public static double ThetaEst_Calc(CATItems it, int[] x, string model = null, double[] priorPar = null, double[] range = null, int[] parInt = null, double D = 1, string method = "BM", string priorDist = "norm")
{
double result = 0; double[] RANGE = null;
#region "Parameter Validation"
if (priorPar == null || priorPar.Length < 2)
{
priorPar = new double[2];
priorPar[0] = 0;
priorPar[1] = 1;
}
if (range == null || range.Length < 2)
{
range = new double[2];
range[0] = -4;
range[1] = 4;
}
if (parInt == null || parInt.Length < 3)
{
parInt = new int[3];
parInt[0] = -4;
parInt[1] = 4;
parInt[2] = 33;
}
#endregion
if (method == ModelNames.EstimaatorMethods.EAP.EnumToString())
{
result = EapEST.EapEST_Calc(it, x, model, priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
}
else
{
if (String.IsNullOrEmpty(model)) // Dichotomous Items
{
#region "Function 'r0' "
Func <double, string, double> r0 = (th, met) =>
{
double res = 0;
if (met == ModelNames.EstimaatorMethods.BM.EnumToString())
{
switch (priorDist)
{
case "norm":
res = (priorPar[0] - th) / Math.Pow(priorPar[1], 2);
break;
case "unif":
res = 0;
break;
case "Jeffreys":
IiList objIi = Ii.Ii_Calc(th, it, model, D);
res = CatRcs.Utils.RowColumn.Sum(objIi.dIi) / (2 * CatRcs.Utils.RowColumn.Sum(objIi.Ii));
break;
}
}
else
{
ModelNames.EstimaatorMethods md = ModelNames.StringToEnumMethods(met);
switch (md)
{
case ModelNames.EstimaatorMethods.ML:
res = 0;
break;
case ModelNames.EstimaatorMethods.WL:
res = CatRcs.Utils.RowColumn.Sum(Ji.Ji_Calc(th, it, model, D).Ji) / (2 * CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(th, it, model, D).Ii));
break;
}
}
return(res);
};
#endregion
#region "Function 'r' "
Func <double, double> r = (th) =>
{
double res = 0;
double[] Q = new double[it.NumOfItems], x_p = new double[it.NumOfItems], p_q = new double[it.NumOfItems], temp = new double[it.NumOfItems];
double[] pi = Pi.Pi_Calc(th, it, model, D).Pi;
double[] dpi = Pi.Pi_Calc(th, it, model, D).dPi;
for (int ind_p = 0; ind_p < pi.Length; ind_p++)
{
Q[ind_p] = 1 - pi[ind_p];
x_p[ind_p] = x[ind_p] - pi[ind_p];
p_q[ind_p] = pi[ind_p] * Q[ind_p];
temp[ind_p] = dpi[ind_p] * (x_p[ind_p] / p_q[ind_p]);
}
res = temp.Sum();
return(res);
};
#endregion
#region "Function 'f' "
Func <double, double> f = (th) =>
{
double res = 0;
return(res);
};
if (method == ModelNames.EstimaatorMethods.BM.EnumToString() && priorDist == "unif")
{
f = (th) =>
{
double res = 0;
string methodName = ModelNames.EstimaatorMethods.ML.EnumToString();
res = r0(th, methodName) + r(th);
return(res);
};
}
else
{
f = (th) =>
{
double res = 0;
res = r0(th, method) + r(th);
return(res);
};
}
#endregion
if (method == ModelNames.EstimaatorMethods.BM.EnumToString() && priorDist == "unif")
{
RANGE = priorPar;
}
else
{
RANGE = range;
}
if (f(RANGE[0]) < 0 && f(RANGE[1]) < 0)
{
result = RANGE[0];
}
else
{
if (f(RANGE[0]) > 0 && f(RANGE[1]) > 0)
{
result = RANGE[1];
}
else
{
result = CatRcs.Utils.Maths.UniRoot(f, RANGE).root;
}
}
}
else // Polytomous Items
{
int met = 0, pd = 0;
ModelNames.EstimaatorMethods md = ModelNames.StringToEnumMethods(method);
#region "Conditional Block"
switch (md)
{
case ModelNames.EstimaatorMethods.ML:
met = 1;
break;
case ModelNames.EstimaatorMethods.BM:
met = 2;
break;
case ModelNames.EstimaatorMethods.WL:
met = 3;
break;
case ModelNames.EstimaatorMethods.EAP:
met = 4;
break;
}
switch (priorDist)
{
case "norm":
pd = 1;
break;
case "unif":
pd = 2;
break;
case "Jeffreys":
pd = 3;
break;
}
if (met == 2 && pd == 2)
{
RANGE = new double[priorPar.Length];
RANGE[0] = Math.Max(priorPar[0], range[0]);
RANGE[1] = Math.Min(priorPar[1], range[1]);
}
else
{
RANGE = range;
}
#endregion
#region "Function 'dl' "
