wmle_ability.c File Reference

Warm's Weighted Maximum Likelihood of the abilities. More...

#include "libirt.h"
#include <math.h>
#include <gsl/gsl_spline.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_roots.h>

Data Structures
struct	wmle_ability_struct
	Used to passed extra parameter to wmle_ability_fdfdf2. More...

Functions
void	wmle_ability_fdfdf2 (double ability, void *params, double *f, double *df, double *df2)
	Compute the log weighted likelihood, gradient and Hessian of the pattern.
double	wmle_ability_f (double ability, void *params)
	Compute the log weighted likelihood of the pattern.
double	wmle_ability_df (double ability, void *params)
	Compute the log weighted likelihood gradient of the pattern.
double	wmle_ability_df2 (double ability, void *params)
	Compute the log weighted likelihood Hessian of the pattern.
void	wmle_ability_dfdf2 (double ability, void *params, double *df, double *df2)
	Compute the log weighted likelihood gradient and Hessian of the pattern.
int	wmle_abilities (int max_iter, double prec, gsl_matrix *like, gsl_vector *info, gsl_vector *quad_points, gsl_vector *abilities, gsl_vector *abilities_stddev)
	Compute the WMLE of the abilities.

Detailed Description

Warm's Weighted Maximum Likelihood of the abilities.

Author

Stephane Germain germs.nosp@m.te@g.nosp@m.mail..nosp@m.com

Function Documentation

void wmle_ability_fdfdf2	(	double	ability,
		void *	params,
		double *	f,
		double *	df,
		double *	df2
	)

Compute the log weighted likelihood, gradient and Hessian of the pattern.

Parameters

[in]	ability	The ability level.
[in]	params	The extra parameter to passes to the function.
[out]	f	The log weighted likelihood.
[out]	df	The gradient of the log weighted likelihood.
[out]	df2	The Hessian of the log weighted likelihood.

This function is not used directly by the root finding functions, but by others functions that comply with the gsl.

double wmle_ability_f	(	double	ability,
		void *	params
	)

Compute the log weighted likelihood of the pattern.

Parameters

[in]	ability	The ability level.
[in]	params	The extra parameter to passes to the function.

This function is just a wrapper around wmle_ability_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log weighted likelihood.

double wmle_ability_df	(	double	ability,
		void *	params
	)

Compute the log weighted likelihood gradient of the pattern.

Parameters

[in]	ability	The ability level.
[in]	params	The extra parameter to passes to the function.

This function is just a wrapper around wmle_ability_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log weighted likelihood gradient.

double wmle_ability_df2	(	double	ability,
		void *	params
	)

Compute the log weighted likelihood Hessian of the pattern.

Parameters

[in]	ability	The ability level.
[in]	params	The extra parameter to passes to the function.

This function is just a wrapper around wmle_ability_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log weighted likelihood Hessian.

void wmle_ability_dfdf2	(	double	ability,
		void *	params,
		double *	df,
		double *	df2
	)

Compute the log weighted likelihood gradient and Hessian of the pattern.

Parameters

[in]	ability	The ability level.
[in]	params	The extra parameter to passes to the function.
[out]	df	The gradient of the log weighted likelihood.
[out]	df2	The Hessian of the log weighted likelihood.

This function is just a wrapper around wmle_ability_fdfdf2 to be used by the root finding functions in the gsl.

int wmle_abilities	(	int	max_iter,
		double	prec,
		gsl_matrix *	like,
		gsl_vector *	info,
		gsl_vector *	quad_points,
		gsl_vector *	abilities,
		gsl_vector *	abilities_stddev
	)

Compute the WMLE of the abilities.

Parameters

[in]	max_iter	The maximum number of Newton iterations performed for each pattern.
[in]	prec	The desired precision of each parameter estimate.
[in]	like	A matrix (patterns x classes) of likelihood functions.
[in]	info	A vecor (classes) with the test information function.
[in]	quad_points	A vector(classes) with the middle points of each class.
[out]	abilities	A vector(patterns) with the estimated abilities.
[out]	abilities_stddev	A vector(items) with the standard errors of the estimated abilities.

Warning

The memory for abilities and abilities_stddev should be allocated before.