Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \). More...

#include <MLRModel.hpp>

Public Types
typedef CommonType< typename Vector< T >::SizeType, typename Matrix< T >::SizeType >::Type	SizeType

typedef T	ValueType

typedef Matrix< T >	MatrixType

typedef Vector< T >	VectorType

Public Member Functions
	MLRModel ()
	Constructs and initializes a regression model with an empty data set. More...

void	resizeDataSet (SizeType num_points, SizeType num_vars)
	Resizes the data set to hold num_points data points with num_vars independent variables. More...

void	clearDataSet ()
	Clears the data set. More...

template<typename V >
void	setXYData (SizeType i, const VectorExpression< V > &x_vars, ValueType y)
	Sets the i-th data point \( (y_i, \vec{X}_i) \) of the data set. More...

template<typename V >
void	addXYData (const VectorExpression< V > &x_vars, ValueType y)
	Adds a new data point \( (y, \vec{X}) \) to the current data set. More...

MatrixType &	getXMatrix ()
	Returns a matrix where each row represents the vector \( \vec{X}_i \) with independent variables of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \). More...

const MatrixType &	getXMatrix () const
	Returns a read-only matrix where each row represents the vector \( \vec{X}_i \) with independent variables of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \). More...

VectorType &	getYValues ()
	Returns a vector containing the dependent variables \( y_i \) of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \). More...

const VectorType &	getYValues () const
	Returns a read-only vector containing the dependent variables \( y_i \) of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \). More...

void	buildModel ()
	Performs linear least squares regression modeling of the set of currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \). More...

template<typename V >
ValueType	calcYValue (const VectorExpression< V > &x_vars) const
	Predicts the value of the dependent variable \( y \) for a vector \( \vec{X} \) of independent variables given by x_vars. More...

template<typename V >
ValueType	operator() (const VectorExpression< V > &x_vars) const
	Predicts the value of the dependent variable \( y \) for a vector \( \vec{X} \) of independent variables given by x_vars. More...

const VectorType &	getCoefficients () const
	Returns a read-only vector containing the estimated regression coefficients \( \beta_i \) which were calculated by buildModel(). More...

ValueType	getChiSquare () const
	Returns the sum of squared residuals \( \chi^2 \). More...

ValueType	getGoodnessOfFit () const
	Returns the goodness of fit \( Q \). More...

ValueType	getCorrelationCoefficient () const
	Returns the correlation coefficient \( r \). More...

ValueType	getStandardDeviation () const
	Returns the standard deviation of the residuals \( s_r \). More...

void	calcStatistics ()
	Calculates various statistical parameters describing the built regression model. More...

template<typename V >
CDPL::Math::MLRModel< T >::ValueType	calcYValue (const VectorExpression< V > &x) const

template<typename V >
CDPL::Math::MLRModel< T >::ValueType	operator() (const VectorExpression< V > &x) const

Detailed Description

template<typename T = double>
class CDPL::Math::MLRModel< T >

Performs Multiple Linear Regression [WLIREG] on a set of data points \( (y_i, \vec{X}_i) \).

For each data point, \( y_i \) is the dependent (response) variable and \( \vec{X}_i \) is a \( M \)-dimensional vector containing the independent (explanatory) variables of the modeled function \( y = f(\vec{X}) \). It is assumed that the relationship between the dependent variables \( y_i \) and the independent variables \( \vec{X}_i \) can be modeled by a linear function of \( M \) parameters \( \beta_i, \, i = 1, 2, \ldots, M \) (regression coefficients) plus an error term \( \epsilon_i \):

\[ y_i = \beta_1 x_{i1} + \beta_2 x_{i2} + \ldots + \beta_M x_{iM} + \epsilon_i \]

The parameters \( \beta_i \) are estimated by Least Squares Analysis [WLSQRS] which minimizes the sum of squared residuals \( \chi^2 \)

\[ \chi^2 = \sum_{i=1}^{N} (y_i - f(\vec{X}_i, \vec{\beta}))^2 \]

of the given set of \( N \) data points with respect to the adjustable parameters \( \vec{\beta} \). The parameters \( \beta_i \) are computed using Singular Value Decomposition [WSVD] as implemented in [NRIC]. This method is computationally intensive, but is particularly useful if the \( X \) matrix is ill-conditioned.

Template Parameters

T	The value type used in calculations and for storage of data points.

Member Typedef Documentation

◆ SizeType

template<typename T = double>

typedef CommonType<typename Vector<T>::SizeType, typename Matrix<T>::SizeType>::Type CDPL::Math::MLRModel< T >::SizeType

◆ ValueType

template<typename T = double>

typedef T CDPL::Math::MLRModel< T >::ValueType

◆ MatrixType

template<typename T = double>

typedef Matrix<T> CDPL::Math::MLRModel< T >::MatrixType

◆ VectorType

template<typename T = double>

typedef Vector<T> CDPL::Math::MLRModel< T >::VectorType

Constructor & Destructor Documentation

◆ MLRModel()

template<typename T = double>

CDPL::Math::MLRModel< T >::MLRModel ( )

inline

Constructs and initializes a regression model with an empty data set.

