Logistic Regression in C# QuickStart Sample

Illustrates how to use the LogisticRegressionModel class to create logistic regression models in C#.

View this sample in: Visual Basic F# IronPython

using System;

using Extreme.Data.Text;
using Extreme.Statistics;
using Index = Extreme.DataAnalysis.Index;

namespace Extreme.Numerics.QuickStart.CSharp

    /// <summary>
    /// Illustrates building logistic regression models using 
    /// the LogisticRegressionModel class in the 
    /// Extreme.Statistics namespace of Extreme Numerics.NET.
    /// </summary>
    class LogisticRegression
        static void Main(string[] args)
            // The license is verified at runtime. We're using
            // a demo license here. For more information, see
            // https://numerics.net/trial-key
            Extreme.License.Verify("Demo license");
            // Logistic regression can be performed using 
            // the LogisticRegressionModel class.
            // This QuickStart sample uses data from a study of factors
            // that determine low birth weight at Baystate Medical Center.
            // from Belsley, Kuh and Welsch. The fields are as follows:
            //   AGE:  Mother's age.
            //   LWT:  Mother's weight.
            //   RACE: 1=white, 2=black, 3=other.
            //   FVT:  Number of physician visits during the 1st trimester.
            //   LOW:  Low birth weight indicator.

            // First, read the data from a file into an ADO.NET DataTable. 
            var data = FixedWidthTextFile.ReadDataFrame(
                new int[] { 4, 11, 18, 25, 33, 42, 49, 55, 61, 68 });

            // Now create the regression model. Parameters are the name 
            // of the dependent variable, a string array containing 
            // the names of the independent variables, and the data frame
            // containing all variables.

            // Categorical variables are automatically expanded into
            // indicator variables if they are marked properly:
            data.MakeCategorical("RACE", Index.Create(new[] { 1, 2, 3 }));

            var model = new LogisticRegressionModel(data, "LOW", 
                new string[] { "AGE", "LWT", "RACE", "FTV" });

            // Alternatively, we can use a formula to describe the variables
            // in the model. The dependent variable goes on the left, the
            // independent variables on the right of the ~:
            model = new LogisticRegressionModel(data, "LOW ~ AGE + LWT + RACE + FTV");

            // The Fit method performs the actual regression analysis.

            // The Parameters collection contains information about the regression 
            // parameters.
            Console.WriteLine("Variable              Value    Std.Error  t-stat  p-Value");
            foreach (var parameter in model.Parameters)
                // Parameter objects have the following properties:
                Console.WriteLine("{0,-20}{1,10:F5}{2,10:F5}{3,8:F2} {4,7:F4}",
                    // Name, usually the name of the variable:
                    // Estimated value of the parameter:
                    // Standard error:
                    // The value of the t statistic for the hypothesis that the parameter
                    // is zero.
                    // Probability corresponding to the t statistic.

            // The log-likelihood of the computed solution is also available:
            Console.WriteLine("Log-likelihood: {0:F4}", model.LogLikelihood);

            // We can test the significance by looking at the results
            // of a log-likelihood test, which compares the model to
            // a constant-only model:
            Extreme.Statistics.Tests.SimpleHypothesisTest lrt = model.GetLikelihoodRatioTest();
            Console.WriteLine("Likelihood-ratio test: chi-squared={0:F4}, p={1:F4}", lrt.Statistic, lrt.PValue);

            // We can compute a model with fewer parameters:
            var model2 = new LogisticRegressionModel(data, "LOW ~ LWT + RACE");

            // Print the results...
            Console.WriteLine("Variable              Value    Std.Error  t-stat  p-Value");
            foreach (var parameter in model2.Parameters)
                Console.WriteLine("{0,-20}{1,10:F5}{2,10:F5}{3,8:F2} {4,7:F4}",
                    parameter.Name, parameter.Value, parameter.StandardError, parameter.Statistic, parameter.PValue);
            // ...including the log-likelihood:
            Console.WriteLine("Log-likelihood: {0:F4}", model2.LogLikelihood);

            // We can now compare the original model to this one, once again
            // using the likelihood ratio test:
            lrt = model.GetLikelihoodRatioTest(model2);
            Console.WriteLine("Likelihood-ratio test: chi-squared={0:F4}, p={1:F4}", lrt.Statistic, lrt.PValue);

            // Multinomial (polytopous) logistic regression

            // The LogisticRegressionModel class can also be used
            // for logistic regression with more than 2 responses.
            // The following example is from "Applied Linear Statistical
            // Models."

            // Load the data into a matrix
            string[] columnNames = { "id", "duration", "x2", "x3", "x4",
                "nutritio", "agecat1", "agecat3", "alcohol", "smoking" };
            var dataFrame = FixedWidthTextFile.ReadDataFrame(
                new FixedWidthTextOptions(
                    new int[] { 5, 10, 15, 20, 25, 32, 37, 42, 47 },
                    columnHeaders: false))

            // For multinomial regression, the response variable must be
            // a categorical variable:

            // The constructor takes an extra argument of type
            // LogisticRegressionMethod:
            var model3 = new LogisticRegressionModel(
                dataFrame, "duration",
                new string[] { "nutritio", "agecat1", "agecat3", "alcohol", "smoking" });
            model3.Method = LogisticRegressionMethod.Nominal;

            // When using a formula, we can use '.' as a shortcut 
            // for all unused variables in the data frame.
            // Because duration has 3 levels, nominal logistic regression
            // is automatically inferred.
            model3 = new LogisticRegressionModel(dataFrame,
                "duration ~ nutritio + agecat1 + agecat3 + alcohol + smoking");

            // Everything else is the same:

            // There is a set of parameters for each level of the
            // response variable. The highest level is the reference 
            // level and has no associated parameters.
            foreach (var p in model3.Parameters) {

            Console.WriteLine("Log likelihood: {0:F4}", model3.LogLikelihood);

            // To test the hypothesis that all the slopes are zero,
            // use the GetLikelihoodRatioTest method.
            lrt = model3.GetLikelihoodRatioTest();
            Console.WriteLine("Test that all slopes are zero: chi-squared={0:F4}, p={1:F4}", lrt.Statistic, lrt.PValue);

            Console.Write("Press any key to exit.");