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);
}
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);
}
internal static double EapSEM_Calc(double thEst, 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] = Math.Pow(s[i] - thEst, 2) * CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "unif":
resList[i] = Math.Pow(s[i] - thEst, 2) * CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * L(s[i], it, x);
break;
case "Jeffreys":
resList[i] = Math.Pow(s[i] - thEst, 2) * 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] = Math.Pow(s[i] - thEst, 2) * CatRcs.Utils.CommonHelper.Dnorm(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "unif":
resList[i] = Math.Pow(s[i] - thEst, 2) * CatRcs.Utils.CommonHelper.Dunif(s[i], priorPar[0], priorPar[1]) * LL(s[i], it, x);
break;
case "Jeffreys":
resList[i] = Math.Pow(s[i] - thEst, 2) * 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 = Math.Sqrt(CatRcs.Integrate_catR.Integrate_CatR_Calc(X, Y1) / CatRcs.Integrate_catR.Integrate_CatR_Calc(X, Y2));
}
return(res);
}
// Function for calculating Next Item
public static NextItemModel NextItem_Calc(CATItems itemBank, string model = null, double theta = 0, int[] Out = null, int[] x = null, int criterion = 5, /* MFI */ string method = "BM",
string priorDist = "norm", double[] priorPar = null, double D = 1, double[] range = null, int[] parInt = null, int infoType = 2, /* observed */ int randomesque = 1, int rule = 1, /* Length */
double thr = 20, double?SETH = null, double AP = 1, int[] nAvailable = null, int maxItems = 50, CBControlList cbControl = null, string[] cbGroup = null)
{
CATItems par = null;
NextItemModel result = 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;
}
ModelNames.CriterionTypes?crit = null;
switch (criterion)
{
case (int)ModelNames.CriterionTypes.bOpt:
crit = ModelNames.CriterionTypes.bOpt;
break;
case (int)ModelNames.CriterionTypes.thOpt:
crit = ModelNames.CriterionTypes.thOpt;
break;
case (int)ModelNames.CriterionTypes.KL:
crit = ModelNames.CriterionTypes.KL;
break;
case (int)ModelNames.CriterionTypes.KLP:
crit = ModelNames.CriterionTypes.KLP;
break;
case (int)ModelNames.CriterionTypes.MEI:
crit = ModelNames.CriterionTypes.MEI;
break;
case (int)ModelNames.CriterionTypes.MEPV:
crit = ModelNames.CriterionTypes.MEPV;
break;
case (int)ModelNames.CriterionTypes.MFI:
crit = ModelNames.CriterionTypes.MFI;
break;
case (int)ModelNames.CriterionTypes.MLWI:
crit = ModelNames.CriterionTypes.MLWI;
break;
case (int)ModelNames.CriterionTypes.MPWI:
crit = ModelNames.CriterionTypes.MPWI;
break;
case (int)ModelNames.CriterionTypes.progressive:
crit = ModelNames.CriterionTypes.progressive;
break;
case (int)ModelNames.CriterionTypes.proportional:
crit = ModelNames.CriterionTypes.proportional;
break;
case (int)ModelNames.CriterionTypes.random:
crit = ModelNames.CriterionTypes.random;
break;
}
if (crit == null)
{
result = new NextItemModel(true, "Invalid 'criterion' name!");
return(result);
}
int mod = 0;
ModelNames.Models modelEnum = ModelNames.StringToEnum(model);
if (!String.IsNullOrEmpty(model))
{
switch (modelEnum)
{
case ModelNames.Models.GRM:
mod = 1;
break;
case ModelNames.Models.MGRM:
mod = 2;
break;
case ModelNames.Models.PCM:
mod = 3;
break;
case ModelNames.Models.GPCM:
mod = 4;
break;
case ModelNames.Models.RSM:
mod = 5;
break;
case ModelNames.Models.NRM:
mod = 6;
break;
}
if (mod == 0)
{
