com.itemanalysis.psychometrics.irt.estimation

Class IrtExaminee

java.lang.Object

com.itemanalysis.psychometrics.irt.estimation.IrtExaminee

All Implemented Interfaces:

org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction, org.apache.commons.math3.analysis.UnivariateFunction

public class IrtExaminee
extends java.lang.Object
implements org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

This class holds an item responseVector vector for an examinee and stores a count of the number of examinees with the same responseVector vector. It computes the loglikelihood and the first derivative of the loglikelihood. These methods can be used for maximum likelihood (ML), Bayes modal (MAP), expected a posteriori (EAP), and proportinal curve fitting (PCF) estimation of person ability in univariate item responseVector models. Note: The PCF method should only be used for members of the Rasch family of item responseVector models. The order of item in the array irm MUST be the same as the order or item responses in the array responses. Missing responses are coded as -1.

Constructor Summary

Constructors

Constructor and Description
IrtExaminee(java.util.ArrayList<ItemResponseModel> irm)
IrtExaminee(ItemResponseModel[] irm) this constructor allows a single instance to be used for estimating ability for multiple people by calling setResponseVector() prior to calling for amethod to compute ability.
IrtExaminee(ItemResponseModel[] irm, ItemResponseVector responseVector)
IrtExaminee(java.util.LinkedHashMap<VariableName,ItemResponseModel> irm)
IrtExaminee(java.lang.String groupID, ItemResponseModel[] irm) this constructor allows a single instance to be used for estimating ability for multiple people by calling setResponseVector() prior to calling for amethod to compute ability.
IrtExaminee(java.lang.String groupID, ItemResponseModel[] irm, ItemResponseVector responseVector)

Method Summary

Modifier and Type	Method and Description
org.apache.commons.math3.analysis.differentiation.DerivativeStructure	derivLogLikelihood(org.apache.commons.math3.analysis.differentiation.DerivativeStructure t) Returns first derivative of loglikelihood using DerivativeStructure per interface requirements
double	derivLogLikelihood(double theta) First derivative of loglikelihood with respect to theta.
double	eapEstimate(DistributionApproximation dist) EAP estimate using a distribution provided by the user such as quadrature points and weights from item calibration.
double	eapEstimate(double mean, double sd, double thetaMin, double thetaMax, int numPoints) Expected a Posteriori (EAP) estimate of examinee ability using a normal distribution.
double	eapStandardErrorAt(double theta) Computes standard error for EAP method.
double	getAdjustedSumScore(double adjustment)
ItemResponseVector	getResponseVector()
double	getTheta()
boolean	isExtreme()
double	logLikelihood(double theta) computes the loglikelihood of a responseVector vector at a given value of theta.
double	mapEstimate(double mean, double sd, double thetaMin, double thetaMax)
double	mapEstimate(double mean, double sd, double thetaMin, double thetaMax, int maxIter, double tolerance) Maximum a Posteriori (MAP) estimate of examinee ability using a normal prior distribution.
double	mapStandardErrorAt(double theta)
double	maximumLikelihoodEstimate(double thetaMin, double thetaMax)
double	maximumLikelihoodEstimate(double thetaMin, double thetaMax, int maxIter, double tolerance) Maximum likelihood estimate (MLE) of examinee ability.
boolean	missingResponseAt(int index)
double	mleStandardErrorAt(double theta)
double	pcfEstimate(int maxIter, double converge, double adjustment) Computes ability estimate using proportional curve fitting.
double	pcfStandardErrorAt(double theta)
void	setResponseVector(byte[] responseVector)
void	setResponseVector(ItemResponseVector responseVector) If the response vector was not set in teh constructor, this method must be called prior to estimating ability.
void	setStartValue(double theta)
double	testInformationAt(double theta)
org.apache.commons.math3.analysis.differentiation.DerivativeStructure	value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure t) Returns value of loglikelihood using DerivativeStructure per interface requirements
double	value(double param)

Methods inherited from class java.lang.Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

IrtExaminee

public IrtExaminee(java.lang.String groupID,
                   ItemResponseModel[] irm,
                   ItemResponseVector responseVector)
            throws org.apache.commons.math3.exception.DimensionMismatchException

Throws:

org.apache.commons.math3.exception.DimensionMismatchException

IrtExaminee

public IrtExaminee(ItemResponseModel[] irm,
                   ItemResponseVector responseVector)
            throws org.apache.commons.math3.exception.DimensionMismatchException

Throws:

org.apache.commons.math3.exception.DimensionMismatchException

IrtExaminee

public IrtExaminee(java.lang.String groupID,
                   ItemResponseModel[] irm)

this constructor allows a single instance to be used for estimating ability for multiple people by calling setResponseVector() prior to calling for amethod to compute ability.

Parameters:

groupID - examinee group ID

irm - an array of item response models

IrtExaminee

public IrtExaminee(ItemResponseModel[] irm)

this constructor allows a single instance to be used for estimating ability for multiple people by calling setResponseVector() prior to calling for amethod to compute ability.

