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GPCM4PL_stuff.cpp
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#include <Rcpp.h>
using namespace Rcpp;
// 4PL Stuff ***************************************************************************************
// P FUNCTION +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericVector P_4pl(NumericVector delta, double alpha, double theta, double la, double ua) {
// resp kann man eigenltich weglassen
// hier wird nur die Wahrscheinlichkeit berechnet zu loesen
//int nthres = delta.size();
//double nenner = 0;
//double zae = 0;
NumericVector PP1I(3);
double beta = delta(1); // weil der erste muss 0 sein, weil ja auch in der thres matrix GPCM items drinstehen koennen
// probability
PP1I(0) = la + (ua - la) * exp(alpha*(theta - beta))/(1+exp(alpha*(theta - beta)));
// first derivate
PP1I(1) = alpha * (ua - PP1I(0)) * (PP1I(0) - la) / (ua - la);
// information
PP1I(2) = (PP1I(1)*PP1I(1))/(PP1I(0)*(1-PP1I(0)));
return PP1I;
}
// P FUNCTION +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericVector P_4pl4wle(NumericVector delta, double alpha, double theta, double la, double ua) {
// resp kann man eigenltich weglassen
// hier wird nur die Wahrscheinlichkeit berechnet zu loesen
//int nthres = delta.size();
//double nenner = 0;
//double zae = 0;
NumericVector PP1I(6);
double beta = delta(1); // weil der erste muss 0 sein, weil ja auch in der thres matrix GPCM items drinstehen koennen
// probability
PP1I(0) = la + (ua - la) * exp(alpha*(theta - beta))/(1+exp(alpha*(theta - beta)));
// first derivate
PP1I(1) = alpha * (ua - PP1I(0)) * (PP1I(0) - la) / (ua - la);
// information
PP1I(2) = (PP1I(1)*PP1I(1))/(PP1I(0)*(1-PP1I(0)));
// second deriv
PP1I(3) = alpha / (ua-la) * (ua*PP1I(1) - 2*PP1I(0)*PP1I(1) + la*PP1I(1));
// third deriv
PP1I(4) = alpha / (ua-la) * (ua*PP1I(3) - 2*PP1I(1)*PP1I(1) - 2*PP1I(0)*PP1I(3) + la*PP1I(3));
// information first deriv
double empp1i = 1-PP1I(0);
double oben = (2*PP1I(1)*PP1I(3)*PP1I(0)*(1-PP1I(0)) - PP1I(1)*PP1I(1)*(PP1I(1)*(1-PP1I(0)) + PP1I(0)*(-PP1I(1))));
double unten = PP1I(0)*PP1I(0)*empp1i*empp1i;
double INF2 = oben/unten;
//PP1I(5) = (PP1I(2) * PP1I(1) * PP1I(3) * PP1I(1) - PP1I(0) * (PP1I(1) * (PP1I(2) * PP1I(4) - PP1I(3) * INF2) + PP1I(2) * PP1I(3) *PP1I(3)))/pow(PP1I(0),2);
double Qj = 1-PP1I(0);
double PP1IQj = PP1I(0) * Qj;
// J'
//PP1I(5) = ((PP1I(3)*PP1I(3) + PP1I(1)*PP1I(4))*PP1I(0)*Qj - PP1I(1)*PP1I(3)*(PP1I(1)*Qj - PP1I(0)*PP1I(1))) / pow(PP1I(0) * Qj,2);
// diese version stimmt mit dem alten PP package ueberein, hat aber mMn einen vorzeichenfehler
double J1 = ((PP1I(3)*PP1I(3) - PP1I(1)*PP1I(4))*PP1I(0)*Qj + PP1I(1)*PP1I(3)*(PP1I(1)*Qj - PP1I(0)*PP1I(1))) / (PP1IQj*PP1IQj);
double J = PP1I(1) * PP1I(3) / (PP1I(0)*Qj);
// this is the whole numerator of the first derivtae of the correction term
PP1I(5) = J1 * PP1I(2) - J * INF2;
//PP1I(6) = INF2; // i hope we wont need this anymore
return PP1I;
}
// [[Rcpp::export]]