Member Function Documentation

◆ resizeDataSet()

template<typename T >

void CDPL::Math::MLRModel< T >::resizeDataSet	(	SizeType	num_points,
		SizeType	num_vars
	)

Resizes the data set to hold num_points data points with num_vars independent variables.

Parameters

num_points	The number of data points.
num_vars	The number of independent variables per data point.

◆ clearDataSet()

template<typename T >

void CDPL::Math::MLRModel< T >::clearDataSet

Clears the data set.

Equivalent to calling resizeDataSet() with both arguments beeing zero.

◆ setXYData()

template<typename T >

template<typename V >

void CDPL::Math::MLRModel< T >::setXYData	(	SizeType	i,
		const VectorExpression< V > &	x_vars,
		ValueType	y
	)

Sets the i-th data point \( (y_i, \vec{X}_i) \) of the data set.

If i is larger or equal to the number of currently stored data points or if the number of independent variables provided by x_vars is larger than the maximum number so far, the data set will be resized accordingly. Emerging space between the data points so far and the new data point is filled up with zeros. If the number of independent variables provided by x_vars is smaller than the number of variables in the current data set, the missing independent variables are assumed to be zero.

Parameters

i	The zero-based index of the data point in the data set.
x_vars	The vector \( \vec{X}_i \) with independent variables.
y	The dependent variable \( y_i \).

◆ addXYData()

template<typename T >

template<typename V >

void CDPL::Math::MLRModel< T >::addXYData	(	const VectorExpression< V > &	x_vars,
		ValueType	y
	)

Adds a new data point \( (y, \vec{X}) \) to the current data set.

If the number of independent variables provided by x_vars is larger than the number in the current data set, the data set is resized accordingly and any emerging space will be filled with zeros. If the number of independent variables provided by x_vars is smaller than the number in the current data set, the missing independent variables are assumed to be zero.

Parameters

x_vars	The vector \( \vec{X} \) with independent variables.
y	The dependent variable \( y \).

Note: If the final size of the data set is known in advance, a call to resizeDataSet() followed by calls to setXYData() for each data point is more efficient than a build-up of the data set by repeatedly calling addXYData().

◆ getXMatrix() [1/2]

template<typename T >

CDPL::Math::Matrix< typename CDPL::Math::MLRModel< T >::ValueType > & CDPL::Math::MLRModel< T >::getXMatrix

Returns a matrix where each row represents the vector \( \vec{X}_i \) with independent variables of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \).

Returns: A non-const reference to the matrix with the independent variables \( \vec{X}_i \).

◆ getXMatrix() [2/2]

template<typename T >

const CDPL::Math::Matrix< typename CDPL::Math::MLRModel< T >::ValueType > & CDPL::Math::MLRModel< T >::getXMatrix

Returns a read-only matrix where each row represents the vector \( \vec{X}_i \) with independent variables of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \).

Returns: A const reference to the matrix with the independent variables \( \vec{X}_i \).

◆ getYValues() [1/2]

template<typename T >

CDPL::Math::Vector< typename CDPL::Math::MLRModel< T >::ValueType > & CDPL::Math::MLRModel< T >::getYValues

Returns a vector containing the dependent variables \( y_i \) of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \).

Returns: A non-const reference to the vector with the dependent variables \( y_i \).

◆ getYValues() [2/2]

template<typename T >

const CDPL::Math::Vector< typename CDPL::Math::MLRModel< T >::ValueType > & CDPL::Math::MLRModel< T >::getYValues

Returns a read-only vector containing the dependent variables \( y_i \) of the currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \).

Returns: A const reference to the vector with the dependent variables \( y_i \).

◆ buildModel()

template<typename T >

void CDPL::Math::MLRModel< T >::buildModel

Performs linear least squares regression modeling of the set of currently stored data points \( (y_i, \vec{X}_i), \, i = 1, 2, \ldots, N \).

Exceptions

Base::CalculationFailed if the data set is empty or the singular value decomposition of the \( X \) matrix failed.

◆ calcYValue() [1/2]

template<typename T = double>

template<typename V >

ValueType CDPL::Math::MLRModel< T >::calcYValue ( const VectorExpression< V > & x_vars ) const

Predicts the value of the dependent variable \( y \) for a vector \( \vec{X} \) of independent variables given by x_vars.

Parameters

x_vars The vector \( \vec{X} \) of independent variables.

Returns: The predicted value for \( y \).

Exceptions

Base::CalculationFailed if the number of regression coefficients \( \beta_i \) does not match the size of x_vars.

◆ operator()() [1/2]

template<typename T = double>

template<typename V >

ValueType CDPL::Math::MLRModel< T >::operator() ( const VectorExpression< V > & x_vars ) const

Predicts the value of the dependent variable \( y \) for a vector \( \vec{X} \) of independent variables given by x_vars.

Equivalent to calling calcYValue().

Parameters

x_vars The vector \( \vec{X} \) of independent variables.

Returns: The predicted value for \( y \).

Exceptions

Base::CalculationFailed if the number of regression coefficients \( \beta_i \) does not match the size of x_vars.

