TMtxLogistReg Class

Summary

Performs logistic regression.

Hierarchy
TMtxLogistReg

Subclasses
None

Description

Use TMtxLogistReg component to perform ordinary or ordinal logistic regression on dataset.Suppose y takes values in k ordered categories, and let p_ij be the cumulative probability that y(i) falls in the j'th category or higher. The ordinal logistic regression model is defined as:

logit(p_ij) = theta(j) + A_i'B , i = 1,..,length(Y), j = 1,..,k-1,

where A_i is the i'th row of A . The number of ordinal categories k is taken to be the number of distinct values of int(y). If k is 2 (two categories) the model is ordinary logistic regression.

How to use TMtxLogistReg component?

1) Drop a TMtxLogistReg component on the form
2) Define A, the matrix of independent variables.
3) Define Y, grouping (categories) vector. NOTE: All values have to be integers.
4) Define initial estimates for Theta and B coefficients. Alternatively you can also set AutoInitEstimates to true and let the algorithm calculate initial estimates for Theta and B.
5) (Optionally) Set Tolerance to define desired B, Theta estimates precision. Set MaxIteration to define maximum number of iterations in main calculation loop. set Constant property to false
6) Call the Recalc method to trigger calculation.

Results:
1) B : B coefficients estimates.
2) Theta : Theta coefficients estimates.
3) TBStdErr : Theta and B coefficients estimates standard errors.

See Also
StatToolsDialogs

Example 1

How to setup and run logistic regression? In the following example we'll perform ordinary (i.e. with two categories) logistic regression on data, taken from NCSS statistics program. Note that TMtxLogistReg.Y vector values are binary integer values.

    Uses ..., StatTools, MtxVecEdit;
    var TestComp: TMtxLogistReg;
    begin
        TestComp := TMtxLogistReg.Create(Self);
        try
          TestComp.A.SetIt(27,3,false,
          [0.8, 1.9, 0.996,
          0.9, 1.4, 0.992,
          0.8, 0.8, 0.982,
          1, 0.7, 0.986,
          0.9,	1.3, 0.98,
          1,	0.6, 0.982,
          0.95,	1,	0.992,
          0.95,	1.9,	1.02,
          1,	0.8,	0.999,
          0.95,	0.5, 1.038,
          0.85, 0.7, 0.988,
          0.7,	1.2, 0.982,
          0.8,	0.4, 1.006,
          0.2,	0.8, 0.99,
          1,	1.1, 0.99,
          1,	1.9, 1.02,
          0.65, 0.5,	1.014,
          1,	1,	1.004,
          0.5,	0.6, 0.99,
          1,	1.1, 0.986,
          1,	0.4,	1.01,
          0.9,	0.6, 1.02,
          1,	1,	1.002,
          0.95, 1.6, 0.988,
          1,	1.7, 0.99,
          1,	0.9, 0.986,
          1,	0.7, 0.986]);
          TestComp.Y.SetIt(false,[1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,0]);
          TestComp.Recalc;
          // Results =>
          // B = (9.65215222458842, 3.86710032907408, -82.073774279211)
          // Theta = (-67.6339061278272)
          // TBStdErr = (56.8875416435276, 7.75107606604495, 1.77827769017976, 61.712376172072)
          // meaning Theta StdErr = 56.8875416435276,
          //         Beta StdErrs = 7.75107606604495, 1.77827769017976, 61.712376172072
          ViewValues(TestComp.b,'B',true);
          ViewValues(TestComp.Theta,'Theta',true);
          ViewValues(TestComp.TBStdErr,'SE',true);
        finally
          TestComp.Destroy;
        end;
    end;

