Accord.Tests.Statistics.MultinomialLogisticRegressionTest.RegressTest2 C# (CSharp) Method

        public void RegressTest2()
        {
            double[][] inputs;
            int[] outputs;

            CreateInputOutputsExample1(out inputs, out outputs);

            // Create a new Multinomial Logistic Regression for 3 categories
            var mlr = new MultinomialLogisticRegression(inputs: 2, categories: 3);

            // Create a estimation algorithm to estimate the regression
            LowerBoundNewtonRaphson lbnr = new LowerBoundNewtonRaphson(mlr);

            // Now, we will iteratively estimate our model. The Run method returns
            // the maximum relative change in the model parameters and we will use
            // it as the convergence criteria.

            double delta;
            int iteration = 0;

            do
            {
                // Perform an iteration
                delta = lbnr.Run(inputs, outputs);
                iteration++;

            } while (iteration < 100 && delta > 1e-6);

            Assert.AreEqual(52, iteration);
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][0]));
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][1]));
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[0][2]));
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][0]));
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][1]));
            Assert.IsFalse(double.IsNaN(mlr.Coefficients[1][2]));


            // This is the same example given in R Data Analysis Examples for
            // Multinomial Logistic Regression: http://www.ats.ucla.edu/stat/r/dae/mlogit.htm

            // brand 2
            Assert.AreEqual(-11.774655, mlr.Coefficients[0][0], 1e-4); // intercept
            Assert.AreEqual(0.523814, mlr.Coefficients[0][1], 1e-4); // female
            Assert.AreEqual(0.368206, mlr.Coefficients[0][2], 1e-4); // age

            // brand 3
            Assert.AreEqual(-22.721396, mlr.Coefficients[1][0], 1e-4); // intercept
            Assert.AreEqual(0.465941, mlr.Coefficients[1][1], 1e-4); // female
            Assert.AreEqual(0.685908, mlr.Coefficients[1][2], 1e-4); // age


            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][0]));
            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][1]));
            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[0][2]));
            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][0]));
            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][1]));
            Assert.IsFalse(double.IsNaN(mlr.StandardErrors[1][2]));

            /*
             // Using the standard Hessian estimation
             Assert.AreEqual(1.774612, mlr.StandardErrors[0][0], 1e-6);
             Assert.AreEqual(0.194247, mlr.StandardErrors[0][1], 1e-6);
             Assert.AreEqual(0.055003, mlr.StandardErrors[0][2], 1e-6);

             Assert.AreEqual(2.058028, mlr.StandardErrors[1][0], 1e-6);
             Assert.AreEqual(0.226090, mlr.StandardErrors[1][1], 1e-6);
             Assert.AreEqual(0.062627, mlr.StandardErrors[1][2], 1e-6);
             */

            // Using the lower-bound approximation
            Assert.AreEqual(1.047378039787443, mlr.StandardErrors[0][0], 1e-6);
            Assert.AreEqual(0.153150051082552, mlr.StandardErrors[0][1], 1e-6);
            Assert.AreEqual(0.031640507386863, mlr.StandardErrors[0][2], 1e-6);

            Assert.AreEqual(1.047378039787443, mlr.StandardErrors[1][0], 1e-6);
            Assert.AreEqual(0.153150051082552, mlr.StandardErrors[1][1], 1e-6);
            Assert.AreEqual(0.031640507386863, mlr.StandardErrors[1][2], 1e-6);

            double ll = mlr.GetLogLikelihood(inputs, outputs);

            Assert.AreEqual(-702.97, ll, 1e-2);
            Assert.IsFalse(double.IsNaN(ll));

            var chi = mlr.ChiSquare(inputs, outputs);
            Assert.AreEqual(185.85, chi.Statistic, 1e-2);
            Assert.IsFalse(double.IsNaN(chi.Statistic));

            var wald00 = mlr.GetWaldTest(0, 0);
            var wald01 = mlr.GetWaldTest(0, 1);
            var wald02 = mlr.GetWaldTest(0, 2);

            var wald10 = mlr.GetWaldTest(1, 0);
            var wald11 = mlr.GetWaldTest(1, 1);
            var wald12 = mlr.GetWaldTest(1, 2);

            Assert.IsFalse(double.IsNaN(wald00.Statistic));
            Assert.IsFalse(double.IsNaN(wald01.Statistic));
            Assert.IsFalse(double.IsNaN(wald02.Statistic));

            Assert.IsFalse(double.IsNaN(wald10.Statistic));
            Assert.IsFalse(double.IsNaN(wald11.Statistic));
            Assert.IsFalse(double.IsNaN(wald12.Statistic));

            /*
            // Using standard Hessian estimation
            Assert.AreEqual(-6.6351, wald00.Statistic, 1e-4);
            Assert.AreEqual( 2.6966, wald01.Statistic, 1e-4);
            Assert.AreEqual( 6.6943, wald02.Statistic, 1e-4);

            Assert.AreEqual(-11.0404, wald10.Statistic, 1e-4);
            Assert.AreEqual( 2.0609, wald11.Statistic, 1e-4);
            Assert.AreEqual(10.9524, wald12.Statistic, 1e-4);
            */

            // Using Lower-Bound approximation
            Assert.AreEqual(-11.241995503283842, wald00.Statistic, 1e-4);
            Assert.AreEqual(3.4202662152119889, wald01.Statistic, 1e-4);
            Assert.AreEqual(11.637150673342207, wald02.Statistic, 1e-4);

            Assert.AreEqual(-21.693553825772664, wald10.Statistic, 1e-4);
            Assert.AreEqual(3.0423802097069097, wald11.Statistic, 1e-4);
            Assert.AreEqual(21.678124991086548, wald12.Statistic, 1e-4);
        }