ETIRM: etirm::ItemPolytomous< LC, M > Class Template Reference

List of all members.


Public Member Functions
	ItemPolytomous (int index, M &icrf, LC *dist)
	Constructor of polytomous response model class.
virtual	~ItemPolytomous ()
	Deconstructor of polytomous response model class.
virtual RealVector	GetAllParameters () const
	Returns a vector of estimated and fixed parameters.
virtual void	SetAllParameters (const RealVector &allParam)
	Assigns values of fixed and estimated parameters.
virtual Real	ICRF (const Response r, const RealVector &parameters, const Real &theta) const
	Returns value of item characteristic curve for response "r", item parameters "parameters", and latent variable value "theta".
virtual int	ScaleParameters (Real slope, Real intercept, bool ignorePrior=false)
	Transforms parameter estimates to new latent variable scale.
virtual std::string	ModelName () const
	Returns string containing name of model used for item.
virtual IRTModel	Model () const
	Returns type of model used for item.
virtual double	f_to_minimize (RealVector &p)
	Function to maximize in M-step.
virtual void	gradient (RealVector &p, RealVector &g)
	Gradient of function to maximize in M-step.
virtual void	hessian (RealVector &, RealMatrix &)
	Computes hessian of function to maximize in M-step.
virtual int	HasAnalyticGradient () const
	Function to indicate that the algebraic gradient of the item (ICCDeriv1) is defined.
virtual int	HasAnalyticHessian () const
	Function to indicate that the algebraic hessian of the item (ICCDeriv2) is defined.
Protected Attributes
M	mICRF
	Object for calculating ICRF and its derivatives.

Detailed Description

template<class LC, class M>
class etirm::ItemPolytomous< LC, M >

Defines functions used in M-step of EM algorithm to compute item parameter estimates.

Template Parameters

Constructor & Destructor Documentation

template<class LC, class M>

etirm::ItemPolytomous< LC, M >::ItemPolytomous	(	int	index,
		M &	icrf,
		LC *	dist
	)			`[inline]`

Constructor of polytomous response model class.

Template Parameters

Parameters:

	LC	Type of container holding possible values of the discrete latent variable.
	M	Type containing functions defining item characteristic response function (ICRF) and derivatives of ICRF.

Function Parameters

Parameters:

`[in]`	index	Zero-offset index of the item in the vector of all item responses.
`[in]`	icrf	Address of item category response function for the model.
`[in]`	dist	Pointer to discrete latent variable points used in calculating the r's.

Definition at line 156 of file ItemPolytomous.h.

00156                                                                                                  :
00157     ItemNR<LC>(icrf.NumParameters(), index, icrf.NumRespCat(), dist), mICRF(icrf)
00158   {
00159     if (ItemNR<LC>::mNRespCat != icrf.NumRespCat()) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00160     {
00161       throw InvalidArgument("Mismatch in number of response categories for item and ICRF",
00162           "ItemPolytomous::ItemPolytomous");
00163     }
00164   }

template<class LC, class M>

etirm::ItemPolytomous< LC, M >::~ItemPolytomous ( ) [inline, virtual]

Deconstructor of polytomous response model class.

Definition at line 167 of file ItemPolytomous.h.

00168   {
00169   }

Member Function Documentation

template<class LC, class M>

virtual RealVector etirm::ItemPolytomous< LC, M >::GetAllParameters ( ) const [inline, virtual]

Returns a vector of estimated and fixed parameters.

The order of the parameters in the vector is determined by the GetAllParameters member function of mICRF.

Reimplemented from etirm::Item< LC::latentvar_type >.

Definition at line 96 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00097     {
00098       RealVector allParam(mICRF.NumAllParameters());
00099       mICRF.GetAllParameters(ItemNR<LC>::mParameterEstimates, allParam); // Added "ItemNR<LC>::" reference. ww, 1/12/2008.
00100       return allParam;
00101     }

template<class LC, class M>

virtual void etirm::ItemPolytomous< LC, M >::SetAllParameters ( const RealVector & allParam ) [inline, virtual]

Assigns values of fixed and estimated parameters.

Reimplemented from etirm::Item< LC::latentvar_type >.

Definition at line 104 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00105     {
00106       mICRF.SetAllParameters(allParam.begin(), allParam.end(), ItemNR<LC>::mParameterEstimates);
00107     } // Added "ItemNR<LC>::" reference. ww, 1/12/2008.

template<class LC, class M>

Real etirm::ItemPolytomous< LC, M >::ICRF	(	const Response	r,
		const RealVector &	parameters,
		const Real &	theta
	)			const `[inline, virtual]`

Returns value of item characteristic curve for response "r", item parameters "parameters", and latent variable value "theta".

