Data Analysis Mathematics Linear Algebra Statistics
New Version 7.0!  QuickStart Samples

# Logistic Regression QuickStart Sample (F#)

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

```// Illustrates building logistic regression models using
// the LogisticRegressionModel class in the
// Extreme.Statistics namespace of the Extreme
// Optimization Numerical Libraries for .NET.

#light

open System

open System.Data
open System.IO

open Extreme.DataAnalysis
open Extreme.Statistics

open Extreme.Mathematics
open Extreme.Mathematics.LinearAlgebra.IO

// 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.
let data =
@"..\..\..\..\Data\lowbwt.txt")
reader.SetColumnBreaks(0, 4, 11, 18, 25, 33, 42, 49, 55, 61, 68)
result

// Race is a categorical variable:
data.MakeCategorical("RACE", Index.Create([|1;2;3|]))

// Now create the regression model. Parameters are the name
// of the dependent variable, a let array containing
// the names of the independent variables, and the VariableCollection
// containing all variables.
let model = LogisticRegressionModel(data, "LOW", [| "AGE"; "LWT"; "RACE"; "FTV" |])

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

// The Parameters collection contains information about the regression
// parameters.
printfn "Variable  Value    Std.Error  t-stat  p-Value"
for parameter in model.Parameters do
// Parameter objects have the following properties:
printfn "%-20s%10.5f%10.5f%8.2f %7.4f"
// Name, usually the name of the variable:
parameter.Name
// Estimated value of the parameter:
parameter.Value
// Standard error:
parameter.StandardError
// The value of the t statistic for the hypothesis that the parameter
// is zero.
parameter.Statistic
// Probability corresponding to the t statistic.
parameter.PValue

// The log-likelihood of the computed solution is also available:
printfn "Log-likelihood: %.4f" (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:
let lrt = model.GetLikelihoodRatioTest()
printfn "Likelihood-ratio test: chi-squared=%.4f, p=%.4f" lrt.Statistic lrt.PValue
printfn ""

// We can compute a model with fewer parameters:
let model2 = LogisticRegressionModel(data, "LOW ~ LWT + RACE")
model2.Compute()

// Print the results...
printfn "Variable  Value    Std.Error  t-stat  p-Value"
for parameter in model2.Parameters do
printfn "%-20s%10.5f%10.5f%8.2f %7.4f" parameter.Name parameter.Value
parameter.StandardError parameter.Statistic parameter.PValue
// ...including the log-likelihood:
printfn "Log-likelihood: %.4f" (model.LogLikelihood)

// We can now compare the original model to this one, once again
// using the likelihood ratio test:
let lrt2 = model.GetLikelihoodRatioTest(model2)
printfn "Likelihood-ratio test: chi-squared=%.4f, p=%.4f" lrt2.Statistic lrt2.PValue
printfn ""

//
// 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
let m =
File.OpenText(@"..\..\..\..\Data\mlogit.txt"),
0, [| 5; 10; 15; 20; 25; 32; 37; 42; 47 |],
System.Globalization.NumberStyles.Integer, null)

// Next, convert the columns to variables.

// For multinomial regression, the response variable must be
// a CategoricalVariable:
let duration = m.GetColumn(1).AsCategorical()
let nutritio = m.GetColumn(5)
let agecat1 = m.GetColumn(6)
let agecat3 = m.GetColumn(7)
let alcohol = m.GetColumn(8)
let smoking = m.GetColumn(9)

let dataFrame =
let cols : IVector[] = [| duration; nutritio; agecat1; agecat3; alcohol; smoking |]
let names = [| "duration"; "nutritio"; "agecat1"; "agecat3"; "alcohol"; "smoking" |]
DataFrame.FromColumns(cols, names)

// 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.
let model3 = new LogisticRegressionModel(dataFrame, "duration ~ .")

// Everything else is the same:
model3.Compute()

// 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.
for p in model3.Parameters do
printfn "%O" p

printfn "Log likelihood: %.4f" (model3.LogLikelihood)

// To test the hypothesis that all the slopes are zero,
// use the GetLikelihoodRatioTest method.
let lrt3 = model3.GetLikelihoodRatioTest()
printfn "Test that all slopes are zero: chi-squared=%.4f, p=%0.4f" lrt3.Statistic lrt3.PValue

printf "Press any key to exit."