etirm::ICCLogistic< 3 > Class Template Reference

Three-parameter logistic item response model. More...

#include <ICCLogistic.h>

Inheritance diagram for etirm::ICCLogistic< 3 >:

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List of all members.

Public Member Functions
	ICCLogistic (Real D)
	Instantiation of logistic item response model, fixing scale constant.
Real	ICC (const RealVector &param, Real theta) const
	Returns value of the 3PL item characteristic curve (ICC) for a set of item parameters and theta value.
Real	OpenICC (const RealVector &param, Real theta) const
	Returns value of the 3PL item characteristic curve (ICC) in open interval (0, 1); for a set of item parameters and theta value.
void	ICCDeriv1 (const RealVector &param, Real theta, RealVector &deriv) const
	Computes (gradient) vector of first partial derivatives of the 3PL model with respect to item parameters.
void	ICCDeriv2 (const RealVector &param, Real theta, RealMatrix &deriv) const
	Computes (hessian) matrix of second partial derivatives of the 3PL model with respect to item parameters.
bool	GradientDefined () const
	Function to indicate that the algebraic gradient of the item (ICCDeriv1) is defined.
bool	HessianDefined () const
	Function to indicate that the algebraic hessian of the item (ICCDeriv2) is defined.
void	Scale (Real slope, Real intercept, RealVector &param)
	Transforms the parameters of a logistic item to a different latent variable scale.
Real	GetD () const
	Returns scaling constant D.
void	GetAllParameters (const RealVector &estParam, RealVector &allParam) const
	Copies a, b, and c parameters from estParam into allParam.
int	NumParameters () const
	Returns number of estimated parameters.
int	NumAllParameters () const
	Returns sum of number of fixed and estimated parameters.
bool	ValidParameters (const RealVector &param) const
	Returns true if vector param contains valid item parameters.
std::string	Name () const
	Returns name of model.
IRTModel	Model () const
	Returns model type from enum defined in etirmtypes.h.
template<class I>
void	SetAllParameters (I begin_param, I end_param, RealVector &estParam)
	Assigns all item parameters (a, b, and c), fixed and estimated.
Private Member Functions
Real	ValidC (Real c) const
	Returns c parameter, if valid, or throws an exception otherwise.

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Detailed Description

template<>
class etirm::ICCLogistic< 3 >

Three-parameter logistic item response model.

Definition at line 179 of file ICCLogistic.h.

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Constructor & Destructor Documentation

etirm::ICCLogistic< 3 >::ICCLogistic

(

Real

D

)

Instantiation of logistic item response model, fixing scale constant.

Function Parameters

Parameters:

[in]

D

Scale constant defining the metric of the parameter estimates. Typical choices are 1 (for the logistic metric) and 1.7 (for the normal-ogive metric).

Constructor for three-parameter logistic ICC object

Definition at line 220 of file ICCLogistic.cpp.

                                    :
    ICC3PLFunc(3, D)
  {
  }

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Member Function Documentation

Real etirm::ICCLogistic< 3 >::ICC	(	const RealVector &	param,
		Real	theta
	)			const [inline]

Returns value of the 3PL item characteristic curve (ICC) for a set of item parameters and theta value.

Function Parameters

Parameters:

[in]	&param	Address of item parameter vector with entries = (a, b, c).
[in]	theta	Examinee ability parameter.

Definition at line 206 of file ICCLogistic.h.

    {
      return ICC3PL(param(1), param(2), ValidC(param(3)), theta);
    }

Real etirm::ICCLogistic< 3 >::OpenICC	(	const RealVector &	param,
		Real	theta
	)			const [inline]

Returns value of the 3PL item characteristic curve (ICC) in open interval (0, 1); for a set of item parameters and theta value.

This function version can be used when the logarithm of the probability or logit of the probability needs to be taken.

Function Parameters

Parameters:

[in]	&param	Address of item parameter vector with entries = (a, b, c).
[in]	theta	Examinee ability parameter.

Definition at line 224 of file ICCLogistic.h.

    {
      return OpenICC3PL(param(1), param(2), ValidC(param(3)), theta);
    }

void etirm::ICCLogistic< 3 >::ICCDeriv1	(	const RealVector &	param,
		Real	theta,
		RealVector &	deriv
	)			const [inline]

Computes (gradient) vector of first partial derivatives of the 3PL model with respect to item parameters.

Returns results in deriv vector.

Function Parameters

Parameters:

[in]	&param	Address of item parameter vector with entries (a, b, c).
[in]	theta	Examinee ability parameter.
[out]	&deriv	Address of gradient vector of length 3.

Definition at line 242 of file ICCLogistic.h.

    {
      ICC3PLDeriv1(3, param(1), param(2), ValidC(param(3)), theta, deriv);
    }

void etirm::ICCLogistic< 3 >::ICCDeriv2	(	const RealVector &	param,
		Real	theta,
		RealMatrix &	deriv
	)			const [inline]

Computes (hessian) matrix of second partial derivatives of the 3PL model with respect to item parameters.

Returns results in deriv matrix.

Function Parameters

Parameters:

[in]	&param	Address of item parameter vector with entries (a, b, c).
[in]	theta	Examinee ability parameter.
[out]	&deriv	Address of 3x3 hessian matrix. Only the lower half and diagonal of the matrix are populated, the upper off-diagonal entries remain undefined.