result = new NextItemModel(true, "Invalid 'model' type!");
return(result);
}
}
#endregion
int[] OUT = null;
double[] empProp = null;
int nrGroup = 0;
double[] thProp = null;
#region Handling "cbControl" Parameter
if (cbControl == null)
{
OUT = Out;
}
else
{
if (cbGroup == null)
{
result = new NextItemModel(true, "'cbGroup' argument must be provided for content balancing!");
return(result);
}
if (RowColumn.Sum(cbControl.Props) != 1)
{
double temp_sum = RowColumn.Sum(cbControl.Props);
for (int i = 0; i < cbControl.Props.Length; i++)
{
cbControl.Props[i] = cbControl.Props[i] / temp_sum;
}
}
nrGroup = cbControl.Names.Length;
empProp = new double[nrGroup];
if (Out == null)
{
empProp = CatRcs.Utils.CommonHelper.Replicate(new double[] { 0 }, nrGroup);
}
else
{
string[] temp_grp = new string[Out.Length];
for (int i = 0; i < Out.Length; i++)
{
temp_grp[i] = cbGroup[Out[i]];
}
for (int j = 0; j < nrGroup; j++)
{
string[] values = temp_grp.Where(m => m == cbControl.Names[j]).ToArray();
if (values != null && values.Length > 0)
{
empProp[j] = values.Length;
}
else
{
empProp[j] = 0;
}
}
empProp = empProp.Select(n => n / CatRcs.Utils.RowColumn.Sum(empProp)).ToArray(); // Functional Testing needed !!
}
thProp = cbControl.Props;
List <int> indGroup = new List <int>(); int selGroup = 0;
// Array of Group Numbers ex: "1 2 3 4 5" for nrGroup = 5.
int[] GrpIndValues = new int[nrGroup];
GrpIndValues = GrpIndValues.Select((a, i) => i + 1).ToArray();
if (empProp.Min() == 0)
{
for (int m = 0; m < empProp.Length; m++)
{
if (empProp[m] == 0)
{
indGroup.Add(GrpIndValues[m]);
}
}
}
else
{
double[] tempProp = thProp.Select((a, i) => a - empProp[i]).ToArray();
for (int n = 0; n < tempProp.Length; n++)
{
if (tempProp[n] == tempProp.Max())
{
indGroup.Add(GrpIndValues[n]);
}
}
}
if (indGroup.Count == 1)
{
selGroup = indGroup[0];
}
else
{
selGroup = CatRcs.Utils.RandomNumberHandler.Sample(indGroup.ToArray(), 1, false)[0];
}
// Populating the OUT array
string[] tempGrp = cbGroup.Where(c => c != cbControl.Names[selGroup]).ToArray();
OUT = tempGrp.Select((a, i) => i + 1).ToArray();
OUT = Out.Concat(OUT).ToArray();
OUT = CatRcs.Utils.CommonHelper.Unique(OUT);
}
#endregion
#region Handling "nAvalilable Parameter"
if (nAvailable != null)
{
List <int> ind_temp = new List <int>();
for (int k = 0; k < nAvailable.Length; k++)
{
if (nAvailable[k] == 0)
{
ind_temp.Add(k);
}
}
OUT = OUT.Concat(ind_temp.ToArray()).ToArray();
OUT = CatRcs.Utils.CommonHelper.Unique(OUT);
}
#endregion
int select = 0;
#region Criterion Type "MFI"
if (crit == ModelNames.CriterionTypes.MFI)
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] info = Ii.Ii_Calc(theta, itemBank, model, D).Ii;
double[] ranks = CatRcs.Utils.CommonHelper.Rank(info).Select(m => m).ToArray();
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
List <double> tempRanks = new List <double>();
for (int j = 0; j < items.Length; j++)
{
if (items[j] == 1)
{
tempRanks.Add(ranks[j]);
}
}
tempRanks = tempRanks.OrderByDescending(n => n).ToList();
double[] keepRank = tempRanks.GetRange(0, nrIt).ToArray();
List <int> keep = new List <int>();
if (ranks.Length == items.Length)
{
for (int m = 0; m < keepRank.Length; m++)
{
for (int n = 0; n < ranks.Length; n++)
{
if ((items[n] == 1) && (ranks[n] == keepRank[m]))
{
keep.Add(n + 1);
}
}
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), info[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "bOpt"