double r_huber_4pl(NumericVector delta, double alpha,
double theta, double la, double ua, double H) {
//double nenner = 0;
//double zae = 0;
double HU = 0;
double beta = delta(1); // weil der erste muss 0 sein, weil ja auch in der thres matrix GPCM items drinstehen koennen
// compute residuum
//double resid = log(la + (ua - la) * exp(alpha*(theta - beta)));
double resid = alpha*(theta - beta);
// compute Huber weight
if(resid < 0)
{
resid = resid * (-1);
}
if(resid <= H)
{
HU = 1;
} else
{
HU = H/resid;
}
return HU;
}
// LIKELIHOOD - L1, L2 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericMatrix L4pl(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector LOWA, NumericVector UPPA, NumericVector THETA, bool map,
NumericVector mu, NumericVector sigma2) {
int npers = awm.nrow();
int nitem = awm.ncol();
int maxca = DELTA.nrow();
// ALPHA muss so lang sein wie nitem anzeigt
// THETA muss so lang sein wie npers anzeigt
// DELTA muss so viele Spalten haben wie nitem anzeigt
// maxca gibt an wieviele maximale kategorien
// 4 columns: 1st deriv of logL; 2nd deriv of logL; delta = 1st/2nd; theta - delta
NumericMatrix l1l2M(npers,4);
for(int it = 0; it < nitem; it++)
{
// Response vector of one item
IntegerVector respvec = awm(_,it);
double alpha = ALPHA(it);
NumericVector delta = DELTA(_,it);
LogicalVector nas(maxca);
double lowerA = LOWA(it);
double upperA = UPPA(it);
// find NA and kill them
for (int fna = 0; fna < maxca; ++fna) {
nas[fna] = NumericVector::is_na(delta[fna]);
}
// parameters without missing values. missing values should only be possible at the end of the matrix
NumericVector delta1 = delta[!nas];
//int kmax = delta1.size();
for(int pe = 0; pe < npers; pe++)
{
int resp = respvec(pe);
double theta = THETA(pe);
NumericVector ergP(3);
// NA handling
// if the i,j obs is NA, add nothing
if(IntegerVector::is_na(resp))
{ // in case of missing value as response
continue;
} else
{
ergP = P_4pl(delta1, alpha, theta, lowerA, upperA);
// l1
double Qj = 1 - ergP(0);
l1l2M(pe,0) += (resp - ergP(0))/(ergP(0)*Qj) * ergP(1);
l1l2M(pe,1) += ergP(2);
}
}
}
if(map)
{
NumericVector corrterm1(npers);
NumericVector corrterm2(npers);
corrterm1 = (THETA - mu)/sigma2;
corrterm2 = 1/sigma2;
l1l2M(_,1) = l1l2M(_,1) * (-1);
l1l2M(_,2) = (l1l2M(_,0) - corrterm1) / (l1l2M(_,1)-corrterm2);
// Korrekturterm um divergieren zu verhindern:
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,2)) <= 5)
{
continue;
} else {
l1l2M(ai,2) = l1l2M(ai,2)/std::abs(l1l2M(ai,2)) * 5;
}
}
l1l2M(_,3) = THETA - l1l2M(_,2);
} else {
l1l2M(_,1) = l1l2M(_,1) * (-1);
l1l2M(_,2) = l1l2M(_,0)/l1l2M(_,1);
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,2)) <= 5)
{
continue;
} else {
l1l2M(ai,2) = l1l2M(ai,2)/std::abs(l1l2M(ai,2)) * 5;
}
}
l1l2M(_,3) = THETA - l1l2M(_,2);
}
return l1l2M;
}
// LIKELIHOOD - L1, L2 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericMatrix L4pl_wle(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector LOWA, NumericVector UPPA, NumericVector THETA) {