Definition at line 261 of file ICCLogistic.h.

    {
      ICC3PLDeriv2(3, param(1), param(2), ValidC(param(3)), theta, deriv);
    }

bool etirm::ICCLogistic< 3 >::GradientDefined

(

)

const [inline]

Function to indicate that the algebraic gradient of the item (ICCDeriv1) is defined.

This function can be used by UNCMIN++.

Definition at line 272 of file ICCLogistic.h.

    {
      return true;
    }

bool etirm::ICCLogistic< 3 >::HessianDefined

(

)

const [inline]

Function to indicate that the algebraic hessian of the item (ICCDeriv2) is defined.

This function can be used by UNCMIN++.

Definition at line 283 of file ICCLogistic.h.

    {
      return true;
    }

void etirm::ICCLogistic< 3 >::Scale	(	Real	slope,
		Real	intercept,
		RealVector &	param
	)			[inline]

Transforms the parameters of a logistic item to a different latent variable scale.

Function Parameters

Parameters:

[in]	slope	Slope parameter of linear scale transformation.
[in]	intercept	Intercept parameter of linear scale transformation.
[in,out]	&param	Address of item parameter vector to be transformed. Only the first two entries (slope and location) will be transformed.

Definition at line 299 of file ICCLogistic.h.

References etirm::ICC3PLFunc::Scale().

    {
      ICC3PLFunc::Scale(slope, intercept, param(1), param(2));
    }

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Real etirm::ICCLogistic< 3 >::GetD

(

)

const [inline]

Returns scaling constant D.

Definition at line 305 of file ICCLogistic.h.

    {
      return mD;
    }

void etirm::ICCLogistic< 3 >::GetAllParameters	(	const RealVector &	estParam,
		RealVector &	allParam
	)			const

Copies a, b, and c parameters from estParam into allParam.

Method to return allParam for 3PL item.

Function Parameters

Parameters:

[in]	&estParam	Address of vector of item parameter estimates.
[out]	&allParam	Address of copied item parameter vector.

Definition at line 244 of file ICCLogistic.cpp.

  {
    allParam = estParam;
  }

int etirm::ICCLogistic< 3 >::NumParameters

(

)

const [inline]

Returns number of estimated parameters.

Definition at line 322 of file ICCLogistic.h.

    {
      return numParameters;
    }

int etirm::ICCLogistic< 3 >::NumAllParameters

(

)

const [inline]

Returns sum of number of fixed and estimated parameters.

Definition at line 328 of file ICCLogistic.h.

    {
      return numParameters;
    }

bool etirm::ICCLogistic< 3 >::ValidParameters

(

const RealVector &

param

)

const [inline]

Returns true if vector param contains valid item parameters.

Function Parameters

Parameters:

[in]

&param

Address of item parameter vector.

Definition at line 341 of file ICCLogistic.h.

    {
      return (param(3) >= 0.0 && param(3) <= 1.0);
    }

std::string etirm::ICCLogistic< 3 >::Name

(

)

const [inline]

Returns name of model.

Definition at line 347 of file ICCLogistic.h.

    {
      return std::string("3PL");
    }

IRTModel etirm::ICCLogistic< 3 >::Model

(

)

const [inline]

Returns model type from enum defined in etirmtypes.h.

Definition at line 353 of file ICCLogistic.h.

References etirm::ThreePL.

    {
      return ThreePL;
    }

template<class I>

void etirm::ICCLogistic< 3 >::SetAllParameters	(	I	begin_param,
		I	end_param,
		RealVector &	estParam
	)			[inline]

Assigns all item parameters (a, b, and c), fixed and estimated.

Template Parameters

Parameters:

I

Type of iterator over item parameters.

Function Parameters

Parameters:

[in]	begin_param	Iterator pointing to first item parameter for the item.
[in]	end_param	Iterator point to one after the last parameter for the item.
[out]	&estParam	Address to vector "all" parameters for this item.

Definition at line 372 of file ICCLogistic.h.

    {
      if ((end_param - begin_param) != 3 || estParam.size() != 3)
        throw InvalidArgument("Wrong number of parameters", "ICCLogistic<3>::SetAllParameters");

      if (begin_param[2] < 0.0 || begin_param[2] > 1.0)
        throw InvalidArgument("Invalid c parameter","ICCLogistic<3>::SetAllParameters");

      RealVector::iterator ie = estParam.begin();
      for (int i = 3; i--; ++ie, ++begin_param)
      {
        *ie = *begin_param;
      }
    }

Real etirm::ICCLogistic< 3 >::ValidC

(

Real

c

)

const [inline, private]

Returns c parameter, if valid, or throws an exception otherwise.

Function Parameters

Parameters:

[in]

c

Pseudo-guessing parameter c for the item.

Definition at line 396 of file ICCLogistic.h.

    {
      if (c < 0.0 || c > 1.0)throw RuntimeError("Invalid c parameter","ICCLogistic<3>::ValidC"); 
    
      return c;
    }

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

• C:/programs/etirm/src/ICCLogistic.h
• C:/programs/etirm/src/ICCLogistic.cpp

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