    #include "StatTools.hpp"
    #include "Math387.hpp"
    #include "MtxVecCpp.h"
    void __fastcall Example(TMtxLogistReg* tc)
    {
      tc->A->SetIt(27,3,false, OPENARRAY(TSample,
          (0.8, 1.9, 0.996,
          0.9, 1.4, 0.992,
          0.8, 0.8, 0.982,
          1, 0.7, 0.986,
          0.9,	1.3, 0.98,
          1,	0.6, 0.982,
          0.95,	1,	0.992,
          0.95,	1.9,	1.02,
          1,	0.8,	0.999,
          0.95,	0.5, 1.038,
          0.85, 0.7, 0.988,
          0.7,	1.2, 0.982,
          0.8,	0.4, 1.006,
          0.2,	0.8, 0.99,
          1,	1.1, 0.99,
          1,	1.9, 1.02,
          0.65, 0.5,	1.014,
          1,	1,	1.004,
          0.5,	0.6, 0.99,
          1,	1.1, 0.986,
          1,	0.4,	1.01,
          0.9,	0.6, 1.02,
          1,	1,	1.002,
          0.95, 1.6, 0.988,
          1,	1.7, 0.99,
          1,	0.9, 0.986,
          1,	0.7, 0.986)));
      tc->Y->SetIt(false,OPENARRAY(TSample,(1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,0)));
      tc->Recalc();
      // Results =>
      // B = (9.65215222458842, 3.86710032907408, -82.073774279211)
      // Theta = (-67.6339061278272)
      // TBStdErr = (56.8875416435276, 7.75107606604495, 1.77827769017976, 61.712376172072)
      // meaning Theta StdErr = 56.8875416435276,
      //         Beta StdErrs = 7.75107606604495, 1.77827769017976, 61.712376172072
    }

    using Dew.Stats;
    using Dew.Stats.Units;
    using Dew.Math;
    namespace Dew.Examples
    {
      private void Example(StatTools.TMtxLogistReg tc)
      {
        tc.A.SetIt(27,3,false, new double[]
          {0.8, 1.9, 0.996,
          0.9, 1.4, 0.992,
          0.8, 0.8, 0.982,
          1, 0.7, 0.986,
          0.9,	1.3, 0.98,
          1,	0.6, 0.982,
          0.95,	1,	0.992,
          0.95,	1.9,	1.02,
          1,	0.8,	0.999,
          0.95,	0.5, 1.038,
          0.85, 0.7, 0.988,
          0.7,	1.2, 0.982,
          0.8,	0.4, 1.006,
          0.2,	0.8, 0.99,
          1,	1.1, 0.99,
          1,	1.9, 1.02,
          0.65, 0.5,	1.014,
          1,	1,	1.004,
          0.5,	0.6, 0.99,
          1,	1.1, 0.986,
          1,	0.4,	1.01,
          0.9,	0.6, 1.02,
          1,	1,	1.002,
          0.95, 1.6, 0.988,
          1,	1.7, 0.99,
          1,	0.9, 0.986,
          1,	0.7, 0.986});;
        tc.Y.SetIt(false,new double[] {1,1,0,0,1,0,1,0,0,0,0,0,0,0,0,1,0,0,0,1,0,0,1,0,1,1,0});
        tc.Recalc();
        // Results =>
        // B = (9.65215222458842, 3.86710032907408, -82.073774279211)
        // Theta = (-67.6339061278272)
        // TBStdErr = (56.8875416435276, 7.75107606604495, 1.77827769017976, 61.712376172072)
        // meaning Theta StdErr = 56.8875416435276,
        //         Beta StdErrs = 7.75107606604495, 1.77827769017976, 61.712376172072
      }
    }

Properties

Name	Summary
A	Independent variables.
Alpha	Desired significant value for the statistical tests.
AutoInitEstimates	Automatically calculate initial estimates for regression coefficients.
AutoUpdate
B	B coefficients estimates.
Dirty
MaxIteration	Defines one of the conditions for terminating the regression coefficient calculation.
TBStdErr	Standard errors of Theta, B estimates.
Theta	Theta coefficients estimates.
Tolerance	Defines one of the conditions for terminating the regression coefficient calculation.
Y	Grouping variable.

Methods

Name	Summary
Loaded
Recalc	Triggers logistic regression recalculation.