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; }