int npers = awm.nrow();
int nitem = awm.ncol();
int maxca = DELTA.nrow();
// ALPHA muss so lang sein wie nitem anzeigt
// THETA muss so lang sein wie npers anzeigt
// DELTA muss so viele Spalten haben wie nitem anzeigt
// maxca gibt an wieviele maximale kategorien
// 4 columns: 1st deriv of logL; 2nd deriv of logL; delta = 1st/2nd; theta - delta
NumericMatrix l1l2M(npers,6);
for(int it = 0; it < nitem; it++)
{
// Response vector of one item
IntegerVector respvec = awm(_,it);
double alpha = ALPHA(it);
NumericVector delta = DELTA(_,it);
LogicalVector nas(maxca);
double lowerA = LOWA(it);
double upperA = UPPA(it);
// find NA and kill them
for (int fna = 0; fna < maxca; ++fna) {
nas[fna] = NumericVector::is_na(delta[fna]);
}
// parameters without missing values. missing values should only be possible at the end of the matrix
NumericVector delta1 = delta[!nas];
//int kmax = delta1.size();
for(int pe = 0; pe < npers; pe++)
{
int resp = respvec(pe);
double theta = THETA(pe);
//NumericVector ergP(3);
// NA handling
// if the i,j obs is NA, add nothing
if(IntegerVector::is_na(resp))
{ // in case of missing value as response
continue;
} else
{
NumericVector ergP = P_4pl4wle(delta1, alpha, theta, lowerA, upperA);
// l1
double Qj = 1 - ergP(0);
l1l2M(pe,0) += (resp - ergP(0))/(ergP(0)*Qj) * ergP(1);
l1l2M(pe,1) += ergP(2);
// oberer korrekturterm
l1l2M(pe,2) += ergP(1) * ergP(3) / (ergP(0)*Qj); // ersetzen?!
// unterer korrekturterm
l1l2M(pe,3) += ergP(5);
// I' - w wont need this
//l1l2M(pe,4) += ergP(6);
}
}
}
//std::cout << "J' 1 = " << l1l2M(0,3) << std::endl ;
//std::cout << "J' 2 = " << l1l2M(1,3) << std::endl ;
//
// I * J' - I' * J
//NumericVector corru = (l1l2M(_,1)*l1l2M(_,3) - l1l2M(_,4)*l1l2M(_,2)) / (2 * pow(l1l2M(_,1),2));
NumericVector corru = l1l2M(_,3) / (2 * l1l2M(_,1)*l1l2M(_,1));
l1l2M(_,4) = (l1l2M(_,0) + l1l2M(_,2) / (2*l1l2M(_,1))) / (l1l2M(_,1) + corru);
// Korrekturterm um divergieren zu verhindern:
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,4)) <= 5)
{
continue;
} else {
l1l2M(ai,4) = l1l2M(ai,4)/std::abs(l1l2M(ai,4)) * 5;
}
}
l1l2M(_,5) = THETA + l1l2M(_,4);
//l1l2M(_,1) = l1l2M(_,1) * (-1); // erst jetzt * (-1)
return l1l2M;
}
// [[Rcpp::export]]
NumericMatrix L4pl_robust(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector LOWA, NumericVector UPPA,
NumericVector THETA, double H) {
int npers = awm.nrow();
int nitem = awm.ncol();
int maxca = DELTA.nrow();
// ALPHA muss so lang sein wie nitem anzeigt
// THETA muss so lang sein wie npers anzeigt
// DELTA muss so viele Spalten haben wie nitem anzeigt
// maxca gibt an wieviele maximale kategorien
// 4 columns: 1st deriv of logL; 2nd deriv of logL; delta = 1st/2nd; theta - delta
NumericMatrix l1l2M(npers,4);
for(int it = 0; it < nitem; it++)
{
// Response vector of one item
IntegerVector respvec = awm(_,it);
double alpha = ALPHA(it);
NumericVector delta = DELTA(_,it);
