Generalized Linear Models in C# QuickStart Sample
Illustrates how to use the GeneralizedLinearModel class to compute probit, Poisson and similar regression models in C#.
View this sample in: Visual Basic F#
using System;
using Extreme.Data.Text;
using Extreme.DataAnalysis;
using Extreme.Mathematics;
using Extreme.Statistics;
namespace Extreme.Numerics.QuickStart.CSharp
{
/// <summary>
/// Illustrates building generalized linear models using
/// the GeneralizedLinearModel class in the
/// Extreme.Statistics namespace of Extreme Numerics.NET.
/// </summary>
class GeneralizedLinearModels
{
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");
// 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: {0:F4}", model.LogLikelihood);
Console.WriteLine("Kernel log likelihood: {0:F4}", model.GetKernelLogLikelihood());
// 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): {0:F3}", model.GetAkaikeInformationCriterion());
Console.WriteLine("Corrected AIC: {0:F3}", model.GetCorrectedAkaikeInformationCriterion());
Console.WriteLine("Bayesian (BIC): {0:F3}", model.GetBayesianInformationCriterion());
Console.WriteLine("Chi Square: {0:F3}", model.GetChiSquare());
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: {0:F4}", model.LogLikelihood);
Console.WriteLine("Kernel log likelihood: {0:F4}", model.GetKernelLogLikelihood());
// 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): {0:F3}", model.GetAkaikeInformationCriterion());
Console.WriteLine("Corrected AIC: {0:F3}", model.GetCorrectedAkaikeInformationCriterion());
Console.WriteLine("Bayesian (BIC): {0:F3}", model.GetBayesianInformationCriterion());
Console.WriteLine("Chi Square: {0:F3}", model.GetChiSquare());
Console.WriteLine();
Console.Write("Press any key to exit.");
Console.ReadLine();
}
public static DataFrame<long, string> ReadAttendanceData()
{
return DelimitedTextFile.ReadDataFrame(@"..\..\..\..\data\PoissonReg.csv");
}
public 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);
}
}
}