public static double MWI_Calc(CATItems itemBank, int item, int[] x, CATItems it_given, string model, int type = 1 /* MLWI */, double[] priorPar = null, double D = 1, string priorDist = "norm", int lower = -4, int upper = 4, int nqp = 33)
{
double res = 0;
if (priorPar == null || priorPar.Length < 2)
{
priorPar = new double[2];
priorPar[0] = 0;
priorPar[1] = 1;
}
if (type != (int)ModelNames.MWI_Type.MLWI && type != (int)ModelNames.MWI_Type.MPWI)
{
return(res);
}
else
{
double[] lik = null; double[] info = null; double[] crit_value = null;
double[] X = CatRcs.Utils.CommonHelper.Sequence(lower, upper, nqp);
if (String.IsNullOrEmpty(model)) // Dichotomous Items
{
#region "Function 'L' "
Func <double, int[], CATItems, double> L = (th, x_in, items) =>
{
double result = 0;
var temp_1 = Pi.Pi_Calc(th, it_given, model, D).Pi.Select((p, i) => Math.Pow(p, x_in[i])).ToArray();
var temp_2 = Pi.Pi_Calc(th, it_given, model, D).Pi.Select((p, i) => Math.Pow(1 - p, 1 - x_in[i])).ToArray();
if (temp_1.Length == temp_2.Length)
{
var temp_3 = temp_1.Select((p, i) => p * temp_2[i]).ToArray();
result = temp_3.Aggregate((acc, val) => acc * val);
}
return(result);
};
#endregion
lik = X.Select((a, i) => L(a, x, it_given)).ToArray(); // "sapply" function shortcut using LINQ
info = X.Select(b => Ii.Ii_Calc(b, itemBank, model, D).Ii[item - 1]).ToArray();
crit_value = lik.Select((c, j) => c * info[j]).ToArray();
}
else // Polytomous Items
{
#region "Function 'LL' "
Func <double, CATItems, int[], double> LL = (th, items, x_in) =>
{
double result = 0;
if (it_given.colSize == 0)
{
result = 1;
}
else
{
result = 1;
double[,] prob = Pi.Pi_Poly_Calc(th, it_given, model, D).Pi;
for (int i = 0; i < x_in.Length; i++)
{
res = res * prob[i, x[i]];
}
}
return(result);
};
#endregion
lik = X.Select((a, i) => LL(a, it_given, x)).ToArray();
CATItems temp_ItemBank = itemBank.FindItem(item);
info = X.Select(b => CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(b, temp_ItemBank, model, D).Ii)).ToArray();
crit_value = lik.Select((c, j) => c * info[j]).ToArray();
}
if (lik.Length > 0 && info.Length > 0)
{
if (type == (int)ModelNames.MWI_Type.MPWI)
{
double[] pd = new double[X.Length];
for (int i = 0; i < X.Length; i++)
{
switch (priorDist)
{
case "norm":
pd[i] = CatRcs.Utils.CommonHelper.Dnorm(X[i], priorPar[0], priorPar[1]);
break;
case "unif":
pd[i] = CatRcs.Utils.CommonHelper.Dunif(X[i], priorPar[0], priorPar[1]);
break;
}
}
crit_value = crit_value.Select((d, k) => d * pd[k]).ToArray();
}
res = CatRcs.Integrate_catR.Integrate_CatR_Calc(X, crit_value);
}
}
return(res);
}
public static double EapEST_Calc(CATItems it, int[] x, string model, double[] priorPar = null, double D = 1, string priorDist = "norm", double lower = -4, double upper = 4, double nqp = 33)
{
double res = 0;
double[] X = CatRcs.Utils.CommonHelper.Sequence(lower, upper, nqp);
double[] Y1 = null; double[] Y2 = null;
if (priorPar == null || priorPar.Length < 2)
{
priorPar = new double[2];
priorPar[0] = 0;
priorPar[1] = 1;
}
if (String.IsNullOrEmpty(model)) // Dichotomous Items
{
#region "Function 'L' "
Func <double, CATItems, int[], double> L = (th, items, x_in) =>
{
double result = 0;
double[] pi = Pi.Pi_Calc(th, it, model, D).Pi;
double[] x_p = new double[pi.Length]; double[] x_q = new double[pi.Length]; double[] p_q = new double[pi.Length];
for (int ind_p = 0; ind_p < pi.Length; ind_p++)
{
x_p[ind_p] = Math.Pow(pi[ind_p], x_in[ind_p]);;
x_q[ind_p] = Math.Pow(1 - pi[ind_p], 1 - x_in[ind_p]);
p_q[ind_p] = x_p[ind_p] * x_q[ind_p];
}
result = p_q.Aggregate((acc, val) => acc * val);
return(result);
};
#endregion
#region "Function 'g' "
Func <double[], double[]> g = (s) =>
{
double[] resList = new double[s.Length];
for (int i = 0; i < s.Length; i++)
{
switch (priorDist)
{
case "norm":
resList[i] = s[i] * CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "unif":
resList[i] = s[i] * CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "Jeffreys":
resList[i] = s[i] * Math.Sqrt(CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(s[i], it, model, D).Ii)) * L(s[i], it, x);