LogicalVector nas(maxca);
double lowerA = LOWA(it);
double upperA = UPPA(it);
// find NA and kill them
for (int fna = 0; fna < maxca; ++fna) {
nas[fna] = NumericVector::is_na(delta[fna]);
}
// parameters without missing values. missing values should only be possible at the end of the matrix
NumericVector delta1 = delta[!nas];
//int kmax = delta1.size();
for(int pe = 0; pe < npers; pe++)
{
int resp = respvec(pe);
double theta = THETA(pe);
NumericVector ergP(3);
// NA handling
// if the i,j obs is NA, add nothing
if(IntegerVector::is_na(resp))
{ // in case of missing value as response
continue;
} else
{
ergP = P_4pl(delta1, alpha, theta, lowerA, upperA);
// compute huber weight
//NumericVector hub = r_huber_4pl(delta=delta1,alpha, theta, lowerA, upperA, H);
double hub = r_huber_4pl(delta=delta1,alpha, theta, lowerA, upperA, H);
// l1
double Qj = 1 - ergP(0);
// huber weighted first deriv and Inf
l1l2M(pe,0) += hub*(resp - ergP(0))/(ergP(0)*Qj) * ergP(1);
//l1l2M(pe,0) += hub(1)*(resp - ergP(0))/(hub(1)*(ergP(0)*Qj)) * ergP(1);
//l1l2M(pe,1) += ergP(2) * hub(1);
l1l2M(pe,1) += ergP(2);
}
}
}
l1l2M(_,1) = l1l2M(_,1) * (-1);
//l1l2M(_,1) = l1l2M(_,1);
l1l2M(_,2) = l1l2M(_,0)/l1l2M(_,1);
// Korrekturterm um divergieren zu verhindern:
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,2)) <= 5)
{
continue;
} else {
l1l2M(ai,2) = l1l2M(ai,2)/std::abs(l1l2M(ai,2)) * 5;
}
}
l1l2M(_,3) = THETA - l1l2M(_,2);
//std::cout << "l1 = " << l1l2M(6,0) << std::endl ;
return l1l2M;
}
// NR - Algorithm --->>> MLE + WLE + MAP + robust <<<<---- +++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
List NR_4PL(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector LOWA, NumericVector UPPA, NumericVector THETA, String wm,
int maxsteps, double exac, NumericVector mu, NumericVector sigma2, double H) {
int npers = awm.nrow();
NumericVector THETAC = Rcpp::clone(THETA);
NumericMatrix resPP(npers,2);
int howlong;
if(wm == "wle")
{
for(int newr = 0; newr < maxsteps; newr++)
{
NumericMatrix reso = L4pl_wle(awm,DELTA,ALPHA,LOWA,UPPA,THETAC);
THETAC = reso(_,5);
NumericVector diffs = reso(_,4);
LogicalVector bxy = is_na(THETAC);
NumericVector diffs1 = diffs[!bxy];
if( (is_true(all(abs(diffs1) < exac))) | (newr == (maxsteps-1)))
{
resPP(_,0) = THETAC;
//resPP(_,1) = pow(1/reso(_,1),0.5); // thank you solaris
resPP(_,1) = 1/reso(_,1);
howlong = newr + 1;
break;
}
}
} else if(wm == "mle")
{
bool map = FALSE;
for(int newr = 0; newr < maxsteps; newr++)
{
NumericMatrix reso = L4pl(awm,DELTA,ALPHA,LOWA,UPPA,THETAC,map,mu,sigma2);
THETAC = reso(_,3);
NumericVector diffs = reso(_,2);
LogicalVector bxy = is_na(THETAC);
NumericVector diffs1 = diffs[!bxy];
if( (is_true(all(abs(diffs1) < exac))) | (newr == (maxsteps-1)))
{
resPP(_,0) = THETAC;
resPP(_,1) = 1/reso(_,1)*(-1);
howlong = newr + 1;
break;
}
}
} else if(wm == "map")
{
bool map = TRUE;
for(int newr = 0; newr < maxsteps; newr++)
{
NumericMatrix reso = L4pl(awm,DELTA,ALPHA,LOWA,UPPA,THETAC,map,mu,sigma2);