if (crit == ModelNames.CriterionTypes.bOpt)
{
if (string.IsNullOrEmpty(model))
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] distance = itemBank.GetItemParamter(CATItems.ColumnNames.b).Select(a => Math.Abs(a - theta)).ToArray();
double[] ranks = CatRcs.Utils.CommonHelper.Rank(distance).Select(m => m).ToArray();
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
ranks[OUT[a] - 1] = -1;
}
}
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
List <double> tempRanks = new List <double>();
for (int j = 0; j < items.Length; j++)
{
if (items[j] == 1)
{
tempRanks.Add(ranks[j]);
}
}
tempRanks = tempRanks.OrderBy(n => n).ToList();
double[] keepRank = tempRanks.GetRange(0, nrIt).ToArray();
keepRank = keepRank.Distinct().ToArray();
List <int> keep = new List <int>();
if (ranks.Length == items.Length)
{
for (int m = 0; m < keepRank.Length; m++)
{
for (int n = 0; n < ranks.Length; n++)
{
if ((items[n] == 1) && (ranks[n] == keepRank[m]))
{
keep.Add(n + 1);
}
}
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), distance[select - 1], criterion, randomesque);
}
else
{
result = new NextItemModel(true, "bOpt's rule cannot be considered with polytomous items!");
return(result);
}
}
#endregion
#region Criterion Type "MLWI" OR "MPWI"
if (crit == ModelNames.CriterionTypes.MLWI || crit == ModelNames.CriterionTypes.MPWI)
{
if (Out != null)
{
if (Out.Length == 1)
{
par = itemBank.FindItem(Out[0]);
}
else
{
par = itemBank.FindItem(Out);
}
}
else
{
result = new NextItemModel(true, "Out parameter can't be empty!");
return(result);
}
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] likInfo = CatRcs.Utils.CommonHelper.Replicate(new double[] { 0 }, itemBank.NumOfItems);
int mwiType = 0;
if (criterion == (int)ModelNames.CriterionTypes.MLWI)
{
mwiType = (int)ModelNames.MWI_Type.MLWI;
}
if (criterion == (int)ModelNames.CriterionTypes.MPWI)
{
mwiType = (int)ModelNames.MWI_Type.MPWI;
}
if (x != null)
{
for (int j = 0; j < itemBank.NumOfItems; j++)
{
if (items[j] == 1)
{
likInfo[j] = MWI.MWI_Calc(itemBank, j + 1, x, par, model, mwiType, priorPar, D, priorDist, parInt[0], parInt[1], parInt[2]);
/* item number is always 1 greater than the index */
}
}
}
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
double likVal = likInfo.ToList().OrderByDescending(n => n).ToArray()[nrIt - 1]; // First value with index 0
List <int> keep = new List <int>();
for (int k = 0; k < items.Length; k++)
{
if (likInfo[k] >= likVal)
{
keep.Add(k + 1); // Converting from index to item number
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), likInfo[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "KL" OR "KLP"
if (crit == ModelNames.CriterionTypes.KL || crit == ModelNames.CriterionTypes.KLP)
{
if (Out != null)
{
if (Out.Length == 1)
{
par = itemBank.FindItem(Out[0]);
}
else
{
par = itemBank.FindItem(Out);
}
}
else
{
result = new NextItemModel(true, "Out parameter can't be empty!");
return(result);
}
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] klValue = CatRcs.Utils.CommonHelper.Replicate(new double[] { 0 }, itemBank.NumOfItems);
double[] X = CatRcs.Utils.CommonHelper.Sequence(parInt[0], parInt[1], parInt[2]);
#region "Function 'L' "
Func <double, int[], CATItems, double> L = (th, r, param) =>
{
double res = 0;
var temp_1 = Pi.Pi_Calc(th, param, model, D).Pi.Select((p, i) => Math.Pow(p, r[i])).ToArray();