break;
}
}
return(resList);
};
#endregion
#region "Function 'h' "
Func <double[], double[]> h = (s) =>
{
double[] resList = new double[s.Length];
for (int i = 0; i < s.Length; i++)
{
switch (priorDist)
{
case "norm":
resList[i] = CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "unif":
resList[i] = CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "Jeffreys":
resList[i] = Math.Sqrt(CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(s[i], it, model, D).Ii)) * L(s[i], it, x);
break;
}
}
return(resList);
};
#endregion
Y1 = g(X);
Y2 = h(X);
}
else // Polytomous Items
{
#region "Function 'LL' "
Func <double, CATItems, int[], double> LL = (th, items, x_in) =>
{
double result = 1;
double[,] prob = Pi.Pi_Poly_Calc(th, it, model, D).Pi;
for (int i = 0; i < x_in.Length; i++)
{
result = result * prob[i, x_in[i]];
}
return(result);
};
#endregion
#region "Function 'gg' "
Func <double[], double[]> gg = (s) =>
{
double[] resList = new double[s.Length];
for (int i = 0; i < s.Length; i++)
{
switch (priorDist)
{
case "norm":
resList[i] = s[i] * CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "unif":
resList[i] = s[i] * CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "Jeffreys":
resList[i] = s[i] * Math.Sqrt(CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(s[i], it, model, D).Ii)) * LL(s[i], it, x);
break;
}
}
return(resList);
};
#endregion
#region "Function 'hh' "
Func <double[], double[]> hh = (s) =>
{
double[] resList = new double[s.Length];
for (int i = 0; i < s.Length; i++)
{
switch (priorDist)
{
case "norm":
resList[i] = CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "unif":
resList[i] = CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "Jeffreys":
resList[i] = Math.Sqrt(CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(s[i], it, model, D).Ii)) * LL(s[i], it, x);
break;
}
}
return(resList);
};
#endregion
Y1 = gg(X);
Y2 = hh(X);
}
if ((Y1 != null) && (Y2 != null))
{
res = CatRcs.Integrate_catR.Integrate_CatR_Calc(X, Y1) / CatRcs.Integrate_catR.Integrate_CatR_Calc(X, Y2);
}
return(res);
}
public static JiList Ji_Calc(double th, CATItems it, string model, double D)
{
JiList objJi = null;
double[] Ji = null; double[] dJi = null;
try
{
if (String.IsNullOrEmpty(model))
{
#region "Calculation for Dichotmous Items"
PiList pr = Pi.Pi_Calc(th, it, model, D);
if (pr == null)
{
objJi = new JiList();
objJi.Exception = "No Pi values found!";
return(objJi);
}
double[] P = pr.Pi; double[] dP = pr.dPi; double[] d2P = pr.d2Pi; double[] d3P = pr.d3Pi;
Ji = new double[dP.Length];
dJi = new double[d2P.Length];
objJi = new JiList(P.Length);
double[] Q = new double[P.Length];
for (int i = 0; i < P.Length; i++)
{
Q[i] = 1 - P[i];
}
for (int j = 0; j < Ji.Length; j++)
{
Ji[j] = dP[j] * d2P[j] / (P[j] * Q[j]);
}
for (int k = 0; k < dJi.Length; k++)
{
dJi[k] = (P[k] * Q[k] * (Math.Pow(d2P[k], 2) + dP[k] * d3P[k]) - Math.Pow(dP[k], 2) * d2P[k] * (Q[k] - P[k])) / (Math.Pow(P[k], 2) * Math.Pow(Q[k], 2));
}
#endregion
}
else
{
#region "Calculation for Polytomous Items"
PiListPoly pr = Pi.Pi_Poly_Calc(th, it, model, D);
if (pr == null)
{
objJi = new JiList();
objJi.Exception = "No Pi values found!";
return(objJi);
}
double[,] P = pr.Pi; double[,] dP = pr.dPi; double[,] d2P = pr.d2Pi; double[,] d3P = pr.d3Pi;
int rowLength = pr.Pi.GetLength(0);
int columnLength = pr.Pi.GetLength(1);
objJi = new JiList(rowLength);
double[,] prov = new double[rowLength, columnLength];
double[,] prov1 = new double[rowLength, columnLength];
Ji = new double[rowLength];
dJi = new double[rowLength];
for (int i = 0; i < rowLength; i++)
{
for (int j = 0; j < columnLength; j++)
{
prov[i, j] = dP[i, j] * d2P[i, j] / P[i, j];
prov1[i, j] = (P[i, j] * Math.Pow(d2P[i, j], 2) + P[i, j] * dP[i, j] * d3P[i, j] - Math.Pow(dP[i, j], 2) * d2P[i, j]) / Math.Pow(P[i, j], 2);
}
}
Ji = RowColumn.rowSums(prov);
dJi = RowColumn.rowSums(prov1);
#endregion
}
objJi.Add(Ji, dJi);
}
catch (Exception ex)
{
if (ex != null)
{
if (objJi == null)
{
objJi = new JiList();
}
objJi.Exception = ex.Message;
}
return(objJi);
}
return(objJi);
}
