/// <summary>
/// Creates a new GeneralizedLinearRegression that is a copy of the current instance.
/// </summary>
///
public object Clone()
{
ILinkFunction function = (ILinkFunction)linkFunction.Clone();
var regression = new GeneralizedLinearRegression(function, coefficients.Length);
regression.coefficients = (double[])this.coefficients.Clone();
regression.standardErrors = (double[])this.standardErrors.Clone();
return(regression);
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] output)
{
double y0 = output.Count(y => y == 0.0);
double y1 = output.Length - y0;
GeneralizedLinearRegression regression = new GeneralizedLinearRegression(linkFunction,
Inputs, Math.Log(y1 / y0));
double ratio = GetLogLikelihoodRatio(input, output, regression);
return(new ChiSquareTest(ratio, coefficients.Length - 1));
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] output)
{
double y0 = 0;
double y1 = 0;
for (int i = 0; i < output.Length; i++)
{
y0 += 1.0 - output[i];
y1 += output[i];
}
var intercept = Math.Log(y1 / y0);
var regression = new GeneralizedLinearRegression(linkFunction, Inputs, intercept);
double ratio = GetLogLikelihoodRatio(input, output, regression);
return(new ChiSquareTest(ratio, coefficients.Length - 1));
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
/// <param name="weights">The weights associated with each input vector.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] output, double[] weights)
{
double y0 = 0;
double y1 = 0;
for (int i = 0; i < output.Length; i++)
{
y0 += (1.0 - output[i]) * weights[i];
y1 += output[i] * weights[i];
}
var regression = new GeneralizedLinearRegression(linkFunction)
{
NumberOfInputs = NumberOfInputs,
Intercept = Math.Log(y1 / y0)
};
double ratio = GetLogLikelihoodRatio(input, output, weights, regression);
return(new ChiSquareTest(ratio, NumberOfInputs));
}
/// <summary>
/// Gets the Log-Likelihood Ratio between two models.
/// </summary>
///
/// <remarks>
/// The Log-Likelihood ratio is defined as 2*(LL - LL0).
/// </remarks>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
/// <param name="regression">Another Logistic Regression model.</param>
///
/// <returns>The Log-Likelihood ratio (a measure of performance
/// between two models) calculated over the given data sets.</returns>
///
public double GetLogLikelihoodRatio(double[][] input, double[] output, GeneralizedLinearRegression regression)
{
return(2.0 * (this.GetLogLikelihood(input, output) - regression.GetLogLikelihood(input, output)));
}
/// <summary>
/// Creates a new GeneralizedLinearRegression that is a copy of the current instance.
/// </summary>
///
public object Clone()
{
ILinkFunction function = (ILinkFunction)linkFunction.Clone();
var regression = new GeneralizedLinearRegression(function, coefficients.Length);
regression.coefficients = (double[])this.coefficients.Clone();
regression.standardErrors = (double[])this.standardErrors.Clone();
return regression;
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
/// <param name="weights">The weights associated with each input vector.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] output, double[] weights)
{
double y0 = 0;
double y1 = 0;
for (int i = 0; i < output.Length; i++)
{
y0 += (1.0 - output[i]) * weights[i];
y1 += output[i] * weights[i];
}
var intercept = Math.Log(y1 / y0);
var regression = new GeneralizedLinearRegression(linkFunction, Inputs, intercept);
double ratio = GetLogLikelihoodRatio(input, output, weights, regression);
return new ChiSquareTest(ratio, coefficients.Length - 1);
}
/// <summary>
/// Gets the Log-Likelihood Ratio between two models.
/// </summary>
///
/// <remarks>
/// The Log-Likelihood ratio is defined as 2*(LL - LL0).
/// </remarks>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
/// <param name="weights">The weights associated with each input vector.</param>
/// <param name="regression">Another Logistic Regression model.</param>
///
/// <returns>The Log-Likelihood ratio (a measure of performance
/// between two models) calculated over the given data sets.</returns>
///
public double GetLogLikelihoodRatio(double[][] input, double[] output, double[] weights, GeneralizedLinearRegression regression)
{
return 2.0 * (this.GetLogLikelihood(input, output, weights) - regression.GetLogLikelihood(input, output, weights));
}
/// <summary>
/// The likelihood ratio test of the overall model, also called the model chi-square test.
