public void LinearLogisticRegression()
{
// do a set of logistic regression fits
// make sure not only that the fit parameters are what they should be, but that their variances/covariances are as returned
Random rng = new Random(314159);
// define logistic parameters
double a0 = 1.0; double b0 = -1.0 / 2.0;
//double a0 = -0.5; double b0 = 2.0;
// keep track of sample of returned a and b fit parameters
BivariateSample ps = new BivariateSample();
// also keep track of returned covariance estimates
// since these vary slightly from fit to fit, we will average them
double caa = 0.0;
double cbb = 0.0;
double cab = 0.0;
// do 50 fits
for (int k = 0; k < 50; k++)
{
Console.WriteLine("k={0}", k);
// generate a synthetic data set
BivariateSample s = new BivariateSample();
for (int i = 0; i < 50; i++)
{
double x = 2.0 * rng.NextDouble() - 1.0;
double ez = Math.Exp(a0 + b0 * x);
double P = ez / (1.0 + ez);
if (rng.NextDouble() < P)
{
s.Add(x, 1.0);
}
else
{
s.Add(x, 0.0);
}
}
// do the regression
LinearLogisticRegressionResult r = s.LinearLogisticRegression();
// record best fit parameters
double a = r.Intercept.Value;
double b = r.Slope.Value;
ps.Add(a, b);
Console.WriteLine("{0}, {1}", a, b);
// record estimated covariances
caa += r.Parameters.CovarianceMatrix[0, 0];
cbb += r.Parameters.CovarianceMatrix[1, 1];
cab += r.Parameters.CovarianceMatrix[0, 1];
}
caa /= ps.Count;
cbb /= ps.Count;
cab /= ps.Count;
// check that mean parameter estimates are what they should be: the underlying population parameters
Assert.IsTrue(ps.X.PopulationMean.ConfidenceInterval(0.95).ClosedContains(a0));
Assert.IsTrue(ps.Y.PopulationMean.ConfidenceInterval(0.95).ClosedContains(b0));
// check that parameter covarainces are what they should be: the reported covariance estimates
Assert.IsTrue(ps.X.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(caa));
Assert.IsTrue(ps.Y.PopulationVariance.ConfidenceInterval(0.95).ClosedContains(cbb));
Assert.IsTrue(ps.PopulationCovariance.ConfidenceInterval(0.95).ClosedContains(cab));
}