Generalized Linear Models in C# QuickStart Sample

Illustrates how to use the GeneralizedLinearModel class to compute probit, Poisson and similar regression models in C#.

This sample is also available in: Visual Basic, F#.

Overview

This QuickStart sample demonstrates how to use generalized linear models (GLM) in Numerics.NET to analyze relationships between variables with non-normal distributions.

The sample walks through two complete examples:

  1. A Poisson regression analyzing student attendance data to examine relationships between absences and factors like math scores, language arts scores, and gender. This demonstrates handling count data using the canonical link function.

  2. A probit regression analyzing graduate school admissions data to model the probability of admission based on GRE scores, GPA, and school ranking. This shows how to work with binary outcome data using the probit link function.

For each example, the code shows how to:

  • Load and prepare the data
  • Specify the model family and link function
  • Fit the model
  • Extract and interpret parameter estimates, standard errors, and p-values
  • Calculate confidence intervals
  • Obtain model fit statistics like log likelihood and information criteria

The sample includes detailed comments explaining each step and interpreting the results, making it an excellent introduction to generalized linear modeling in Numerics.NET.

The code

using System;

using Numerics.NET.Data.Text;
using Numerics.NET.DataAnalysis;
using Numerics.NET;
using Numerics.NET.Statistics;


// Illustrates building generalized linear models using
// the GeneralizedLinearModel class in the
// Numerics.NET.Statistics namespace of Numerics.NET.

// The license is verified at runtime. We're using
// a 30 day trial key here. For more information, see
//     https://numerics.net/trial-key
Numerics.NET.License.Verify("your-trial-key-here");

// Generalized linear models can be computed using
// the GeneralizedLinearModel class.

//
// Poisson regression
//

// This QuickStart sample uses data about the attendance of 316 students
// from two urban high schools. The fields are as follows:
//   daysabs: The number of days the student was absent.
//   male:    A binary indicator of gender.
//   math:    The student's standardized math score.
//   langarts:The student's standardized language arts score.
//
// We want to investigate the relationship between these variables.
//
// See http://www.ats.ucla.edu/stat/stata/dae/poissonreg.htm

// First, read the data from a file into a VariableCollection.
// The ReadAttendanceData method is defined later in this file.
var data = ReadAttendanceData();

// 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 VariableCollection
// containing all variables.
var model = new GeneralizedLinearModel(data,
    "daysabs", new string[] { "math", "langarts", "male" });

model = new GeneralizedLinearModel(data,
    "daysabs ~ math + langarts + male");

// The ModelFamily specifies the distribution of the dependent variable.
// Since we're dealing with count data, we use a Poisson model:
model.ModelFamily = ModelFamily.Poisson;

// The LinkFunction specifies the relationship between the dependent variable
// and the linear predictor of independent variables. In this case,
// we use the canonical link function, which is the default.
model.LinkFunction = ModelFamily.Poisson.CanonicalLinkFunction;

// The Fit method performs the actual regression analysis.
model.Fit();

// The Parameters collection contains information about the regression
// parameters.
Console.WriteLine("Variable              Value    Std.Error    z     p-Value");
foreach (var parameter in model.Parameters)
{
    // Parameter objects have the following properties:
    Console.WriteLine("{0,-20}{1,10:F6}{2,10:F6}{3,8:F2} {4,7:F5}",
        // Name, usually the name of the variable:
        parameter.Name,
        // Estimated value of the parameter:
        parameter.Value,
        // Standard error:
        parameter.StandardError,
        // The value of the z score for the hypothesis that the parameter
        // is zero.
        parameter.Statistic,
        // Probability corresponding to the t statistic.
        parameter.PValue);
}
Console.WriteLine();

// In addition to these properties, Parameter objects have a GetConfidenceInterval
// method that returns a confidence interval at a specified confidence level.
// Notice that individual parameters can be accessed using their numeric index.
// Parameter 0 is the intercept, if it was included.
Interval confidenceInterval = model.Parameters[0].GetConfidenceInterval(0.95);
Console.WriteLine("95% confidence interval for math score: {0:F4} - {1:F4}",
    confidenceInterval.LowerBound, confidenceInterval.UpperBound);