Template Parameters

Parameters:

	LC	Type of container holding possible values of the discrete latent variable.
	M	Type containing functions defining item characteristic response function (ICRF) and derivatives of ICRF.

Function Parameters

Parameters:

`[in]`	r	Response category.
`[in]`	&parameters	Item parameter vector.
`[in]`	&theta	Ability parameter.

Definition at line 189 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00191   {
00192     return mICRF.ICRF(r, parameters, theta);
00193   }

template<class LC, class M>

int etirm::ItemPolytomous< LC, M >::ScaleParameters	(	Real	slope,
		Real	intercept,
		bool	ignorePriors = `false`
	)			`[inline, virtual]`

Transforms parameter estimates to new latent variable scale.

Returns 1 if scaling results in invalid parameters. In this case, the parameters are not modified.

Template Parameters

Parameters:

	LC	Type of container holding possible values of the discrete latent variable.
	M	Type containing functions defining item characteristic response function (ICRF) and derivatives of ICRF.

Function Parameters

Parameters:

`[in]`	slope	Scale parameter for transformation.
`[in]`	intercept	Intercept parameter for transformation.
`[in]`	ignorePriors	Flag to ignore prior information when checking validity of transformed parameters.

Implements etirm::Item< LC::latentvar_type >.

Definition at line 349 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00351   {
00352     RealVector scaledParam(ItemNR<LC>::mParameterEstimates); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00353 
00354     mICRF.Scale(slope, intercept, scaledParam);
00355 
00356     // Check if scaled parameters are valid
00357     if (!(ItemNR<LC>::ValidParameters(scaledParam, ignorePriors)))
00358       return 1; // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00359 
00360     ItemNR<LC>::mParameterEstimates = scaledParam; // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00361 
00362     return 0;
00363   }

template<class LC, class M>

virtual std::string etirm::ItemPolytomous< LC, M >::ModelName ( ) const [inline, virtual]

Returns string containing name of model used for item.

Implements etirm::Item< LC::latentvar_type >.

Definition at line 115 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

template<class LC, class M>

virtual IRTModel etirm::ItemPolytomous< LC, M >::Model ( ) const [inline, virtual]

Returns type of model used for item.

Implements etirm::Item< LC::latentvar_type >.

Definition at line 121 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

template<class LC, class M>

double etirm::ItemPolytomous< LC, M >::f_to_minimize ( RealVector & param ) [inline, virtual]

Function to maximize in M-step.

Template Parameters

Parameters:

	LC	Type of container holding possible values of the discrete latent variable.
	M	Type containing functions defining item characteristic response function (ICRF) and derivatives of ICRF.

Function Parameters

Parameters:

[in] &param Address of item parameter vector.

Note: Technically, negative value of function is being minimized, so the negative function value is being returned.

Implements etirm::ItemNR< LC >.

Definition at line 213 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00214   {
00215     int i, j, grp;
00216     Real value = 0.0;
00217     int ngroups = ItemNR<LC>::mLatentDist->NumGroupsUnique(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00218 
00219     /* Compute loglikelihood */
00220     for (grp=1; grp<=ngroups; ++grp)
00221     {
00222       Response r = ItemNR<LC>::FirstResponse(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00223       for (i = ItemNR<LC>::mNRespCat; i--; ++r) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00224       {
00225         typename ItemNR<LC>::r_iterator ir = ItemNR<LC>::RVector(r, grp); // Added "typename" and "ItemNR<LC>::" references. ww, 1/13/2008.
00226         typename ItemNR<LC>::point_iterator it = ItemNR<LC>::mLatentDist->begin_points(grp); // Added "typename" and "ItemNR<LC>::" reference. ww, 1/13/2008.
00227         for (j=ItemNR<LC>::mNumLatentVarCat; j--; ++ir, ++it) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00228         {
00229           Real prob = mICRF.OpenICRF(r, param, *it);
00230           value += *ir * std::log(prob);
00231         }
00232       }
00233     }
00234 
00235     /* Add priors */
00236     PriorVector::const_iterator iprior = ItemNR<LC>::mPriors.begin(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00237     RealVector::iterator iparam = param.begin();
00238     for (int j = ItemNR<LC>::NumParameters(); j--; ++iprior, ++iparam) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00239     {
00240       if (*iprior)
00241       {
00242         if ((*iprior)->ZeroDensity(*iparam))
00243         {
00244           // If density of prior is zero then log of prior density is
00245           // minus infinity (negative of minus infinity is returned
00246           // because the function is being minimized)
00247           if (std::numeric_limits<Real>::has_infinity)
00248           {
00249             return std::numeric_limits<Real>::infinity();
00250           }
00251           else
00252           {
00253             return std::numeric_limits<Real>::max();
00254           }
00255         }
00256         else
00257         {
00258           value += (*iprior)->LogDensity(*iparam);
00259         }
00260       }
00261     }
00262 
00263     return -value; // return negative value to find minimum rather than maximum
00264   }

template<class LC, class M>

void etirm::ItemPolytomous< LC, M >::gradient	(	RealVector &	param,
		RealVector &	g
	)			`[inline, virtual]`

Gradient of function to maximize in M-step.

