// 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);
}
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);
}