// Parameters can also be accessed by name:
confidenceInterval = model.Parameters.Get("math").GetConfidenceInterval(0.95);
Console.WriteLine("95% confidence interval for math score: {0:F4} - {1:F4}",
    confidenceInterval.LowerBound, confidenceInterval.UpperBound);
Console.WriteLine();

// There is also a wealth of information about the analysis available
// through various properties of the GeneralizedLinearModel object:
Console.WriteLine($"Log likelihood:         {model.LogLikelihood:F4}");
Console.WriteLine($"Kernel log likelihood:  {model.GetKernelLogLikelihood():F4}");

// Note that some statistical applications (notably stata) use
// a different definition of some of these "information criteria":
Console.WriteLine("\"Information Criteria\"");
Console.WriteLine($"Akaike (AIC):           {model.GetAkaikeInformationCriterion():F3}");
Console.WriteLine($"Corrected AIC:          {model.GetCorrectedAkaikeInformationCriterion():F3}");
Console.WriteLine($"Bayesian (BIC):         {model.GetBayesianInformationCriterion():F3}");
Console.WriteLine($"Chi Square:             {model.GetChiSquare():F3}");
Console.WriteLine();

//
// Probit regression
//

// In a second example, we investigate the relationship between whether a student
// graduates, and the student's GRE scores,grade point averages, the level
// of the school from a "top notch" school. The fields are as follows:
//   admit:    Dependent variable
//   gre:      The student's GRE score.
//   topnotch: A binary indicator of the type of school
//   gpa:      The student's Grade Point Average.
//
// The data was generated.
// See http://www.ats.ucla.edu/stat/stata/dae/probit.htm

// First, read the data from a file into a VariableCollection.
// The ReadGraduateData method is defined later in this file.
data = ReadGraduateData();

// 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 VariableCollection
// containing all variables.
model = new GeneralizedLinearModel(data,
    "admit", new string[] { "gre", "topnotch", "gpa" });

// The ModelFamily specifies the distribution of the dependent variable.
// Since we're dealing with binary data, we use a Binomial model:
model.ModelFamily = ModelFamily.Binomial;

// We use the probit link function.
model.LinkFunction = LinkFunction.Probit;

// The Fit method performs the actual regression analysis.
model.Fit();

// The Parameters collection contains information about the regression
// parameters.
Console.WriteLine("Variable              Value    Std.Error    z     p-Value");
foreach (var parameter in model.Parameters)
{
    Console.WriteLine("{0,-20}{1,10:F6}{2,10:F6}{3,8:F2} {4,7:F5}",
        parameter.Name,
        parameter.Value,
        parameter.StandardError,
        parameter.Statistic,
        parameter.PValue);
}
Console.WriteLine();

// There is also a wealth of information about the analysis available
// through various properties of the GeneralizedLinearModel object:
Console.WriteLine($"Log likelihood:         {model.LogLikelihood:F4}");
Console.WriteLine($"Kernel log likelihood:  {model.GetKernelLogLikelihood():F4}");

// Note that some statistical applications (notably stata) use
// a different definition of some of these "information criteria":
Console.WriteLine("\"Information Criteria\"");
Console.WriteLine($"Akaike (AIC):           {model.GetAkaikeInformationCriterion():F3}");
Console.WriteLine($"Corrected AIC:          {model.GetCorrectedAkaikeInformationCriterion():F3}");
Console.WriteLine($"Bayesian (BIC):         {model.GetBayesianInformationCriterion():F3}");
Console.WriteLine($"Chi Square:             {model.GetChiSquare():F3}");
Console.WriteLine();

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

static DataFrame<long, string> ReadAttendanceData()
{
    return DelimitedTextFile.ReadDataFrame(@"..\..\..\..\..\data\PoissonReg.csv");
}

static DataFrame<long, string> ReadGraduateData()
{
    var df = FixedWidthTextFile.ReadDataFrame(@"..\..\..\..\..\data\probit.dat",
        new FixedWidthTextOptions(new int[] { 9, 18, 27 }, columnHeaders:false));
    var columnNames = new string[] { "admit", "gre", "topnotch", "gpa" };
    return df.WithColumnIndex(columnNames);
}