public void LogLikelihoodSecondDerivative_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);
double alpha3 = .1;
double delta3 = .2;
double chi3 = .4;
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 derivativeFunction = x => logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, x);
FiniteDifferencer finiteDifferencer = new FiniteDifferencer(derivativeFunction);
double logLikelihoodDerivative = logLikelihoodFunction.LogLikelihoodSecondDerivative(responseVector, theta);
double finiteDifferenceDerivative = finiteDifferencer.ApproximateDerivative(theta);
Assert.AreEqual(finiteDifferenceDerivative, logLikelihoodDerivative, Tolerance);
}
public double GetMle(List<int> responseVector)
{
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(_modelParametersList);
const double initialGuess = 0;
OneDimensionalFunction firstDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, x);
OneDimensionalFunction secondDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodSecondDerivative(responseVector, x);
//NewtonRhapsonSolver rootSolver = new NewtonRhapsonSolver(firstDerivativeFunction, secondDerivativeFunction, initialGuess);
BisectionSolver rootSolver = new BisectionSolver(firstDerivativeFunction, -5, 5);
double mle = rootSolver.FindRoot();
return mle;
}
public double GetMle(List <int> responseVector)
{
LogLikelihoodFunction logLikelihoodFunction = new LogLikelihoodFunction(_modelParametersList);
//const double initialGuess = 0;
OneDimensionalFunction function = x => logLikelihoodFunction.LogLikelihood(responseVector, x);
OneDimensionalFunction firstDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodFirstDerivative(responseVector, x);
//OneDimensionalFunction secondDerivativeFunction = x => logLikelihoodFunction.LogLikelihoodSecondDerivative(responseVector, x);
//NewtonRhapsonSolver rootSolver = new NewtonRhapsonSolver(firstDerivativeFunction, secondDerivativeFunction, initialGuess);
//BisectionSolver rootSolver = new BisectionSolver(firstDerivativeFunction, -6, 6);
//double mle = rootSolver.FindRoot();
//double mle = rootSolver.FindRoot();
GlobalMaximizer globalMaximizer = new GlobalMaximizer(function, firstDerivativeFunction, -6, 6, _gradientDescentTolerance);
var mle = globalMaximizer.FindPosOfMaximum();
return(mle);
}
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);
}