public void ProbabilityOfCorrectReponse_DeltaNotEqualToTheta_ReturnsCorrectValue()
{
double alpha = .2;
double delta = .3;
double chi = .4;
ThreeParamModelParameters parameters = new ThreeParamModelParameters(alpha, delta, chi);
ThreeParamProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(parameters);
double theta = .1;
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double expectedValue = chi + (1 - chi)*Math.Exp(alpha * (theta - delta)) / (1 + Math.Exp(alpha * (theta - delta)));
Assert.IsTrue(Math.Abs(expectedValue - p) < Tolerance);
}
public void ProbabilityOfCorrectReponse_DeltaEqualsTheta_ReturnsOneHalf()
{
double alpha = .2;
double delta = .3;
double chi = .4;
ThreeParamModelParameters parameters = new ThreeParamModelParameters(alpha, delta, chi);
ThreeParamProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(parameters);
double theta = delta;
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double expectedProbability = chi + (1 - chi)*.5;
Assert.AreEqual(expectedProbability, p);
}
public void SecondThetaDerivative_NonTrivialInput_CloseToFiniteDifferenceValue()
{
double alpha = .2;
double delta = .3;
double chi = .4;
ThreeParamModelParameters parameters = new ThreeParamModelParameters(alpha, delta, chi);
ThreeParamProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(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 GetInformation_NonzeroChi_ReturnsCorrectInfo()
{
double alpha = 2;
double chi = .5;
double delta = 1;
ThreeParamModelParameters modelParameters = new ThreeParamModelParameters(alpha, delta, chi);
ThreeParamItemInformationFunction informationFunction = new ThreeParamItemInformationFunction(modelParameters);
const double theta = .3;
ThreeParamProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(new ThreeParamModelParameters(alpha, delta, chi));
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double expectedInfo = alpha*alpha*Math.Pow((p - chi)/(1 - chi), 2)*((1 - p)/p);
var calculatedInformation = informationFunction.GetInformation(theta);
Assert.AreEqual(expectedInfo, calculatedInformation, Tolerance);
}
public void LogLikelihood_OneIncorrectResponseOneCorrectResponse_ReturnsCorrectValue()
{
double alpha1 = .3;
double delta1 = .1;
double chi1 = .2;
ThreeParamModelParameters modelParameters1 = new ThreeParamModelParameters(alpha1, delta1, chi1);
double alpha2 = .5;
double delta2 = .6;
double chi2 = .7;
ThreeParamModelParameters modelParameters2 = new ThreeParamModelParameters(alpha2, delta2, chi2);
List<IModelParameters> modelParameterList = new List<IModelParameters>();
modelParameterList.Add(modelParameters1);
modelParameterList.Add(modelParameters2);
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(modelParameterList);
double theta = .4;
List<int> responseVector = new List<int>() { 1, 0 };
double logLikelihood = logLikelihoodFunction.LogLikelihood(responseVector, theta);
IProbabilityFunction probabilityFunction1 = new ThreeParamProbabilityFunction(modelParameters1);
double p1 = probabilityFunction1.ProbabilityOfCorrectResponse(theta);
IProbabilityFunction probabilityFunction2 = new ThreeParamProbabilityFunction(modelParameters2);
double p2 = probabilityFunction2.ProbabilityOfCorrectResponse(theta);
double expectedLikelihood = Math.Log(p1) + Math.Log(1 - p2);
Assert.AreEqual(expectedLikelihood, logLikelihood, Tolerance);
}
public void LogLikelihood_SingleIncorrectResponse_ReturnsCorrectValue()
{
double alpha = .3;
double delta = .1;
double chi = .2;
ThreeParamModelParameters modelParameters = new ThreeParamModelParameters(alpha, delta, chi);
List<IModelParameters> modelParameterList = new List<IModelParameters>();
modelParameterList.Add(modelParameters);
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(modelParameterList);
double theta = .4;
List<int> responseVector = new List<int>() { 0 };
double logLikelihood = logLikelihoodFunction.LogLikelihood(responseVector, theta);
IProbabilityFunction probabilityFunction = new ThreeParamProbabilityFunction(modelParameters);
double p = probabilityFunction.ProbabilityOfCorrectResponse(theta);
double expectedLikelihood = Math.Log(1 - p);
Assert.AreEqual(expectedLikelihood, logLikelihood, Tolerance);
}