THETAC = reso(_,3);
NumericVector diffs = reso(_,2);
LogicalVector bxy = is_na(THETAC);
NumericVector diffs1 = diffs[!bxy];
if( (is_true(all(abs(diffs1) < exac))) | (newr == (maxsteps-1)))
{
resPP(_,0) = THETAC;
resPP(_,1) = 1/reso(_,1)*(-1);
howlong = newr + 1;
break;
}
}
} else if(wm == "robust")
{
for(int newr = 0; newr < maxsteps; newr++)
{
NumericMatrix reso = L4pl_robust(awm,DELTA,ALPHA,LOWA,UPPA,THETAC,H);
THETAC = reso(_,3);
NumericVector diffs = reso(_,2);
LogicalVector bxy = is_na(THETAC);
NumericVector diffs1 = diffs[!bxy];
if( (is_true(all(abs(diffs1) < exac))) | (newr == (maxsteps-1)))
{
resPP(_,0) = THETAC;
resPP(_,1) = 1/reso(_,1)*(-1);
howlong = newr + 1;
break;
}
}
}
// ----
return List::create(_["resPP"] = resPP, _["nsteps"] = howlong);
}
// GPCM Stuff ***************************************************************************************
// P FUNCTION +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
double P_gpcm(NumericVector delta, double alpha, double theta, int resp) {
int nthres = delta.size();
double nenner = 0;
double zae = 0;
for(int aus = 0; aus < nthres; aus++)
{
double imex = 0;
for(int i = 0; i < aus+1; i++)
{
imex += alpha * (theta - delta(i));
}
nenner += exp(imex);
}
for(int cat = 0; cat < resp+1; cat++)
{
zae += alpha * (theta - delta(cat));
}
double P = exp(zae) / nenner;
return P;
}
// [[Rcpp::export]]
double r_huber_gpcm(NumericVector delta, double alpha,
double theta, double H) {
int nthres = delta.size();
//double zae = 0;
int nthresm1 = nthres - 1;
//double deltaw0 = delta(-0);
double resid = 0;
double HU = 0;
// compute residuum
// dont start with the first - because this is always zero!
for(int ru = 1; ru < nthres; ru++)
{
resid += alpha * (theta - delta(ru))/nthresm1;
}
// compute Huber weight
if(resid < 0)
{
resid = resid * (-1);
}
if(resid <= H)
{
HU = 1;
} else
{
HU = H/resid;
}
//std::cout << "hu = " << HU << std::endl ;
return HU;
}
// P FUNCTION L1, L2 +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericMatrix L12gpcm(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector THETA, NumericVector mu, NumericVector sigma2, bool map) {
// awm = antwortmatrix
//
int npers = awm.nrow();
int nitem = awm.ncol();
int maxca = DELTA.nrow();
// ALPHA muss so lang sein wie nitem anzeigt
// THETA muss so lang sein wie npers anzeigt
// DELTA muss so viele Spalten haben wie nitem anzeigt
// maxca gibt an wieviele maximale kategorien
// l1 fuer die personen
//NumericVector l1vec(npers);
//NumericVector l2vec(npers);
// 4 columns: 1st deriv of logL; 2nd deriv of logL; delta = 1st/2nd; theta - delta
NumericMatrix l1l2M(npers,4);
for(int it = 0; it < nitem; it++)
{
// Response vector of one item
IntegerVector respvec = awm(_,it);
double alpha = ALPHA(it);
NumericVector delta = DELTA(_,it);
LogicalVector nas(maxca);
// find NA and kill them
for (int fna = 0; fna < maxca; ++fna) {
nas[fna] = NumericVector::is_na(delta[fna]);
}