var temp_2 = Pi.Pi_Calc(th, param, model, D).Pi.Select((p, i) => Math.Pow(1 - p, 1 - r[i])).ToArray();
if (temp_1.Length == temp_2.Length)
{
var temp_3 = temp_1.Select((p, i) => p * temp_2[i]).ToArray();
res = temp_3.Aggregate((acc, val) => acc * val);
}
return(res);
};
#endregion
#region "Function 'LL' "
Func <double, int[], CATItems, double> LL = (th, r, param) =>
{
double res = 0;
if (param.NumOfItems == 0)
{
res = 1;
}
else
{
double[,] prob = Pi.Pi_Poly_Calc(th, param, model, D).Pi;
for (int i = 0; i < r.Length; i++)
{
res = res * prob[i, r[i] + 1];
}
}
return(res);
};
#endregion
double[] LF = null;
if (string.IsNullOrEmpty(model))
{
LF = X.Select(p => L(p, x, par)).ToArray();
}
else
{
LF = X.Select(p => LL(p, x, par)).ToArray();
}
int kType = 0;
if (criterion == (int)ModelNames.CriterionTypes.KL)
{
kType = (int)ModelNames.KLTypes.KL;
}
if (criterion == (int)ModelNames.CriterionTypes.KLP)
{
kType = (int)ModelNames.KLTypes.KLP;
}
for (int j = 0; j < itemBank.NumOfItems; j++)
{
if (items[j] == 1)
{
klValue[j] = KL.KL_Calc(itemBank, j + 1, x, par, model, theta, priorPar, X, LF, kType, D, priorDist, parInt[0], parInt[1], parInt[2]);
/* item number is always 1 greater than the index */
}
}
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
double klVal = klValue.ToList().OrderByDescending(n => n).ToArray()[nrIt - 1];
List <int> keep = new List <int>();
for (int k = 0; k < items.Length; k++)
{
if (klValue[k] >= klVal)
{
keep.Add(k + 1);
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), klValue[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "MEI"
if (crit == ModelNames.CriterionTypes.MEI)
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] infos = CatRcs.Utils.CommonHelper.Replicate(new double[] { 0 }, itemBank.NumOfItems);
for (int j = 0; j < items.Length; j++)
{
if (items[j] > 0)
{
infos[j] = MEI.MEI_Calc(itemBank, j + 1, x, theta, itemBank.FindItem(Out), model, method, D, priorPar, priorDist, range, parInt, infoType);
}
}
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
double infoVal = infos.ToList().OrderByDescending(n => n).ToArray()[nrIt - 1];
List <int> keep = new List <int>();
for (int k = 0; k < items.Length; k++)
{
if (infos[k] >= infoVal)
{
keep.Add(k + 1);
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), infos[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "MEPV"
if (crit == ModelNames.CriterionTypes.MEPV)
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] epvs = CatRcs.Utils.CommonHelper.Replicate(new double[] { 1000 }, itemBank.NumOfItems);
for (int j = 0; j < items.Length; j++)
{
if (items[j] > 0)
{
epvs[j] = EPV.EPV_Calc(itemBank, j + 1, x, theta, itemBank.FindItem(Out), model, priorPar, parInt, D, priorDist);
}
}
var tempVal = new int[] { randomesque, items.Sum() }.Min();
double epVal = epvs.ToList().OrderBy(n => n).ToArray()[tempVal - 1];
List <int> keep = new List <int>();
for (int k = 0; k < itemBank.NumOfItems; k++)
{
if (epvs[k] <= epVal)
{
keep.Add(k + 1);
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), epvs[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "random"
if (crit == ModelNames.CriterionTypes.random)
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a]] = 0;
}
}
int gen = Convert.ToInt32(Convert.ToInt32(CatRcs.Utils.RandomNumberHandler.Runif(1, 0, 1)[0]) * items.Sum()) + 1;
List <int> indexs = new List <int>();
for (int k = 0; k < itemBank.NumOfItems; k++)
