LogisticRegress Routines

Summary

Ordinal logistic regression.

Declaration

Function LogisticRegress(y: TVec; A: TMtx; B, Theta: TVec; StdErr: TVec; out FMin: TSample; out StopReason: TOptStopReason; MaxIter: Integer = 100; Tolerance: TSample = SQRTEPS; AutoInitEstimates: boolean = true): integer;

Parameter	Description
A	Matrix of independent variables. It is assumed to have full column rank.
B	Set it to define initial estimates for B. After the call to LogisticRegress returns regression parameter estimates for B.
Theta	Set it to define initial estimates for Theta. After the call to LogisticRegress returns regression parameter estimates for Theta.
FMin	Returns logistic log-likehood function, evaluated at minimum.
StopReason	Returns why the internal Marquardt optimization method stopped.
MaxIter	Maximum number of allowed iterations in main optimisation loop.
Tolerance	Desired tolerance for optimisation minimum.
StdErr	Returns Theta and B coefficients standard error. This is an estimate of the precision of the Theta and B estimates. The covariance matrix is obtained by inverting the observed information matrix evaluated at the maximum likelihood estimates. The standard errors are the square roots of the diagonal elements of this covariance matrix.
AutoInitEstimates	If true then B and Theta initial estimates will be calculated. If false then you must specify initial values for B and Theta.

Result

number of iterations needed to converge to solution with Tolerance precision.

Description

Performs logistic or ordinal logistic regression. 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 the model is ordinary logistic regression[1].

See Also
[1] Statbox 4.2: Statistics ToolBox for Matlab.
[2] Code adapted from Gordon K Smyth, U of Queensland, Australia, gks@maths.uq.oz.au

Example 1

The following example performs ordinal logistic regression. There are three levels of response and two intercepts in the output to distinguish the three levels.

  Uses Math387, MtxExp, Regress, Optimization;
  procedure Example;
  var y, b, theta, StdErr: Vector;
      A: Matrix;
      FMin: TSample;
      StopReason: TOptStopReason;
  begin
     y.SetIt(false,[1,1,2,1,3,2,3,2,3,3]);
    A.SetIt(false,10,1,[1,
                        2,
                        3,
                        4,
                        5,
                        6,
                        7,
                        8,
                        9,
                        10]);
    LogisticRegress(y,A,b,theta,StdErr,FMin,StopReason);
    // Result => b = (0.801), theta=(2.779,5.366)
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math387.hpp"
  void __fastcall Example()
  {
    Matrix A;
    Vector y,b,theta,se;
    double min;
    TOptStopReason stopreason;
    y->SetIt(false,OPENARRAY(TSample,(1,1,2,1,3,2,3,2,3,3)));
    A->SetIt(false,10,1,OPENARRAY(TSample,(1,2,3,4,5,6,7,8,9,10)));
    LogisticRegress(y,A,b,theta,se,min,stopreason);
    // Result => b = (0.801), theta=(2.779,5.366)

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector y = new Vector(0);
      Vector b = new Vector(0);
      Vector theta = new Vector(0);
      Vector se = new Vector(0);
      Matrix A = new Matrix(0,0,false);
      double min;
      TOptStopReason stopreason;
      y.SetIt(false,new double[] {1,1,2,1,3,2,3,2,3,3});
      A.SetIt(false,10,1,new double[] {1,2,3,4,5,6,7,8,9,10});
      Regression.LogisticRegress(y,A,b,theta,se,out min, out stopreason,
        100,1.0e-8,true);
      // Result => b = (0.801), theta=(2.779,5.366)
    }
  }

Declaration

Procedure LogisticRegress(y, n: TVec; b: TVec; A: TMtx = nil; Offset: TSample = 0.0; YCalc: TVec = nil; BStd: TVec = nil; Tolerance: TSample = EPS);

Summary

Logistic regression.

Parameter	Description
Y	response vector containing binomial counts.
n	number of trials for each count. Y is assumed to be binomial(p,N).
A	matrix of covariates, including the constant vector if required.
Offset	offset if required.
B	regression parameter estimates.
YCalc	fitted values.
BStd	Regression parameter estimates errors.This is an estimate of the precision of the B estimates.
Tolerance	Default precision for reweighted LQR.

Description

Fit logistic regression model.

Example 1

The following example calculates coefficients for simple logistic regression. The counts are out of 10 in each case and there is one covariate[1].

  Uses MtxExpr, Regress;
  procedure Example;
  var y,n,B: Vector;
    X: Matrix;
  begin
    y.SetIt(false,[2,0,3,1,5,5,6,9,5,9]);
    n.Size(y);
    n.SetVal(10.0);
    X.SetIt(false,10,2
            [1,1,
            1,2,
            1,3,
            1,4,
            1,5,
            1,6,
            1,7,
            1,8,
            1,9,
            1,10]);
    LogisticRegress(y,n,B);
    // Result =>  B = (-2.58,0.42)
  end;

  #include "MtxVecCpp.h"
  #include "Regress.hpp"
  #include "Math387.hpp"
  void __fastcall Example()
  {
    Matrix X;
    Vector y,n,B;
    y->SetIt(false,OPENARRAY(TSample,(2,0,3,1,5,5,6,9,5,9)));
    n->Size(y);
    n->SetVal(10.0);
    X->SetIt(false,10,2, OPENARRAY(TSample,(
          1,1,
          1,2,
          1,3,
          1,4,
          1,5,
          1,6,
          1,7,
          1,8,
          1,9,
          1,10)));
    LogisticRegress(y,n,B,NULL);
    // Result =>  B = (-2.58,0.42)
  }

  using Dew.Math;
  using Dew.Stats;
  using Dew.Stats.Units;
  namespace Dew.Examples
  {
    private void Example()
    {
      Vector y = new Vector(0);
      Vector n = new Vector(0);
      Vector B = new Vector(0);
      Matrix X = new Matrix(0,0);
      y.SetIt(false,new double[] {2,0,3,1,5,5,6,9,5,9});
      n.Size(y);
      n.SetVal(10.0);
      X.SetIt(false,10,2, new double[]
            {1,1,
            1,2,
            1,3,
            1,4,
            1,5,
            1,6,
            1,7,
            1,8,
            1,9,
            1,10});
      Regress.LogisticRegress(y,n,B,null);
      // Result =>  B = (-2.58,0.42)
    }
  }