public void LogLikelihood_TwoCorrectResponses_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, 1
};
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(p2);
Assert.AreEqual(expectedLikelihood, logLikelihood, Tolerance);
}
public void LogLikelihoodDerivative_MultipleResponses_MatchesFiniteDifferenceDerivative()
{
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);
ThreeParamModelParameters modelParameters3 = new ThreeParamModelParameters(alpha2, delta2, chi2);
List <IModelParameters> modelParameterList = new List <IModelParameters>();
modelParameterList.Add(modelParameters1);
modelParameterList.Add(modelParameters2);
modelParameterList.Add(modelParameters3);
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(modelParameterList);
double theta = .4;
List <int> responseVector = new List <int>()
{
1, 0, 1
};
OneDimensionalFunction function = x => logLikelihoodFunction.LogLikelihood(responseVector, x);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(function);
double logLikelihoodDerivative = logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, theta);
double finiteDifferenceDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.AreEqual(finiteDifferenceDerivative, logLikelihoodDerivative, 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);
}
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);
}
public ThreeParamItemInformationFunction(ThreeParamModelParameters modelParameters)
{
_alpha = modelParameters.Alpha;
_chi = modelParameters.Chi;
_probabilityFunction = new ThreeParamProbabilityFunction(modelParameters);
}
// Second line of the table on page 379 of Ayala. The three parameter model matches two parameter model when chi = 0
public void GetInformation_SecondValueLineFromAyala_ReturnsCorrectInfo()
{
ThreeParamModelParameters modelParameters = new ThreeParamModelParameters(2.954, .560, 0);
ThreeParamItemInformationFunction informationFunction = new ThreeParamItemInformationFunction(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;
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 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);
}
// In this case the exponent is zero
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 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 ThreeParamProbabilityFunction(ThreeParamModelParameters parameters)
{
_alpha = parameters.Alpha;
_delta = parameters.Delta;
_chi = parameters.Chi;
}
