector<double> &P, const vector<double> &par,
const NumericMatrix &Theta, const int &N, const int &nfact)
{
vector<double> a(nfact), d(nfact);
for(int j = 0; j < nfact; ++j){
a[j] = par[j];
d[j] = par[j+nfact];
}
const double gtmp = par[nfact*2];
const double g = antilogit(>mp);
for(int i = 0; i < N; ++i) P[i+N] = 1.0;
for(int j = 0; j < nfact; ++j)
for(int i = 0; i < N; ++i)
P[i+N] = P[i+N] * (1.0 / (1.0 + exp(-(a[j] * Theta(i,j) + d[j]))));
for(int i = 0; i < N; ++i){
P[i+N] = g + (1.0 - g) * P[i+N];
if(P[i+N] < 1e-20) P[i+N] = 1e-20;
else if (P[i+N] > 1.0 - 1e-20) P[i+N] = 1.0 - 1e-20;
P[i] = 1.0 - P[i+N];
}
}
static void
irt_rpf_mdim_drm_deriv1(const double *spec,
const double *param,
const double *where,
const double *weight, double *out)
{
const int numDims = spec[RPF_ISpecDims];
double QP[2];
double QPstar[2];
irt_rpf_mdim_drm_prob2(spec, param, where, QPstar, QP);
const double r1 = weight[1];
const double r2 = weight[0];
const double r1_P = r1/QP[1];
const double r1_P2 = r1/(QP[1] * QP[1]);
const double r2_Q = r2/QP[0];
const double r2_Q2 = r2/(QP[0] * QP[0]);
const double r1_Pr2_Q = (r1_P - r2_Q);
const double Pstar = QPstar[1];
const double Pstar2 = Pstar * Pstar;
const double Pstar3 = Pstar2 * Pstar;
const double Qstar = QPstar[0];
if (numDims == 0) {
out[0] -= Pstar * Qstar * r1_Pr2_Q;
double chunk1 = (Pstar - Pstar2);
out[1] -= (r1_P * ((Pstar - 3*Pstar2 + 2*Pstar3)) -
r1_P2 * chunk1*chunk1 +
r2_Q * ((-Pstar + 3*Pstar2 - 2*Pstar3)) -
r2_Q2 * chunk1*chunk1); // cc^2
return;
}
const double expgg = param[numDims+1];
const double expuu = param[numDims+2];
const double gg = antilogit(expgg);
const double uu = antilogit(expuu);
const double difexpgg = gg * (1-gg);
const double difexpuu = uu * (1-uu);
const double gm1 = (1.0 - gg);
const double um1 = (1.0 - uu);
const double u_1u = uu * um1;
const double g_1g = gg * gm1;
const double ugD = (uu-gg);
for (int dx=0; dx < numDims; dx++) {
out[dx] -= where[dx] * Pstar * Qstar * ugD * r1_Pr2_Q;
}
out[numDims] -= ugD * Pstar * Qstar * r1_Pr2_Q;
out[numDims+1] -= difexpgg * QPstar[0] * r1_Pr2_Q;
out[numDims+2] -= difexpuu * QPstar[1] * r1_Pr2_Q;
int ox = numDims+2;
for(int ix=0; ix < numDims; ix++) {
for(int jx=0; jx <= ix; jx++) {
out[++ox] -= (r1_P * (ugD * where[ix] * where[jx] *
(Pstar - 3*Pstar2 + 2*Pstar3)) -
r1_P2 * (ugD * where[ix] * (Pstar - Pstar2) *
(ugD * where[jx] * (Pstar - Pstar2))) +
r2_Q * (ugD * where[ix] * where[jx] *
(-Pstar + 3*Pstar2 - 2*Pstar3)) -
r2_Q2 * (ugD * where[ix] * (-Pstar + Pstar2) *
(ugD * where[jx] * (-Pstar + Pstar2)))); // aa_k aa_k
}
}
for(int ix=0; ix < numDims; ix++) {
out[++ox] -= (r1_P * (ugD * where[ix] * (Pstar - 3*Pstar2 + 2*Pstar3)) -
r1_P2 * (ugD * where[ix] * (Pstar - Pstar2) *
(ugD * (Pstar - Pstar2))) +
r2_Q * (ugD * where[ix] * (-Pstar + 3*Pstar2 - 2*Pstar3)) -
r2_Q2 * (ugD * where[ix] * (-Pstar + Pstar2) *
(ugD * (-Pstar + Pstar2)))); // cc aa_k
}
double chunk1 = ugD * (Pstar - Pstar2);
out[++ox] -= (r1_P * (ugD * (Pstar - 3*Pstar2 + 2*Pstar3)) -
r1_P2 * chunk1*chunk1 +
r2_Q * (ugD * (-Pstar + 3*Pstar2 - 2*Pstar3)) -
r2_Q2 * chunk1*chunk1); // cc^2
for(int ix=0; ix < numDims; ix++) {
out[++ox] -= (r1_P * (g_1g * where[ix] * (-Pstar + Pstar2)) -
r1_P2 * (ugD * where[ix] * (Pstar - Pstar2)) * g_1g * Qstar +
r2_Q * (g_1g * where[ix] * (Pstar - Pstar2)) -
r2_Q2 * (ugD * where[ix] * (-Pstar + Pstar2) ) * g_1g * (Pstar - 1)); // gg aa_k
}
out[++ox] -= (r1_P * (g_1g * (-Pstar + Pstar2)) -
r1_P2 * (ugD * (Pstar - Pstar2)) * g_1g * Qstar +
r2_Q * (g_1g * (Pstar - Pstar2)) -
r2_Q2 * (ugD * (-Pstar + Pstar2)) * g_1g * -Qstar); // gg cc
out[++ox] -= (r1_P * (g_1g * (2.0*gm1 - 1.0 - 2.0*gm1*Pstar + Pstar)) -
r1_P2 * (g_1g * (1.0 - Pstar)) * (g_1g * (1.0 - Pstar)) +
r2_Q * (g_1g * (-2.0*gm1 + 1.0 + 2.0*gm1*Pstar - Pstar)) -
r2_Q2 * (g_1g * (-1.0 + Pstar)) * (g_1g * (-1.0 + Pstar))); // gg^2
for(int ix=0; ix < numDims; ix++) {
out[++ox] -= (r1_P * (u_1u * where[ix] * (Pstar - Pstar2)) -
r1_P2 * (ugD * where[ix] * (Pstar - Pstar2)) * u_1u * Pstar +
r2_Q * (u_1u * where[ix] * (-Pstar + Pstar2)) +
r2_Q2 * (ugD * where[ix] * (-Pstar + Pstar2) ) * u_1u * Pstar); // uu aa_k
}
out[++ox] -= (r1_P * (u_1u * (Pstar - Pstar2)) -
r1_P2 * (ugD * (Pstar - Pstar2)) * u_1u * Pstar +
r2_Q * (u_1u * (-Pstar + Pstar2)) +
r2_Q2 * (ugD * (-Pstar + Pstar2)) * u_1u * Pstar); // uu cc
out[++ox] -= (-r1_P2 * (g_1g * (1.0 - Pstar)) * u_1u * Pstar +
r2_Q2 * (g_1g * (-1.0 + Pstar)) * u_1u * Pstar); // uu gg
out[++ox] -= (r1_P * (2.0*u_1u*um1*Pstar) - r1_P * (u_1u*Pstar) - r1_P2 *(u_1u*u_1u*Pstar2) -
r2_Q * (2.0*u_1u*um1*Pstar) + r2_Q * (u_1u*Pstar) - r2_Q2 *(u_1u*u_1u*Pstar2)); // uu^2
}
