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);
}
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);
}