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 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 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 void FirstThetaDerivative_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.ProbabilityOfCorrectResponse(x));

            double theta            = .1;
            double derivative       = probabilityFunction.FirstThetaDerivative(theta);
            double approxDerivative = finiteDifferencer.ApproximateDerivative(theta);

            Assert.IsTrue(Math.Abs(derivative - approxDerivative) < Tolerance);
        }