/// </summary>
///
/// <param name="input">A set of input data.</param>
/// <param name="output">A set of output data.</param>
///
/// <remarks>
/// <para>
/// The Chi-square test, also called the likelihood ratio test or the log-likelihood test
/// is based on the deviance of the model (-2*log-likelihood). The log-likelihood ratio test
/// indicates whether there is evidence of the need to move from a simpler model to a more
/// complicated one (where the simpler model is nested within the complicated one).</para>
/// <para>
/// The difference between the log-likelihood ratios for the researcher's model and a
/// simpler model is often called the "model chi-square".</para>
/// </remarks>
///
public ChiSquareTest ChiSquare(double[][] input, double[] output)
{
double y0 = output.Count(y => y == 0.0);
double y1 = output.Length - y0;
GeneralizedLinearRegression regression = new GeneralizedLinearRegression(linkFunction,
Inputs, Math.Log(y1 / y0));
double ratio = GetLogLikelihoodRatio(input, output, regression);
return new ChiSquareTest(ratio, coefficients.Length - 1);
}
public void ComputeTest()
{
// Example from http://bayes.bgsu.edu/bcwr/vignettes/probit_regression.pdf
double[][] input =
{
new double[] { 525 },
new double[] { 533 },
new double[] { 545 },
new double[] { 582 },
new double[] { 581 },
new double[] { 576 },
new double[] { 572 },
new double[] { 609 },
new double[] { 559 },
new double[] { 543 },
new double[] { 576 },
new double[] { 525 },
new double[] { 574 },
new double[] { 582 },
new double[] { 574 },
new double[] { 471 },
new double[] { 595 },
new double[] { 557 },
new double[] { 557 },
new double[] { 584 },
new double[] { 599 },
new double[] { 517 },
new double[] { 649 },
new double[] { 584 },
new double[] { 463 },
new double[] { 591 },
new double[] { 488 },
new double[] { 563 },
new double[] { 553 },
new double[] { 549 }
};
double[] output =
{
0, 0, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 0, 0, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 1
};
var regression = new GeneralizedLinearRegression(new ProbitLinkFunction(), inputs: 1);
var teacher = new IterativeReweightedLeastSquares(regression);
double delta = 0;
do
{
// Perform an iteration
delta = teacher.Run(input, output);
} while (delta > 1e-6);
Assert.AreEqual(2, regression.Coefficients.Length);
Assert.AreEqual(-17.6984, regression.Coefficients[0], 1e-4);
Assert.AreEqual(0.03293, regression.Coefficients[1], 1e-4);
Assert.AreEqual(2, regression.StandardErrors.Length);
Assert.AreEqual(9.2731983954911374, regression.StandardErrors[0], 1e-5);
Assert.AreEqual(0.016768779446085, regression.StandardErrors[1], 1e-6);
}
public void ComputeTest2()
{
double[][] input =
{
new double[] { 55, 0 }, // 0 - no cancer
new double[] { 28, 0 }, // 0
new double[] { 65, 1 }, // 0
new double[] { 46, 0 }, // 1 - have cancer
new double[] { 86, 1 }, // 1
new double[] { 56, 1 }, // 1
new double[] { 85, 0 }, // 0
new double[] { 33, 0 }, // 0
new double[] { 21, 1 }, // 0
new double[] { 42, 1 }, // 1
};
double[] output =
{
0, 0, 0, 1, 1, 1, 0, 0, 0, 1
};
var regression = new GeneralizedLinearRegression(new ProbitLinkFunction(), inputs: 2);
var teacher = new IterativeReweightedLeastSquares(regression);
double delta = 0;
do
{
// Perform an iteration
delta = teacher.Run(input, output);
} while (delta > 0.001);
Assert.AreEqual(3, regression.Coefficients.Length);
Assert.AreEqual(-1.4807594445304693, regression.Coefficients[0],1e-8);
Assert.AreEqual(0.012417175632016827, regression.Coefficients[1], 1e-8);
Assert.AreEqual(1.072665379969842, regression.Coefficients[2], 1e-8);
Assert.IsFalse(regression.Coefficients.HasNaN());
Assert.AreEqual(3, regression.StandardErrors.Length);
Assert.AreEqual(1.6402037052797314, regression.StandardErrors[0], 1e-8);
Assert.AreEqual(0.026119425452145524, regression.StandardErrors[1], 1e-8);
Assert.AreEqual(1.1297252500874606, regression.StandardErrors[2], 1e-8);
Assert.IsFalse(regression.StandardErrors.HasNaN());
}
