# Logistic Regression in Visual Basic QuickStart Sample

Illustrates how to use the LogisticRegressionModel class to create logistic regression models in Visual Basic.

View this sample in: C# F# IronPython

``````Option Infer On

Imports Extreme.Data.Text
Imports Extreme.DataAnalysis
Imports Extreme.Statistics
Imports Extreme.Statistics.Tests

' Illustrates building logistic regression models using
' the LogisticRegressionModel class in the
' Extreme.Statistics namespace of Extreme Numerics.NET.
Module LogisticRegression

Sub Main()
' The license is verified at runtime. We're using
' https://numerics.net/trial-key

' 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.
' For the sake of clarity, we put this code in its own method.
"..\..\..\..\Data\lowbwt.txt",
{4, 11, 18, 25, 33, 42, 49, 55, 61, 68})

' We need indicator variables for the race. All we need to do
' is mark the variable as categorical:
data.MakeCategorical("RACE", Index.Create({1, 2, 3}))

' 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.

' Note that RACE, which is a categorical variable, is automatically
' expanded into indicator variables.
Dim model As LogisticRegressionModel = 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.
model.Fit()

' The Parameters collection contains information about the regression
' parameters.
Console.WriteLine("Variable              Value    Std.Error  t-stat  p-Value")
For Each parameter In model.Parameters
' Parameter objects have the following properties:
' 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.
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)
Next

' 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:
Dim lrt As SimpleHypothesisTest = 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:
Dim model2 As LogisticRegressionModel = New LogisticRegressionModel(data, "LOW",
New String() {"LWT", "RACE"})
model2.Fit()

' Print the results...
Console.WriteLine("Variable              Value    Std.Error  t-stat  p-Value")
For Each 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:
Next

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
Dim columnNames = {"id", "duration", "x2", "x3", "x4",
"nutritio", "agecat1", "agecat3", "alcohol", "smoking"}
"..\..\..\..\Data\mlogit.txt",
New FixedWidthTextOptions(
{5, 10, 15, 20, 25, 32, 37, 42, 47},

' For multinomial regression, the response variable must be
' a CategoricalVariable:
frame.MakeCategorical("duration")

' The constructor takes an extra argument of type
' LogisticRegressionMethod:
Dim model3 As New LogisticRegressionModel(frame, "duration",
{"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(frame,
"duration ~ nutritio + agecat1 + agecat3 + alcohol + smoking")

' Everything else is the same:
model3.Fit()

' 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 Each p In model3.Parameters
Console.WriteLine(p.ToString())
Next

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.WriteLine("Press Enter key to continue.")