mle_ability_3plm.c File Reference

Functions to estimate the abilities by ML. More...

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

Data Structures
struct	mle_ability_3plm_struct
	Used to passed extra parameter to mle_ability_3plm_fdfdf2. More...

Functions
void	mle_ability_3plm_fdfdf2 (double ability, void *params, double *f, double *df, double *df2)
	Compute the log likelihood, gradient and Hessian of the pattern.
double	mle_ability_3plm_f (double ability, void *params)
	Compute the log likelihood of the pattern.
double	mle_ability_3plm_df (double ability, void *params)
	Compute the log likelihood gradient of the pattern.
double	mle_ability_3plm_df2 (double ability, void *params)
	Compute the log likelihood Hessian of the pattern.
void	mle_ability_3plm_dfdf2 (double ability, void *params, double *df, double *df2)
	Compute the log likelihood gradient and Hessian of the pattern.
int	mle_abilities_3plm (int max_iter, double prec, gsl_matrix_int *patterns, gsl_vector *slopes, gsl_vector *thresholds, gsl_vector *asymptotes, gsl_vector *abilities, gsl_vector *abilities_stddev)
	Estimate the abilities by maximum likelihood.

Detailed Description

Functions to estimate the abilities by ML.

Author

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

Function Documentation

void mle_ability_3plm_fdfdf2	(	double	ability,
		void *	params,
		double *	f,
		double *	df,
		double *	df2
	)

Compute the log 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 likelihood.
[out]	df	The gradient of the log likelihood.
[out]	df2	The Hessian of the log likelihood.

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

double mle_ability_3plm_f	(	double	ability,
		void *	params
	)

Compute the log 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 mle_ability_3plm_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log likelihood.

double mle_ability_3plm_df	(	double	ability,
		void *	params
	)

Compute the log 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 mle_ability_3plm_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log likelihood gradient.

double mle_ability_3plm_df2	(	double	ability,
		void *	params
	)

Compute the log 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 mle_ability_3plm_fdfdf2 to be used by the root finding functions in the gsl.

Returns

The log likelihood Hessian.

void mle_ability_3plm_dfdf2	(	double	ability,
		void *	params,
		double *	df,
		double *	df2
	)

Compute the log 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 likelihood.
[out]	df2	The Hessian of the log likelihood.

This function is just a wrapper around mle_ability_3plm_fdfdf2 to be used by the root finding functions in the gsl.

int mle_abilities_3plm	(	int	max_iter,
		double	prec,
		gsl_matrix_int *	patterns,
		gsl_vector *	slopes,
		gsl_vector *	thresholds,
		gsl_vector *	asymptotes,
		gsl_vector *	abilities,
		gsl_vector *	abilities_stddev
	)

Estimate the abilities by maximum likelihood.

Parameters

[in]	max_iter	The maximum number of Newton iterations performed for each pattern.
[in]	prec	The desired precision of each parameter estimate.
[in]	patterns	A matrix(patterns x items) of binary responses.
[in]	slopes	A vector(items) with the slope parameters of each item.
[in]	thresholds	A vector(items) with the threshold parameters of each item.
[in]	asymptotes	A vector(items) with the asymptote parameters of each item. Can be NULL for the 2PLM.
[in,out]	abilities	A vector(patterns) with the estimated abilities. They should be initialize first.
[out]	abilities_stddev	A vector(items) with the standard errors of the estimated abilities.

Returns

The number of pattern that did not converged.

detect the degenerates patterns.