// The item information function for the three parameter model. See formula (6.12) on page 144 in Ayala. Note that 'p_j' here represents
// the three parameter model probability of obtaining a correct answer
public double GetInformation(double theta)
{
double p = _probabilityFunction.ProbabilityOfCorrectResponse(theta);
double term1 = (p - _chi) / (1 - _chi);
double term2 = (1 - p) / p;
return(_alpha * _alpha * term1 * term1 * term2);
}
// Formula given on page 307 of https://ppw.kuleuven.be/okp/_pdf/Magis2013ANOTI.pdf
public double GetInformation(double theta)
{
double p = _probabilityFunction.ProbabilityOfCorrectResponse(theta);
double term1 = (p - _chi) / (_epsilon - _chi);
double term2 = (_epsilon - p);
double term3 = p * (1 - p);
return(_alpha * _alpha * term1 * term1 * term2 * term2 / term3);
}
// The standard error of estimate (SEE) for the location parameter theta. The general formula is given by (2.11) on page 28.
public double Calculate(List <QuestionInfo> questionHistory, double theta)
{
List <IModelParameters> modelParametersList = questionHistory.Select(x => x.Question.ModelParameters).ToList();
List <int> responseVector = questionHistory.Select(x => (int)x.Score).ToList();
double sum = 0;
for (int i = 0; i < responseVector.Count; i++)
{
IModelParameters modelParameters = modelParametersList[i];
IProbabilityFunction probabilityFunction = _probabilityFunctionFactory.Build(modelParameters);
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double pPrime = probabilityFunction.FirstThetaDerivative(theta);
sum += pPrime * pPrime / (p * (1 - p));
}
return(1 / Math.Sqrt(sum));
}
// The item information function for the two parameter model. See formula (5.3) on page 102 of Ayala
public double GetInformation(double theta)
{
double p = _twoParamProbabilityFunction.ProbabilityOfCorrectResponse(theta);
return(_alpha * _alpha * p * (1 - p));
}