// parameters without missing values. missing values should only be possible at the end of the matrix
NumericVector delta1 = delta[!nas];
int kmax = delta1.size();
for(int pe = 0; pe < npers; pe++)
{
int resp = respvec(pe);
double theta = THETA(pe);
// NA handling
// if the i,j obs is NA, add nothing
if(IntegerVector::is_na(resp))
{
continue;
// jumps to next iteration step
// l1l2M(pe,0) += 0;
// l1l2M(pe,1) += 0;
} else
{
// rattert die ks durch
double rs = 0;
double rs2 = 0;
double ls2 = 0;
double ergP = 0;
for(int ks = 0; ks < kmax; ks++)
{
ergP = P_gpcm(delta1, alpha, theta, ks);
rs += ks * alpha * ergP;
// second derivates right and left side
rs2 += ks * alpha * ergP;
//ls2 += pow(ks,2) * pow(alpha,2) * ergP;
ls2 += ks*ks * alpha*alpha * ergP;
}
rs2 = rs2*rs2;
// write first and second derivs in 2 column matrix - for each person
l1l2M(pe,0) += resp * alpha - rs;
l1l2M(pe,1) += ls2 - rs2;
}
// double showme = l1l2M(pe,0); // weg
// std::cout << "l1 = " << showme << std::endl ; // weg
}
}
if(map)
{
NumericVector corrterm1(npers);
NumericVector corrterm2(npers);
corrterm1 = (THETA - mu)/sigma2;
corrterm2 = 1/sigma2;
l1l2M(_,1) = l1l2M(_,1) * (-1);
l1l2M(_,2) = (l1l2M(_,0) - corrterm1) / (l1l2M(_,1)-corrterm2);
// Korrekturterm um divergieren zu verhindern:
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,2)) <= 5)
{
continue;
} else {
l1l2M(ai,2) = l1l2M(ai,2)/std::abs(l1l2M(ai,2)) * 5;
}
}
l1l2M(_,3) = THETA - l1l2M(_,2);
} else
{
l1l2M(_,1) = l1l2M(_,1) * (-1);
l1l2M(_,2) = l1l2M(_,0)/l1l2M(_,1);
// Korrekturterm um divergieren zu verhindern:
for(int ai = 0; ai<npers; ai++)
{
if(std::abs(l1l2M(ai,2)) <= 5)
{
continue;
} else {
l1l2M(ai,2) = l1l2M(ai,2)/std::abs(l1l2M(ai,2)) * 5;
}
}
l1l2M(_,3) = THETA - l1l2M(_,2);
}
return l1l2M;
}
// CORRECTION TERM FUNCTION +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericVector Pcorr1_gpcm(NumericVector delta, double alpha, double theta) {
int nthres = delta.size();
// double which will contain the sum of weighted probs
double overac = 0;
double overac2 = 0;
double overac3 = 0;
NumericVector ps(nthres);
NumericVector fds(nthres);
NumericVector sds(nthres);
NumericVector tds(nthres);
// Probs for each category
for(int i = 0; i < nthres; i++)
{
ps(i) = P_gpcm(delta, alpha, theta, i);
}
for(int i = 0; i < nthres; i++)
{
//overac += i * P_gpcm(delta, alpha, theta, i);
overac += i * ps(i);
}
// first derivs of P for each category
for(int i = 0; i < nthres; i++)
{
fds(i) = alpha * P_gpcm(delta, alpha, theta, i) * (i - overac);
}
// second derivates of P for each category
for(int i = 0; i < nthres; i++)
{
//overac2 += i * alpha * P_gpcm(delta, alpha, theta, i) * (i - overac);
overac2 += i * fds(i);
}
for(int i = 0; i < nthres; i++)
{
//sds(i) = alpha * fds(i) * (i - overac) + alpha * P_gpcm(delta, alpha, theta, i) * overac2;
sds(i) = alpha * fds(i) * (i - overac) - alpha * P_gpcm(delta, alpha, theta, i) * overac2;
}
// information
NumericVector corrts(3); //corrterm1 und INF
double INF = alpha * overac2;