{
if (items[k] > 0)
{
indexs.Add(k + 1);
}
}
select = indexs.ElementAt(gen);
result = new NextItemModel(select, itemBank.FindItem(select), double.NaN, criterion, randomesque);
}
#endregion
#region Criterion Type "progressive"
if (crit == ModelNames.CriterionTypes.progressive)
{
int item_administered = Out.Length;
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] info = Ii.Ii_Calc(theta, itemBank, model, D).Ii;
List <double> tempItems = new List <double>();
for (int j = 0; j < items.Length; j++)
{
if (items[j] == 1)
{
tempItems.Add(info[j]);
}
}
double wq = 0;
double itemMaxInfo = tempItems.Max();
double[] randomValues = CatRcs.Utils.RandomNumberHandler.Runif(items.Length, 0, itemMaxInfo);
if (rule == (int)ModelNames.RuleType.Precision)
{
double infostop = Math.Pow((1 / thr), 2);
double cuminfo = Math.Pow(double.Parse((1 / SETH).ToString()), 2);
if (item_administered > 0)
{
wq = Math.Pow(new double[] { cuminfo / infostop, item_administered / (maxItems - 1) }.Max(), AP);
}
}
if (rule == (int)ModelNames.RuleType.Length)
{
if (item_administered > 0)
{
List <double> tempNum = new List <double>();
for (int i = 1; i <= item_administered; i++)
{
tempNum.Add(Math.Pow(i, AP));
}
double numerador = tempNum.Sum();
List <double> tempDenom = new List <double>();
for (int j = 1; j <= thr - 1; j++)
{
tempDenom.Add(Math.Pow(j, AP));
}
double denominador = tempDenom.Sum();
wq = numerador / denominador;
}
}
double[] funcPR = info.Select((d, i) => d * wq + randomValues[i] * (1 - wq)).ToArray();
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
funcPR[OUT[a] - 1] = 0;
}
}
List <int> keep = new List <int>();
for (int k = 0; k < funcPR.Length; k++)
{
if (funcPR[k] == funcPR.Max())
{
keep.Add(k + 1);
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), info[select - 1], criterion, randomesque);
}
#endregion
#region Criterion Type "proportional"
if (crit == ModelNames.CriterionTypes.proportional)
{
int item_administered = Out.Length;
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double wq = 0;
if (rule == (int)ModelNames.RuleType.Precision)
{
double infostop = Math.Pow((1 / thr), 2);
double cuminfo = Math.Pow(double.Parse((1 / SETH).ToString()), 2);
if (item_administered > 0)
{
wq = infostop * Math.Pow(new double[] { cuminfo / infostop, item_administered / (maxItems - 1) }.Max(), AP);
}
}
if (rule == (int)ModelNames.RuleType.Length)
{
if (item_administered > 0)
{
List <double> tempNum = new List <double>();
for (int i = 1; i <= item_administered; i++)
{
tempNum.Add(Math.Pow(i, AP));
}
double numerador = tempNum.Sum();
List <double> tempDenom = new List <double>();
for (int j = 1; j <= thr - 1; j++)
{
tempDenom.Add(Math.Pow(j, AP));
}
double denominador = tempDenom.Sum();
wq = thr * numerador / denominador;
}
}
double[] info = Ii.Ii_Calc(theta, itemBank, model, D).Ii;
double[] infoPR = info.Select(s => Math.Pow(s, wq)).ToArray();
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
infoPR[OUT[a] - 1] = 0;
}
}
List <double> tempInfoPR = new List <double>();
for (int k = 0; k < items.Length; k++)
{
if (items[k] == 1)
{
tempInfoPR.Add(infoPR[k]);
}
}
double totalInfoPR = tempInfoPR.Sum();
double[] probSelect = infoPR.Select(m => m / totalInfoPR).ToArray();
int[] selectItems = items.Select((n, i) => i + 1).ToArray();
select = CatRcs.Utils.RandomNumberHandler.Sample(selectItems, 1, false)[0]; // prob parameter will be added after Sample functiom modification