◆ getCoefficients()

template<typename T >

const CDPL::Math::Vector< typename CDPL::Math::MLRModel< T >::ValueType > & CDPL::Math::MLRModel< T >::getCoefficients

Returns a read-only vector containing the estimated regression coefficients \( \beta_i \) which were calculated by buildModel().

Returns: A const reference to the vector with the estimated regression coefficients \( \beta_i \).

◆ getChiSquare()

template<typename T >

CDPL::Math::MLRModel< T >::ValueType CDPL::Math::MLRModel< T >::getChiSquare

Returns the sum of squared residuals \( \chi^2 \).

\( \chi^2 \) is calculated by:

\[ \chi^2 = \sum_{i=1}^{N} (y_i - \sum_{j=1}^{M}(x_{ij} \beta_j))^2 \]

Returns: The sum of squared residuals \( \chi^2 \).

Note: The returned value is only valid if calcStatistics() has been called before.

◆ getGoodnessOfFit()

template<typename T >

CDPL::Math::MLRModel< T >::ValueType CDPL::Math::MLRModel< T >::getGoodnessOfFit

Returns the goodness of fit \( Q \).

The goodness of fit \( Q \) is given by:

\[ Q = gammaq(\frac{N - 2}{2}, \frac{\chi^2}{2}) \]

where \( gammaq \) is the incomplete gamma function (see [NRIC] for details).

Returns: The goodness of fit \( Q \).

Note: The returned value is only valid if calcStatistics() has been called before.

See also: Math::gammaQ()

◆ getCorrelationCoefficient()

template<typename T >

CDPL::Math::MLRModel< T >::ValueType CDPL::Math::MLRModel< T >::getCorrelationCoefficient

Returns the correlation coefficient \( r \).

The correlation coefficient \( r \) is calculated by:

\[ r = \frac{\sum_{i=1}^{N} (\hat{y}_i - \bar{\hat{y}})(y_i - \bar{y})} {\sqrt{\sum_{i=1}^{N} (\hat{y}_i - \bar{\hat{y}})^2 \sum_{i=1}^{N} (y_i - \bar{y})^2 }} \]

where

\begin{eqnarray*} \hat{y}_i &=& \sum_{j=1}^{M}(x_{ij} \beta_j) \\ \bar{\hat{y}} &=& \frac{\sum_{i=1}^{N} \hat{y}_i}{N} \\ \bar{y} &=& \frac{\sum_{i=1}^{N} y_i}{N} \end{eqnarray*}

Returns: The correlation coefficient \( r \).

Note: The returned value is only valid if calcStatistics() has been called before.

◆ getStandardDeviation()

template<typename T >

CDPL::Math::MLRModel< T >::ValueType CDPL::Math::MLRModel< T >::getStandardDeviation

Returns the standard deviation of the residuals \( s_r \).

The standard deviation \( s_r \) is calculated by:

\[ s_r = \sqrt{\frac{\sum_{i=1}^{N} (y_i - \sum_{j=1}^{M} (x_{ij} \beta_j))^2} {N - M}} \]

Returns: The standard deviation of the residuals \( s_r \).

Note: \( s_r \) is only definded if \( N > M \) and calcStatistics() has been called before.

◆ calcStatistics()

template<typename T >

void CDPL::Math::MLRModel< T >::calcStatistics

Calculates various statistical parameters describing the built regression model.

Exceptions

Base::CalculationFailed if the data set is in an inconsistent state (e.g. the number of estimated regression coefficients does not match the number of independent variables that make up the data points).

See also: buildModel(), getChiSquare(), getGoodnessOfFit(), getCorrelationCoefficient(), getStandardDeviation()

◆ calcYValue() [2/2]

template<typename T = double>

template<typename V >

CDPL::Math::MLRModel<T>::ValueType CDPL::Math::MLRModel< T >::calcYValue ( const VectorExpression< V > & x ) const

◆ operator()() [2/2]

template<typename T = double>

template<typename V >

CDPL::Math::MLRModel<T>::ValueType CDPL::Math::MLRModel< T >::operator() ( const VectorExpression< V > & x ) const

The documentation for this class was generated from the following file:

MLRModel.hpp

Public Types

Public Member Functions

Detailed Description

template<typename T = double> class CDPL::Math::MLRModel< T >

Member Typedef Documentation

◆ SizeType

◆ ValueType

◆ MatrixType

◆ VectorType

Constructor & Destructor Documentation

◆ MLRModel()

Member Function Documentation

◆ resizeDataSet()

◆ clearDataSet()

◆ setXYData()

◆ addXYData()

◆ getXMatrix() [1/2]

◆ getXMatrix() [2/2]

◆ getYValues() [1/2]

◆ getYValues() [2/2]

◆ buildModel()

◆ calcYValue() [1/2]

◆ operator()() [1/2]

◆ getCoefficients()

◆ getChiSquare()

◆ getGoodnessOfFit()

◆ getCorrelationCoefficient()

◆ getStandardDeviation()

◆ calcStatistics()

◆ calcYValue() [2/2]

◆ operator()() [2/2]

template<typename T = double>
class CDPL::Math::MLRModel< T >