private static Question GetNextQuestion(string line)
{
string[] words = line.Split(' ');
string questionNumber = Convert.ToString(words[0]);
IModelParameters modelParameters;
if (words.Length == 4)
{
double alpha = Convert.ToDouble(words[1]);
double delta = Convert.ToDouble(words[2]);
double chi = Convert.ToDouble(words[3]);
modelParameters = new ThreeParamModelParameters(alpha, delta, chi);
}
else if (words.Length == 3)
{
double alpha = Convert.ToDouble(words[1]);
double delta = Convert.ToDouble(words[2]);
modelParameters = new TwoParamModelParameters(alpha, delta);
}
else
{
throw new NotImplementedException();
}
Question question = new Question()
{
ModelParameters = modelParameters,
QuestionLabel = questionNumber
};
return(question);
}
// In this case the exponent is zero
public void ProbabilityOfCorrectReponse_DeltaEqualsTheta_ReturnsOneHalf()
{
double alpha = .2;
double delta = .3;
TwoParamModelParameters parameters = new TwoParamModelParameters(alpha, delta);
TwoParamProbabilityFunction probabilityFunction = new TwoParamProbabilityFunction(parameters);
double theta = delta;
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
Assert.AreEqual(.5, p);
}
// Second line of the table on page 379 of Ayala.
public void GetInformation_SecondValueLineFromAyala_ReturnsCorrectInfo()
{
TwoParamModelParameters modelParameters = new TwoParamModelParameters(2.954, .560);
TwoParamItemInformationFunction informationFunction = new TwoParamItemInformationFunction(modelParameters);
const double theta = .3;
var calculatedInformation = informationFunction.GetInformation(theta);
const double expectedInfo = 1.889;
Assert.AreEqual(expectedInfo, calculatedInformation, Tolerance);
}
public void SecondThetaDerivative_NonTrivialInput_CloseToFiniteDifferenceValue()
{
double alpha = .2;
double delta = .3;
TwoParamModelParameters parameters = new TwoParamModelParameters(alpha, delta);
TwoParamProbabilityFunction probabilityFunction = new TwoParamProbabilityFunction(parameters);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(x => probabilityFunction.FirstThetaDerivative(x));
double theta = .1;
double secondDerivative = probabilityFunction.SecondThetaDerivative(theta);
double approxSecondDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.IsTrue(Math.Abs(secondDerivative - approxSecondDerivative) < Tolerance);
}
public void ProbabilityOfCorrectReponse_DeltaNotEqualToTheta_ReturnsCorrectValue()
{
double alpha = .2;
double delta = .3;
TwoParamModelParameters parameters = new TwoParamModelParameters(alpha, delta);
TwoParamProbabilityFunction probabilityFunction = new TwoParamProbabilityFunction(parameters);
double theta = .1;
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double expectedValue = Math.Exp(alpha * (theta - delta)) / (1 + Math.Exp(alpha * (theta - delta)));
Assert.IsTrue(Math.Abs(expectedValue - p) < Tolerance);
}
public TwoParamProbabilityFunction(TwoParamModelParameters parameters)
{
_alpha = parameters.Alpha;
_delta = parameters.Delta;
}
public TwoParamItemInformationFunction(TwoParamModelParameters modelParameters)
{
_alpha = modelParameters.Alpha;
_twoParamProbabilityFunction = new TwoParamProbabilityFunction(modelParameters);
}