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);
}
}
//if (k != 27) continue;
// do the regression
FitResult r = s.LinearLogisticRegression();
// record best fit parameters
double a = r.Parameter(0).Value;
double b = r.Parameter(1).Value;
ps.Add(a, b);
Console.WriteLine("{0}, {1}", a, b);
// record estimated covariances
caa += r.Covariance(0, 0);
cbb += r.Covariance(1, 1);
cab += r.Covariance(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));
}
public void BivariateLogisticRegression()
{
double[] c = new double[] { -0.1, 1.0 };
Random rng = new Random(1);
UniformDistribution pointDistribution = new UniformDistribution(Interval.FromEndpoints(-4.0, 4.0));
BivariateSample sample1 = new BivariateSample();
MultivariateSample sample2 = new MultivariateSample(2);
for (int k = 0; k < 1000; k++) {
double x = pointDistribution.GetRandomValue(rng);
double z = c[0] * x + c[1];
double ez = Math.Exp(z);
double p = ez / (1.0 + ez);
double y = (rng.NextDouble() < p) ? 1.0 : 0.0;
sample1.Add(x, y);
sample2.Add(x, y);
}
Console.WriteLine(sample1.Covariance / sample1.X.Variance / sample1.Y.Mean / (1.0 - sample1.Y.Mean));
Console.WriteLine(sample1.Covariance / sample1.X.Variance / sample1.Y.Variance);
FitResult result1 = sample1.LinearLogisticRegression();
FitResult result2 = sample2.TwoColumns(0, 1).LinearLogisticRegression();
FitResult result3 = sample2.LogisticLinearRegression(1);
for (int i = 0; i < result1.Dimension; i++) {
Console.WriteLine("{0} {1} {2}", i, result1.Parameter(i), result3.Parameter(i) );
}
}