//double INF = sum(-sds * ps);
//double INF = sum(pow(fds,2)/ps);
//NumericVector corrts(2);
// compute correction term
//double corrts = sum(fds * sds / ps)/(2*INF);
corrts(0) = sum(fds * sds / ps);
corrts(1) = INF;
// *******************************
// compute the first derivates of the correction term
// *******************************
// P - third deriv
for(int i = 0; i < nthres; i++)
{
overac3 += i * sds(i);
}
for(int i = 0; i < nthres; i++)
{
//tds(i) = alpha * sds(i) * (i - overac) + alpha*fds(i)*overac2 + alpha*fds(i) * overac2 + alpha*ps(i) * overac3;
tds(i) = alpha * sds(i) * (i - overac) - alpha*fds(i)*overac2 - alpha*fds(i) * overac2 + alpha*ps(i) * overac3;
}
double INF2 = alpha * overac3;
corrts(2) = sum((INF * fds * sds * fds - ps * (fds * (INF * tds - sds * INF2) + INF * sds *sds))/(ps*ps));
return corrts;
}
// P FUNCTION L1, L2 --->>> WLE <<<<---- +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
// [[Rcpp::export]]
NumericMatrix L12gpcm_wle(IntegerMatrix awm, NumericMatrix DELTA, NumericVector ALPHA,
NumericVector THETA) {
// awm = antwortmatrix
//
int npers = awm.nrow();
int nitem = awm.ncol();
int maxca = DELTA.nrow();
// ALPHA muss so lang sein wie nitem anzeigt
// THETA muss so lang sein wie npers anzeigt
// DELTA muss so viele Spalten haben wie nitem anzeigt
// maxca gibt an wieviele maximale kategorien
// l1 fuer die personen
//NumericVector l1vec(npers);
//NumericVector l2vec(npers);
//
NumericMatrix l1l2M(npers,6);
NumericVector ct(npers); //weg
for(int it = 0; it < nitem; it++)
{
// Response vector of one item
IntegerVector respvec = awm(_,it);
double alpha = ALPHA(it);
NumericVector delta = DELTA(_,it);
LogicalVector nas(maxca);
// find NA and kill them
for (int fna = 0; fna < maxca; fna++) {
nas[fna] = NumericVector::is_na(delta[fna]);
}
// parameters without missing values. missing values should only be possible at the end of the matrix
NumericVector delta1 = delta[!nas];
int kmax = delta1.size();
for(int pe = 0; pe < npers; pe++)
{
int resp = respvec(pe);
double theta = THETA(pe);
// NA handling
// if the i,j obs is NA, add nothing
if(IntegerVector::is_na(resp))
{
continue;
// jumps to next iteration step
// l1l2M(pe,0) += 0;
// l1l2M(pe,1) += 0;
} else
{
// rattert die ks durch
double rs = 0;
double rs2 = 0;
double ls2 = 0;
double ergP = 0;
for(int ks = 0; ks < kmax; ks++)
{
ergP = P_gpcm(delta1, alpha, theta, ks);
rs += ks * alpha * ergP;
// second derivates right and left side
rs2 += ks * alpha * ergP;
//ls2 += pow(ks,2) * pow(alpha,2) * ergP;
ls2 += ks*ks * alpha*alpha * ergP;
}
rs2 = rs2*rs2;
// Pcorr2_gpcm(NumericVector delta, double alpha, double theta)
// ********** VERSION 1
NumericVector ct = Pcorr1_gpcm(delta1,alpha,theta);
l1l2M(pe,1) += ct(1); // summierte information
l1l2M(pe,2) += ct(0); // summiert korrekturterm - korrekturterm oben
//l1l2M(pe,3) += ct(1); // summierte information
l1l2M(pe,3) += ct(2); // unterer korrekturterm
// *********************