VB.NET Advanced Two Way Anova Example

Imports System
Imports System.Collections

Imports CenterSpace.NMath.Core
Imports CenterSpace.NMath.Stats

Namespace CenterSpace.NMath.Stats.Examples.VisualBasic

  ' A .NET example in VB.NET showing some of the advanced features of the class
  ' TwoWayAnova.
  Module AdvancedTwoWayAnovaExample

    Private MaterialColumnName_ As String = "Material"
    Private TempColumnName_ As String = "Temperature"
    Private LifetimeColumnName_ As String = "Lifetime"

    Sub Main()

      ' Create the DataFrame that will hold the data to analyze. The variable
      ' being measured is battery lifetime. The two factors are material and 
      ' temperature. The data must have at least three columns. One column
      ' must be numeric and contain the values of the variable being measured,
      ' battery life in this case, the other two columns must contain the values
      ' of the two factors that correspond to the measurement. Thus a row of the
      ' the DataFrame that we are going to use contains a value for the battery
      ' material (M1, M2, or M3), a temperature (15, 70, or 175), and a lifetime
      ' (in hours). The method CreateBatteryData() builds the DataFrame.
      Dim BatteryData As DataFrame = CreateBatteryData()

      ' Now create a TwoWayAnova object from the battery data. The three
      ' integer arguments indicate the following column indicies, respectively:
      ' index of the column containing factor A, index of the column containing
      ' factor B, index of the column containing the measured values.
      Dim Anova As TwoWayAnova = New TwoWayAnova(BatteryData, 0, 1, 2)

      ' Class TwoWayAnova provides access to the data in a particular
      ' cell. A cell is defined by the values of the two factors. For 
      ' example, the following code prints out all the battery lifetimes
      ' for batteries made from material M2 at temperature 70.
      Dim MTwoSeventyValues As DFNumericColumn = Anova.GetCellData(MaterialColumnName_, "M2", TempColumnName_, "70")
      Console.WriteLine()
      Console.WriteLine("Lifetimes of M2 batteries at 70 degrees: " & MTwoSeventyValues.ToString())

      ' You can also get the means for each cell:
      Dim Mean As Double = Anova.GetMeanForCell(MaterialColumnName_, "M2", TempColumnName_, "70")
      Console.WriteLine("Mean lifetime of M2 batteries at 70 degrees: " & Mean)

      ' Means for a given factor level can also be accessed. For example, the 
      ' following code gets the mean lifetime for all batteries made from material
      ' M1
      Mean = Anova.GetMeanForFactorLevel(MaterialColumnName_, "M1")
      Console.WriteLine("Mean lifetime for M1 batteries = " & Mean)

      ' You can also get the grand mean.
      Console.WriteLine("Overall mean lifetime is " & Anova.GrandMean)
      Console.WriteLine()

      ' The TwoWayAnovaTable class is used to access all the traditional 
      ' two way ANOVA data.
      Dim AnovaTable As TwoWayAnovaTable = Anova.AnovaTable
      Console.Write("Source: ")
      Console.WriteLine(MaterialColumnName_)
      Console.WriteLine("  Degrees of Freedom: " & AnovaTable.DegreesOfFreedom(MaterialColumnName_))
      Console.WriteLine("  Sum of Squares    : " & AnovaTable.SumOfSquares(MaterialColumnName_))
      Console.WriteLine("  Mean Square       : " & AnovaTable.MeanSquare(MaterialColumnName_))
      Console.WriteLine("  F                 : " & AnovaTable.Fstatistic(MaterialColumnName_))
      Console.WriteLine("  P                 : " & AnovaTable.FstatisticPvalue(MaterialColumnName_))
      Console.WriteLine()

      Console.WriteLine("Source: " & TempColumnName_)
      Console.WriteLine("  Degrees of Freedom: " & AnovaTable.DegreesOfFreedom(TempColumnName_))
      Console.WriteLine("  Sum of Squares    : " & AnovaTable.SumOfSquares(TempColumnName_))
      Console.WriteLine("  Mean Square       : " & AnovaTable.MeanSquare(TempColumnName_))
      Console.WriteLine("  F                 : " & AnovaTable.Fstatistic(TempColumnName_))
      Console.WriteLine("  P                 : " & AnovaTable.FstatisticPvalue(TempColumnName_))
      Console.WriteLine()

      Console.WriteLine("Source: Interaction")
      Console.WriteLine("  Degrees of Freedom: " & AnovaTable.InteractionDegreesOfFreedom)
      Console.WriteLine("  Sum of Squares    : " & AnovaTable.InteractionSumOfSquares)
      Console.WriteLine("  Mean Square       : " & AnovaTable.InteractionMeanSquare)
      Console.WriteLine("  F                 : " & AnovaTable.InteractionFstatistic)
      Console.WriteLine("  P                 : " & AnovaTable.InteractionFstatisticPvalue)
      Console.WriteLine()