Parameters:

irm - an array of item response models

IrtExaminee

public IrtExaminee(java.util.ArrayList<ItemResponseModel> irm)

IrtExaminee

public IrtExaminee(java.util.LinkedHashMap<VariableName,ItemResponseModel> irm)

Method Detail

setResponseVector

public void setResponseVector(ItemResponseVector responseVector)

If the response vector was not set in teh constructor, this method must be called prior to estimating ability.

Parameters:

responseVector -

setResponseVector

public void setResponseVector(byte[] responseVector)

setStartValue

public void setStartValue(double theta)

getResponseVector

public ItemResponseVector getResponseVector()

missingResponseAt

public boolean missingResponseAt(int index)

getAdjustedSumScore

public double getAdjustedSumScore(double adjustment)

isExtreme

public boolean isExtreme()

logLikelihood

public double logLikelihood(double theta)

computes the loglikelihood of a responseVector vector at a given value of theta.

Parameters:

theta - examinee ability

Returns:

derivLogLikelihood

public double derivLogLikelihood(double theta)

First derivative of loglikelihood with respect to theta.

Parameters:

theta - examinee ability

Returns:

first derivative

maximumLikelihoodEstimate

public double maximumLikelihoodEstimate(double thetaMin,
                                        double thetaMax,
                                        int maxIter,
                                        double tolerance)

Maximum likelihood estimate (MLE) of examinee ability.

Parameters:

thetaMin - smallest possible ability estimate (lower bound on BrentOptimizer)

thetaMax - largest possible ability estimate (upper bound on BrentOptimizer)

Returns:

MLE of examinee ability

maximumLikelihoodEstimate

public double maximumLikelihoodEstimate(double thetaMin,
                                        double thetaMax)

mapEstimate

public double mapEstimate(double mean,
                          double sd,
                          double thetaMin,
                          double thetaMax,
                          int maxIter,
                          double tolerance)

Maximum a Posteriori (MAP) estimate of examinee ability using a normal prior distribution.

Parameters:

mean - mean of normal prior distribution

sd - standard deviation of prior distribution

thetaMin - smallest possible ability estimate (lower bound on BrentOptimizer)

thetaMax - largest possible ability estimate (upper bound on BrentOptimizer)

Returns:

MAP estimate of examinee ability

mapEstimate

public double mapEstimate(double mean,
                          double sd,
                          double thetaMin,
                          double thetaMax)

eapEstimate

public double eapEstimate(double mean,
                          double sd,
                          double thetaMin,
                          double thetaMax,
                          int numPoints)

Expected a Posteriori (EAP) estimate of examinee ability using a normal distribution.

Parameters:

mean - mean of normal distribution

sd - standard deviation of normal distribution

thetaMin - smallest possible ability score

thetaMax - largest possible ability score

numPoints - number of quadrature points

Returns:

eap ability estimate

eapEstimate

public double eapEstimate(DistributionApproximation dist)

EAP estimate using a distribution provided by the user such as quadrature points and weights from item calibration.

Parameters:

dist - User specified quadrature points and weights.

Returns:

pcfEstimate

public double pcfEstimate(int maxIter,
                          double converge,
                          double adjustment)

Computes ability estimate using proportional curve fitting. This method is only appropriate with the Rasch, Partial Credit, and Rating Scale models. It may not converge to the maximum value if used with other models. This method is the same method used for person estimation in the Rasch package.

Parameters:

maxIter - maximum number of iterations

converge - convergence criterion (e.g. 0.01)

adjustment - extreme score (i.e. all items correct) adjustment factor

Returns:

examinee ability estimate

testInformationAt

public double testInformationAt(double theta)

eapStandardErrorAt

public double eapStandardErrorAt(double theta)

Computes standard error for EAP method.

Parameters:

theta - person ability value

Returns:

standard error

mleStandardErrorAt

public double mleStandardErrorAt(double theta)

mapStandardErrorAt

public double mapStandardErrorAt(double theta)

pcfStandardErrorAt

public double pcfStandardErrorAt(double theta)

getTheta

public double getTheta()

value

public org.apache.commons.math3.analysis.differentiation.DerivativeStructure value(org.apache.commons.math3.analysis.differentiation.DerivativeStructure t)

Returns value of loglikelihood using DerivativeStructure per interface requirements

Specified by:

value in interface org.apache.commons.math3.analysis.differentiation.UnivariateDifferentiableFunction

Parameters:

t -

Returns:

derivLogLikelihood

public org.apache.commons.math3.analysis.differentiation.DerivativeStructure derivLogLikelihood(org.apache.commons.math3.analysis.differentiation.DerivativeStructure t)

Returns first derivative of loglikelihood using DerivativeStructure per interface requirements

Parameters:

t -

Returns:

value

public double value(double param)

Specified by:

value in interface org.apache.commons.math3.analysis.UnivariateFunction