public static double SemTheta_Calc(double thEst, CATItems it, int[] x = null, string model = null, double[] priorPar = null, int[] parInt = null, double D = 1, string method = "BM", string priorDist = "norm")
{
double result = 0;
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 (method == ModelNames.EstimaatorMethods.EAP.EnumToString())
{
result = EapSEM.EapSEM_Calc(thEst, it, x, model, priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
}
else
{
if (String.IsNullOrEmpty(model)) // Dichotomous Items
{
#region "Function 'dr0' "
Func <double> dr0 = () =>
{
double res = 0;
if (method == ModelNames.EstimaatorMethods.BM.EnumToString())
{
switch (priorDist)
{
case "norm":
res = -1 / (Math.Pow(priorPar[1], 2));
break;
case "unif":
res = 0;
break;
case "Jeffreys":
IiList objIi = Ii.Ii_Calc(thEst, it, model, D);
res = (CatRcs.Utils.RowColumn.Sum(objIi.d2Ii) * CatRcs.Utils.RowColumn.Sum(objIi.Ii)
- Math.Pow(CatRcs.Utils.RowColumn.Sum(objIi.dIi), 2)) / (2 * Math.Pow(CatRcs.Utils.RowColumn.Sum(objIi.Ii), 2));
break;
}
}
else
{
if (method == ModelNames.EstimaatorMethods.ML.EnumToString() || method == ModelNames.EstimaatorMethods.WL.EnumToString())
{
res = 0;
}
}
return(res);
};
#endregion
result = 1 / Math.Sqrt(-dr0() + CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(thEst, it, model, D).Ii));
}
else // Polytomous Items
{
double met = 0, pd = 0, optI = 0;
ModelNames.EstimaatorMethods md = ModelNames.StringToEnumMethods(method);
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 == 1 || (met == 2 && pd == 2))
{
optI = CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(thEst, it, model, D).Ii);
}
if (met == 2 && pd == 1)
{
optI = CatRcs.Utils.RowColumn.Sum(Ii.Ii_Calc(thEst, it, model, D).Ii) + (1 / Math.Pow(priorPar[1], 2));
}
if (met == 3 || (met == 2 && pd == 3))
{
IiList objIi = Ii.Ii_Calc(thEst, it, model, D);
if (met == 2)
{
optI = CatRcs.Utils.RowColumn.Sum(objIi.Ii) + (Math.Pow(CatRcs.Utils.RowColumn.Sum(objIi.dIi), 2) - CatRcs.Utils.RowColumn.Sum(objIi.d2Ii) *
CatRcs.Utils.RowColumn.Sum(objIi.Ii)) / (2 * Math.Pow(CatRcs.Utils.RowColumn.Sum(objIi.Ii), 2));
}
else
{
optI = CatRcs.Utils.RowColumn.Sum(objIi.Ii);
}
}
result = 1 / Math.Sqrt(optI);
}
}
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);
}