      Console.WriteLine("Source: Error")
      Console.WriteLine("  Degrees of Freedom: " & AnovaTable.ErrorDegreesOfFreedom)
      Console.WriteLine("  Sum of Squares    : " & AnovaTable.ErrorSumOfSquares)
      Console.WriteLine("  Mean Square       : " & AnovaTable.ErrorMeanSquare)
      Console.WriteLine()

      Console.WriteLine("Total")
      Console.WriteLine("  Degrees of Freedom: " & AnovaTable.TotalDegreesOfFreedom)
      Console.WriteLine("  Sum of Squares    : " & AnovaTable.TotalSumOfSquares)
      Console.WriteLine()

      ' Class TwoWayAnova computes a two way ANOVA using a multiple linear
      ' regression. The following function prints out details of the regression.
      ' See the function WriteRegressionInfo() for more information.
      Console.WriteLine("-------- Regression Information -----------")
      Console.WriteLine()

      WriteRegressionInfo(Anova)

      Console.WriteLine()
      Console.WriteLine("Press Enter Key")
      Console.Read()

    End Sub

    ' Two way ANOVAs are computed using a multiple linear regression. The
    ' details of this regression are available from the TwoWayAnova class.
    ' This functions shows how to access these details and sends the 
    ' information to the Console.
    Private Sub WriteRegressionInfo(ByRef Anova As TwoWayAnova)

      ' A multiple linear regression is used to solve a two way ANOVA
      ' problem by creating dummy variables using an encoding. The
      ' TwoWayAnova class uses "effects" encoding to accomplish this.
      ' In effects encoding we define k - 1 dummy variables to encode
      ' k levels of the factor in interest. A dummy variable di for the
      ' the ith level is then defined as
      ' 
      ' di =  1 if ith level,
      ' di = -1 if kth level,
      ' di =  0 otherwise
      '
      ' If factor A has k levels, and factor B has m levels, there will also
      ' be (k - 1) * (m - 1) interaction variables in the regression. It
      ' follows that there will not be a regression parameter for every factor
      ' level, or interaction. In the code below you will notice that we check
      ' for a null return value when attempting to retrieve a regression 
      ' parameter object for a particular factor level or interaction of
      ' factor levels. This is the reason.


      ' First print out information for the intercept parameter. The class
      ' AnovaRegressionParameter is derived from LinearRegressionParameter.
      ' It merely adds the SumOfSquares property.
      Dim InterceptParam As AnovaRegressionParameter = Anova.RegressionInterceptParameter
      Console.WriteLine("Parameter: Intercept")
      Console.WriteLine("  Estimate              : " & InterceptParam.Value)
      Console.WriteLine("  Standard Error        : " & InterceptParam.StandardError)
      Console.WriteLine("  T for H0 Parameter = 0: " & InterceptParam.TStatistic(0))
      Console.WriteLine("  Prob > |T|            : " & InterceptParam.TStatisticPValue(0))
      Console.WriteLine("  Type I SS             : " & InterceptParam.SumOfSquares)
      Console.WriteLine("  Variable Label: INTERCEPT")
      Console.WriteLine()

      ' Next print out information for the Material factor parameters. Since there
      ' is one less paramters than there are levels, we'll have to check for null
      ' return values from GetRegressionFactorParameter().
      ' AnovaRegressionFactorParam is derived from AnovaRegressionParameter, and
      ' hence from LinearRegressionParameter, adding the Encoding property. 
      Dim FactorParam As AnovaRegressionFactorParam
      Dim MaterialLevels() As String = {"M1", "M2", "M3"}

      Dim I As Integer
      For I = 0 To MaterialLevels.Length - 1
        FactorParam = Anova.GetRegressionFactorParameter(MaterialColumnName_, MaterialLevels(I))
        If FactorParam Is Nothing Then
        Else
          Console.WriteLine(String.Format("Parameter: {0}", MaterialLevels(I)))
          Console.WriteLine("  Estimate              : " & FactorParam.Value)
          Console.WriteLine("  Standard Error        : " & FactorParam.StandardError)
          Console.WriteLine("  T for H0 Parameter = 0: " & FactorParam.TStatistic(0))
          Console.WriteLine("  Prob > |T|            : " & FactorParam.TStatisticPValue(0))
          Console.WriteLine("  Type I SS             : " & FactorParam.SumOfSquares)
          Dim Encoding As String
          Encoding = "  Variable Label: dummy variable = "
          Encoding += FactorParam.Encoding.ToString()
          Encoding += " if "
          Encoding += MaterialColumnName_
          Encoding += " = "
          Encoding += MaterialLevels(I)
          Console.WriteLine(Encoding)
          Console.WriteLine()
        End If
      Next

      ' Now, do the same for the temperature factor parameter.
      Dim TempLevels() As String = {"15", "70", "125"}

