TMtxNonLinReg Class

Summary

Performs nonlinear regression.

Hierarchy
TMtxNonLinReg

Subclasses
None

Description

How to use TMtxNonLinReg component?

1) Drop a TMtxNonLinReg component on the form.
2) Define X the vector of independent variables.
3) Define Y the vector of dependent variables. Make sure that X and Y have the same length.
4) Define initial estimates for B regression parameters.
5) (Optionaly) define Weights. If you'll use weights, set UseWeights property to true.
6) Define regression function.
7) (Optionally) define the derivative procedure. If you don't define derivative procedure then the numeric approximation will be used to calculate the derivative at specific point.
8) Define the optimization method. Depending on your function different methods will give better/worse results.
9) (Optionally) define desired tolerance for result.
10) Define the maximum number of steps for optimization method. Internal optimization method will stop when number of iterations exceeds MaxIter or internal minimum precision is within Tolerance.

Results:
1) B : Regression coefficients estimates.
2) YCalc : Fitted Y values.

Example 1

In the following example we use the TMtxNonLinReg component to fit generated data to non-linear function B[0]/Power((1.0 + Exp(B[1]-B[2]*X)),1/B[3]). In this example exact derivate procedure is not used - algorithm uses numerical derivatives:

    // regress function
    function Rat43(B: TVec; X: TSample): TSample;
    begin
      Result := B[0] / Power((1.0 + Exp(B[1]-B[2]*X)),1/B[3]);
    end;

    procedure TfrmNonLinTest.FormCreate(Sender: TObject);
    var MtxNonLinReg: TMtxNonLinReg;
    begin
      MtxNonLinReg := TMtxNonLinReg.Create;
      try
        // Load data - independent variable
        MtxNonLinReg.X.SetIt(false,[9.000, 14.000, 21.000, 28.000,
                                    42.000, 57.000, 63.000, 70.000,
                                    79.000]);
        // Load data - dependent variable
        MtxNonLinReg.Y.SetIt(false,[8.930, 10.800, 18.590, 22.330,
                                    39.350, 56.110, 61.730, 64.620,
                                    67.080]);
        // Initial estimates for regression coefficients
        MtxNonLinReg.b.SetIt(false,[100,10,1,1]);
        // setup optimization parameters
        MtxNonLinReg.Tolerance := 1.0e-6; // 6 digits should do the trick
        MtxNonLinReg.GradTolerance := 1.0e-3 // 3 digits
        MtxNonLinReg.MaxIterations := 400;
        MtxNonLinReg.RegressFunction := Rat43; // regression function
        // Nelder-Marquardt method
        MtxNonLinReg.OptMethod := optMarquardt;
        MtxNonLinReg.Recalc;
        // MtxNinLinReg.b now stores calculated regression parameter estimates
      finally
        MtxNonLinReg.Destroy;
      end;
    end;

    #include "MtxVecCpp.h"
    #include "StatTools.hpp"
    #include "Math387.hpp"
    double Rat43(TVec* b,double x)
    {
      double* B = b->PValues(0);

      return b[0] / Power((1.0 + Exp(b[1]-b[2]*x)),1/b[3]);
    }

    void __fastcall Example()
    {
      TMtxNonLinReg *nlr = new TMtxNonLinReg(this);
      try
      {
        // Load data - independent variable
        nlr->X->SetIt(false,OPENARRAY(TSample,9.000, 14.000, 21.000, 28.000,
                                    42.000, 57.000, 63.000, 70.000,
                                    79.000)));
        // Load data - dependent variable
        nlr->Y->SetIt(false,OPENARRAY(TSample,(8.930, 10.800, 18.590, 22.330,
                                    39.350, 56.110, 61.730, 64.620,
                                    67.080)));
        // Initial estimates for regression coefficients
        nlr->b->SetIt(false,OPENARRAY(TSample,(100,10,1,1)));
        // setup optimization parameters
        nlr->Tolerance = 1.0e-6; // 6 digits should do the trick
        nlr->GradTolerance = 1.0e-3 // 3 digits
        nlr->MaxIterations = 400;
        nlr->RegressFunction = Rat43; // regression function
        // Nelder-Marquardt method
        nlr->OptMethod = optMarquardt;
        nlr->Recalc();
        // MtxNinLinReg->b now stores calculated regression parameter estimates
      }
      __finally
      {
        nlr->Free();
      }
    }

    using Dew.Math;
    using Dew.Stats;
    using Dew.Stats.Units;
    using System;
    namespace Dew.Examples
    {
      private double Rat43(TVec b, double x)
      {
        return b[0] / Math.Pow((1.0 + Math.Exp(b[1]-b[2]*x)),1/b[3]);
      }
      private void Example(StatTools.TMtxNonLinReg nlr)
      {
        // Load data - independent variable
        nlr.X.SetIt(false,new double[] {9.000, 14.000, 21.000, 28.000,
                                    42.000, 57.000, 63.000, 70.000,
                                    79.000});
        // Load data - dependent variable
        nlr.Y.SetIt(false,new double[] {8.930, 10.800, 18.590, 22.330,
                                    39.350, 56.110, 61.730, 64.620,
                                    67.080});
        // Initial estimates for regression coefficients
        nlr.b.SetIt(false,new double[] {100,10,1,1});
        // setup optimization parameters
        nlr.Tolerance = 1.0e-6; // 6 digits should do the trick
        nlr.GradTolerance = 1.0e-3 // 3 digits
        nlr.MaxIterations = 400;
        nlr.RegressFunction = Rat43; // regression function
        // Nelder-Marquardt method
        nlr.OptMethod = Dew.Math.Units.Optimization.optMarquardt;
        nlr.Recalc();
        // MtxNinLinReg->b now stores calculated regression parameter estimates
      }
    }

Properties

Name	Summary
AutoUpdate
B	Stores the regression coefficients.
DeriveProcedure	Defines derivatives of regression function.
Dirty
GradTolerance	Defines minimal allowed gradient C-Norm.
MaxIteration	Defines one of the conditions for terminating the regression coefficient calculation.
OptMethod	Optimization method used.
RegressFunction	Defines the regression function of several regression parameters.
SoftSearch	Defines line search algorithm for Quasi-Newton and Conjugate methods.
StopReason	Returns the reason why regression parameters calculation stopped.
Tolerance	Defines one of the conditions for terminating the regression coefficient calculation.
UseWeights	Weighted non-linear regression.
Weights	Weights.
X	Vector of independant variables.
Y	Vector of dependant variables.
YCalc	Vector of calculated values.

Methods

Name	Summary
Loaded
Recalc	Triggers non-linear regression recalculation.