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// --------------------------------------------------------------------------
// OpenMS -- Open-Source Mass Spectrometry
// --------------------------------------------------------------------------
// Copyright The OpenMS Team -- Eberhard Karls University Tuebingen,
// ETH Zurich, and Freie Universitaet Berlin 2002-2013.
//
// This software is released under a three-clause BSD license:
// * Redistributions of source code must retain the above copyright
// notice, this list of conditions and the following disclaimer.
// * Redistributions in binary form must reproduce the above copyright
// notice, this list of conditions and the following disclaimer in the
// documentation and/or other materials provided with the distribution.
// * Neither the name of any author or any participating institution
// may be used to endorse or promote products derived from this software
// without specific prior written permission.
// For a full list of authors, refer to the file AUTHORS.
// --------------------------------------------------------------------------
// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
// ARE DISCLAIMED. IN NO EVENT SHALL ANY OF THE AUTHORS OR THE CONTRIBUTING
// INSTITUTIONS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
// EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
// PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS;
// OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
// WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR
// OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF
// ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
//
// --------------------------------------------------------------------------
// $Maintainer: Clemens Groepl $
// $Authors: $
// --------------------------------------------------------------------------
#include <OpenMS/MATH/STATISTICS/LinearRegression.h>
namespace OpenMS
{
namespace Math
{
DoubleReal LinearRegression::getIntercept() const
{
return intercept_;
}
DoubleReal LinearRegression::getSlope() const
{
return slope_;
}
DoubleReal LinearRegression::getXIntercept() const
{
return x_intercept_;
}
DoubleReal LinearRegression::getLower() const
{
return lower_;
}
DoubleReal LinearRegression::getUpper() const
{
return upper_;
}
DoubleReal LinearRegression::getTValue() const
{
return t_star_;
}
DoubleReal LinearRegression::getRSquared() const
{
return r_squared_;
}
DoubleReal LinearRegression::getStandDevRes() const
{
return stand_dev_residuals_;
}
DoubleReal LinearRegression::getMeanRes() const
{
return mean_residuals_;
}
DoubleReal LinearRegression::getStandErrSlope() const
{
return stand_error_slope_;
}
DoubleReal LinearRegression::getChiSquared() const
{
return chi_squared_;
}
DoubleReal LinearRegression::getRSD() const
{
return rsd_;
}
void LinearRegression::computeGoodness_(double * X, double * Y, int N, double confidence_interval_P)
{
// Variance and Covariances
double var_X = gsl_stats_variance(X, 1, N);
double var_Y = gsl_stats_variance(Y, 1, N);
double cov_XY = gsl_stats_covariance(X, 1, Y, 1, N);
// Mean of abscissa and ordinate values
double x_mean = gsl_stats_mean(X, 1, N);
double y_mean = gsl_stats_mean(Y, 1, N);
// S_xx
double s_XX = 0;
for (int i = 0; i < N; ++i)
{
double d = (X[i] - x_mean);
s_XX += d * d;
}
// Compute the squared Pearson coefficient
r_squared_ = (cov_XY * cov_XY) / (var_X * var_Y);
// The standard deviation of the residuals
double sum = 0;
for (Int i = 0; i < N; ++i)
{
double x_i = fabs(Y[i] - (intercept_ + slope_ * X[i]));
sum += x_i;
}
mean_residuals_ = sum / N;
stand_dev_residuals_ = sqrt((chi_squared_ - (sum * sum) / N) / (N - 1));
// The Standard error of the slope
stand_error_slope_ = stand_dev_residuals_ / sqrt(s_XX);
// and the intersection of Y_hat with the x-axis
x_intercept_ = -(intercept_ / slope_);
double P = 1 - (1 - confidence_interval_P) / 2;
t_star_ = gsl_cdf_tdist_Pinv(P, N - 2);
//Compute the asymmetric 95% confidence intervall of around the X-intercept
double g = (t_star_ / (slope_ / stand_error_slope_));
g *= g;
double left = (x_intercept_ - x_mean) * g;
double bottom = 1 - g;
double d = (x_intercept_ - x_mean);
double right = t_star_ * (stand_dev_residuals_ / slope_) * sqrt((d * d) / s_XX + (bottom / N));
// Confidence intervall lower_ <= X_intercept <= upper_
lower_ = x_intercept_ + (left + right) / bottom;
upper_ = x_intercept_ + (left - right) / bottom;
if (lower_ > upper_)
{
std::swap(lower_, upper_);
}
double tmp = 0;
for (Int i = 0; i < N; ++i)
{
tmp += (X[i] - x_mean) * (X[i] - x_mean);
}
// cout << "100.0 / abs( x_intercept_ ) " << (100.0 / fabs( x_intercept_ )) << endl;
// cout << "tmp : " << tmp << endl;
// cout << "slope_ " << slope_ << endl;
// cout << "y_mean " << y_mean << endl;
// cout << "N " << N << endl;
// cout << "stand_dev_residuals_ " << stand_dev_residuals_ << endl;
// cout << " (1.0/ (double) N) " << (1.0/ (double) N) << endl;
// cout << "sx hat " << (stand_dev_residuals_ / slope_) * sqrt( (1.0/ (double) N) * (y_mean / (slope_ * slope_ * tmp ) ) ) << endl;
// compute relative standard deviation (non-standard formula, taken from Mayr et al. (2006) )
rsd_ = (100.0 / fabs(x_intercept_)) * (stand_dev_residuals_ / slope_) * sqrt((1.0 / (double) N) * (y_mean / (slope_ * slope_ * tmp)));
if (rsd_ < 0.0)
{
std::cout << "rsd < 0.0 " << std::endl;
std::cout << "Intercept " << intercept_
<< "\nSlope " << slope_
<< "\nSquared pearson coefficient " << r_squared_
<< "\nValue of the t-distribution " << t_star_
<< "\nStandard deviation of the residuals " << stand_dev_residuals_
<< "\nStandard error of the slope " << stand_error_slope_
<< "\nThe X intercept " << x_intercept_
<< "\nThe lower border of confidence interval " << lower_
<< "\nThe higher border of confidence interval " << upper_
<< "\nChi squared value " << chi_squared_
<< "\nx mean " << x_mean
<< "\nstand_error_slope/slope_ " << (stand_dev_residuals_ / slope_)
<< "\nCoefficient of Variation " << (stand_dev_residuals_ / slope_) / x_mean * 100 << std::endl
<< "========================================="
<< std::endl;
}
}
}
}
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