      For I = 0 To MaterialLevels.Length - 1
        FactorParam = Anova.GetRegressionFactorParameter(TempColumnName_, TempLevels(I))
        If FactorParam Is Nothing Then
        Else
          Console.WriteLine(String.Format("Parameter: {0}", TempLevels(I)))
          Console.WriteLine("  Estimate              : " & FactorParam.Value)
          Console.WriteLine("  Standard Error        : " & FactorParam.StandardError)
          Console.WriteLine("  T for H0 Parameter = 0: " & FactorParam.TStatistic(0))
          Console.WriteLine("  Prob > |T|            : " & FactorParam.TStatisticPValue(0))
          Console.WriteLine("  Type I SS             : " & FactorParam.SumOfSquares)
          Dim Encoding As String
          Encoding = "  Variable Label: dummy variable = "
          Encoding += FactorParam.Encoding.ToString()
          Encoding += " if "
          Encoding += TempColumnName_
          Encoding += " = "
          Encoding += TempLevels(I)
          Console.WriteLine(Encoding)
          Console.WriteLine()
        End If
      Next

      ' Finally, print out information for the interaction parameters. 
      ' AnovaRegressionInteractionParam is derived from AnovaRegressionParameter, and
      ' hence from LinearRegressionParameter. It does not contain an Encoding 
      ' property. The value of the interaction variables is just the product of
      ' the values of their corresponding factor variables.
      Dim InteractionParam As AnovaRegressionInteractionParam

      Dim J As Integer
      For I = 0 To MaterialLevels.Length - 1
        For J = 0 To TempLevels.Length - 1
          InteractionParam = Anova.GetRegressionInteractionParameter(MaterialColumnName_, MaterialLevels(I), TempColumnName_, TempLevels(J))
          If InteractionParam Is Nothing Then
          Else
            Console.WriteLine(String.Format("Parameter: {0}, {1}", MaterialLevels(I), TempLevels(J)))
            Console.WriteLine("  Estimate              : " & InteractionParam.Value)
            Console.WriteLine("  Standard Error        : " & InteractionParam.StandardError)
            Console.WriteLine("  T for H0 Parameter = 0: " & InteractionParam.TStatistic(0))
            Console.WriteLine("  Prob > |T|            : " & InteractionParam.TStatisticPValue(0))
            Console.WriteLine("  Type I SS             : " & InteractionParam.SumOfSquares)
            Dim Encoding As String = String.Format("  Variable Label: interaction of {0} and {1}", MaterialLevels(I), TempLevels(J))
            Console.WriteLine(Encoding)
            Console.WriteLine()
          End If
        Next
      Next
    End Sub

    Private Function CreateBatteryData() As DataFrame
      Dim Data As New DataFrame()
      Data.AddColumn(New DFStringColumn(MaterialColumnName_))
      Data.AddColumn(New DFStringColumn(TempColumnName_))
      Dim BatteryLifetimeColumn As New DFIntColumn(LifetimeColumnName_)
      Data.AddColumn(BatteryLifetimeColumn)

      Dim RowNumber As Integer = 0
      Data.AddRow(++RowNumber, "M1", "15", 130)
      Data.AddRow(++RowNumber, "M1", "15", 155)
      Data.AddRow(++RowNumber, "M1", "15", 74)
      Data.AddRow(++RowNumber, "M1", "15", 180)
      Data.AddRow(++RowNumber, "M1", "70", 34)
      Data.AddRow(++RowNumber, "M1", "70", 40)
      Data.AddRow(++RowNumber, "M1", "70", 80)
      Data.AddRow(++RowNumber, "M1", "70", 75)
      Data.AddRow(++RowNumber, "M1", "125", 20)
      Data.AddRow(++RowNumber, "M1", "125", 70)
      Data.AddRow(++RowNumber, "M1", "125", 82)
      Data.AddRow(++RowNumber, "M1", "125", 58)
      Data.AddRow(++RowNumber, "M2", "15", 150)
      Data.AddRow(++RowNumber, "M2", "15", 188)
      Data.AddRow(++RowNumber, "M2", "15", 159)
      Data.AddRow(++RowNumber, "M2", "15", 126)
      Data.AddRow(++RowNumber, "M2", "70", 136)
      Data.AddRow(++RowNumber, "M2", "70", 122)
      Data.AddRow(++RowNumber, "M2", "70", 106)
      Data.AddRow(++RowNumber, "M2", "70", 115)
      Data.AddRow(++RowNumber, "M2", "125", 25)
      Data.AddRow(++RowNumber, "M2", "125", 70)
      Data.AddRow(++RowNumber, "M2", "125", 58)
      Data.AddRow(++RowNumber, "M2", "125", 45)
      Data.AddRow(++RowNumber, "M3", "15", 138)
      Data.AddRow(++RowNumber, "M3", "15", 110)
      Data.AddRow(++RowNumber, "M3", "15", 168)
      Data.AddRow(++RowNumber, "M3", "15", 160)
      Data.AddRow(++RowNumber, "M3", "70", 174)
      Data.AddRow(++RowNumber, "M3", "70", 120)
      Data.AddRow(++RowNumber, "M3", "70", 150)
      Data.AddRow(++RowNumber, "M3", "70", 139)
      Data.AddRow(++RowNumber, "M3", "125", 96)
      Data.AddRow(++RowNumber, "M3", "125", 104)
      Data.AddRow(++RowNumber, "M3", "125", 82)
      Data.AddRow(++RowNumber, "M3", "125", 60)

      Return Data

    End Function

  End Module

End Namespace