result = new NextItemModel(select, itemBank.FindItem(select), info[select], criterion, randomesque);
}
#endregion
#region Criterion Type "thOpt"
if (crit == ModelNames.CriterionTypes.thOpt)
{
if (string.IsNullOrEmpty(model)) // Only for Dichotomous Items
{
int[] items = CatRcs.Utils.CommonHelper.Replicate(new int[] { 1 }, itemBank.NumOfItems);
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
items[OUT[a] - 1] = 0;
}
}
double[] u = itemBank.GetItemParamter(CATItems.ColumnNames.c).Select((s, i) => - 0.75 + (s + itemBank.GetItemParamter(CATItems.ColumnNames.d)[i] + -2 * s * itemBank.GetItemParamter(CATItems.ColumnNames.d)[i]) / 2).ToArray();
double[] v = itemBank.GetItemParamter(CATItems.ColumnNames.c).Select((n, i) => (n + itemBank.GetItemParamter(CATItems.ColumnNames.d)[i] - 1) / 4).ToArray();
double[] xstar = u.Select((m, i) => 2 * Math.Sqrt(-m / 3) * Math.Cos(Math.Acos(-v[i] * Math.Sqrt(-27 / Math.Pow(m, 3)) / 2) / 3 + 4 * (Math.PI / 3)) + 0.5).ToArray();
double[] thstar = itemBank.GetItemParamter(CATItems.ColumnNames.b).Select((o, i) => o + Math.Log((xstar[i] - itemBank.GetItemParamter(CATItems.ColumnNames.c)[i]) / (itemBank.GetItemParamter(CATItems.ColumnNames.d)[i] - xstar[i])) / (D * itemBank.GetItemParamter(CATItems.ColumnNames.a)[i])).ToArray();
double[] distance = thstar.Select(p => Math.Abs(p - theta)).ToArray();
double[] ranks = CatRcs.Utils.CommonHelper.Rank(distance).Select(m => m).ToArray();
if (OUT != null)
{
for (int a = 0; a < OUT.Length; a++)
{
ranks[OUT[a] - 1] = -1;
}
}
int nrIt = new int[] { randomesque, (int)CatRcs.Utils.RowColumn.Sum(items) }.Min();
List <double> tempRanks = new List <double>();
for (int j = 0; j < items.Length; j++)
{
if (items[j] == 1)
{
tempRanks.Add(ranks[j]);
}
}
tempRanks = tempRanks.OrderBy(n => n).ToList();
double[] keepRank = tempRanks.GetRange(0, nrIt).ToArray();
keepRank = keepRank.Distinct().ToArray();
List <int> keep = new List <int>();
if (ranks.Length == items.Length)
{
for (int m = 0; m < keepRank.Length; m++)
{
for (int n = 0; n < ranks.Length; n++)
{
if ((items[n] == 1) && (ranks[n] == keepRank[m]))
{
keep.Add(n + 1);
}
}
}
}
if (keep.Count == 1)
{
select = keep[0];
}
else
{
select = CatRcs.Utils.RandomNumberHandler.Sample(keep.ToArray(), 1, false)[0];
}
result = new NextItemModel(select, itemBank.FindItem(select), distance[select - 1], criterion, randomesque);
}
else
{
result = new NextItemModel(true, "thOpt's rule cannot be considered with polytomous items!");
return(result);
}
}
#endregion
#region Handling "cbControl" Parameter
if (cbControl == null)
{
if (result != null)
{
result.prior_prop = null;
result.post_prop = null;
result.cb_prop = null;
}
}
else
{
result.prior_prop = empProp;
double[] postProp = new double[nrGroup];
string[] temp_grp = new string[Out.Length + 1];
for (int i = 0; i < temp_grp.Length; i++)
{
if (i == 0)
{
temp_grp[i] = cbGroup[result.item];
}
temp_grp[i] = cbGroup[Out[i]];
}
for (int j = 0; j < postProp.Length; j++)
{
string[] values = temp_grp.Where(m => m == cbControl.Names[j]).ToArray();
if (values != null && values.Length > 0)
{
postProp[j] = values.Length;
}
else
{
postProp[j] = 0;
}
}
result.post_prop = postProp.Select(n => n / CatRcs.Utils.RowColumn.Sum(postProp)).ToArray();
result.cb_prop = thProp;
}
#endregion
return(result);
}
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);
}