Func <double, double> dl = (th) =>
{
double res = 0;
PiListPoly p = Pi.Pi_Poly_Calc(th, it, model, D);
double[,] pr = p.Pi;
double[,] dpr = p.dPi;
for (int i = 0; i < x.Length; i++)
{
res = res + dpr[i, x[i]] / pr[i, x[i]];
}
return(res);
};
#endregion
#region "Function 'f0' "
Func <double, double> f0 = (th) =>
{
double res = 0;
if (met == 2)
{
switch (pd.ToString())
{
case "1":
res = (priorPar[0] - th) / Math.Pow(priorPar[1], 2);
break;
case "2":
res = 0;
break;
case "3":
IiList objIi = CatRcs.Ii.Ii_Calc(th, it, model, D);
res = CatRcs.Utils.RowColumn.Sum(objIi.dIi) / (2 * CatRcs.Utils.RowColumn.Sum(objIi.Ii));
break;
}
}
else
{
switch (met.ToString())
{
case "1":
res = 0;
break;
case "2":
res = 0;
break;
case "3":
res = CatRcs.Utils.RowColumn.Sum(CatRcs.Ji.Ji_Calc(th, it, model, D).Ji) / (2 * CatRcs.Utils.RowColumn.Sum(CatRcs.Ii.Ii_Calc(th, it, model, D).Ii));
break;
}
}
return(res);
};
#endregion
#region "Function 'optF' "
Func <double, double> optF = (th) =>
{
double res = 0;
res = dl(th) + f0(th);
return(res);
};
#endregion
if (optF(RANGE[0]) < 0 && optF(RANGE[1]) < 0)
{
result = RANGE[0];
}
else
{
if (optF(RANGE[0]) > 0 && optF(RANGE[1]) > 0)
{
result = RANGE[1];
}
else
{
result = CatRcs.Utils.Maths.UniRoot(optF, RANGE).root;
}
}
}
}
return(result);
}
// Optimized CAT Items
public static double EPV_Calc(CATItems itemBank, int item, int[] x, double theta, CATItems it_given, string model, double[] priorPar = null, int[] parInt = null, double D = 1, string priorDist = "norm")
{
double res = 0;
double th = theta;
if (priorPar == null || priorPar.Length < 2)
{
priorPar = new double[2];
priorPar[0] = 0;
priorPar[1] = 1;
}
if (parInt == null || parInt.Length < 3)
{
parInt = new int[3];
parInt[0] = -4;
parInt[1] = 4;
parInt[2] = 33;
}
if (String.IsNullOrEmpty(model)) // Dichotomous Items
{
CATItems itj = itemBank.AddItem_D(it_given, new int[] { item });
double p1 = Pi.Pi_Calc(th, itemBank, model, D).Pi[item - 1]; // item is matched with the array index
double p0 = 1 - p1;
int[] temp_x = new int[x.Length + 1];
for (int i = 0; i < x.Length; i++)
{
temp_x[i] = x[i];
}
temp_x[x.Length - 1] = 0;
double th0 = EapEST.EapEST_Calc(itj, temp_x, "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
double var0 = Math.Pow(EapSEM.EapSEM_Calc(th0, itj, temp_x, "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]), 2);
temp_x = new int[x.Length + 1];
for (int i = 0; i < x.Length; i++)
{
temp_x[i] = x[i];
}
temp_x[x.Length - 1] = 1;
double th1 = EapEST.EapEST_Calc(itj, temp_x, "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
double var1 = Math.Pow(EapSEM.EapSEM_Calc(th1, itj, temp_x, "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]), 2);
res = (p0 * var0) + (p1 * var1);
}
else // Polytomous Items !!!! Optimization needed !!!!
{
double[,] temp_Pi = Pi.Pi_Poly_Calc(th, itemBank, model, D).Pi; // Already returns a NA free list of values.
// !! Optimize !!
List <double> probs = new List <double>();
for (int i = 0; i < temp_Pi.GetLength(1); i++)
{
probs.Add(temp_Pi[0, i]);
}
// !!!! Add new method for polytomous items !!!!
CATItems it_new = it_given;
double[] th_new = new double[probs.Count];
double[] se_new = new double[probs.Count];
List <int> temp_x = new List <int>();
for (int j = 0; j < probs.Count; j++)
{
temp_x = x.ToList();
temp_x.Add(j);
th_new[j] = EapEST.EapEST_Calc(it_new, temp_x.ToArray(), "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
se_new[j] = Math.Pow(EapSEM.EapSEM_Calc(th_new[j], it_new, temp_x.ToArray(), "", priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]), 2);
}
res = CatRcs.Utils.RowColumn.Sum(probs.Select((p, s) => p * se_new[s]).ToArray());
}
return(res);
}