Template Parameters

Parameters:

	LC	Type of container holding possible values of the discrete latent variable.
	M	Type containing functions defining item characteristic response function (ICRF) and derivatives of ICRF.

Function Parameters

Parameters:

`[in]`	&param	Address of item parameter vector.
`[out]`	&g	Address of gradient vector. Gradient values are returned in the vector elements.

Note: Technically, negative value of function is being minimized, so the negative gradient is being returned.

Implements etirm::ItemNR< LC >.

Definition at line 285 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00287   {
00288     g = 0.0;
00289     RealVector deriv(ItemNR<LC>::NumParameters(), 0.0); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00290 
00291     int i, j, grp;
00292     int ngroups = ItemNR<LC>::mLatentDist->NumGroupsUnique(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00293 
00294     for (grp=1; grp<=ngroups; ++grp)
00295     {
00296       Response r = ItemNR<LC>::FirstResponse(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00297       for (i = ItemNR<LC>::mNRespCat; i--; ++r) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00298       {
00299 
00300         typename ItemNR<LC>::r_iterator ir = ItemNR<LC>::RVector(r, grp); // Added "typename" and "ItemNR<LC>::" references. ww, 1/13/2008.
00301         typename ItemNR<LC>::point_iterator itheta = ItemNR<LC>::mLatentDist->begin_points(grp); // Added "typename" and "ItemNR<LC>::" references. ww, 1/13/2008.
00302         for (j=ItemNR<LC>::mNumLatentVarCat; j--; ++ir, ++itheta) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00303         {
00304           Real t = *ir / mICRF.OpenICRF(r, param, *itheta);
00305 
00306           mICRF.ICRFDeriv1(r, param, *itheta, deriv);
00307 
00308           // use -t since function is to be minimized, not maximized
00309           deriv *= -t;
00310           g += deriv;
00311 
00312         }
00313       }
00314     }
00315 
00316     /* Add priors */
00317     PriorVector::const_iterator iprior = ItemNR<LC>::mPriors.begin(); // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00318     RealVector::iterator iparam = param.begin();
00319     RealVector::iterator ig = g.begin();
00320     for (int j = ItemNR<LC>::NumParameters(); j--; ++iprior, ++iparam, ++ig) // Added "ItemNR<LC>::" reference. ww, 1/13/2008.
00321     {
00322       // subtract because function is to be minimized
00323       if (*iprior)
00324         *ig -= (*iprior)->DerivLogDensity1(*iparam);
00325     }
00326 
00327   }

template<class LC, class M>

virtual void etirm::ItemPolytomous< LC, M >::hessian	(	RealVector &	x,
		RealMatrix &	h
	)			`[inline, virtual]`

Computes hessian of function to maximize in M-step.

Note: Technically, the negative value of the function is to be minimized by UNCMIN++, see inline comments in function code.

Note: The hessian is stored in the lower trangle of h.

Implements etirm::ItemNR< LC >.

Definition at line 134 of file ItemPolytomous.h.

00135     {
00136     }

template<class LC, class M>

virtual int etirm::ItemPolytomous< LC, M >::HasAnalyticGradient ( ) const [inline, virtual]

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

This function can be used by UNCMIN++.

Implements etirm::ItemNR< LC >.

Definition at line 138 of file ItemPolytomous.h.

References etirm::ItemPolytomous< LC, M >::mICRF.

00139     {
00140       return mICRF.GradientDefined();
00141     }

template<class LC, class M>

virtual int etirm::ItemPolytomous< LC, M >::HasAnalyticHessian ( ) const [inline, virtual]

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

This function can be used by UNCMIN++.

Implements etirm::ItemNR< LC >.

Definition at line 143 of file ItemPolytomous.h.

00144     {
00145       return 0;
00146     }

etirm::ItemPolytomous< LC, M > Class Template Reference

Public Member Functions

Protected Attributes

Detailed Description

template<class LC, class M> class etirm::ItemPolytomous< LC, M >

Constructor & Destructor Documentation

Member Function Documentation

Member Data Documentation

template<class LC, class M>
class etirm::ItemPolytomous< LC, M >