etirm::ItemParamPriorBeta4 Class Reference

Class representing a four-parameter beta prior distribution of item parameters in Bayes modal estimation. More...

#include <ItemParamPriorBeta4.h>

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List of all members.

Public Member Functions
	ItemParamPriorBeta4 ()
	Default constructor - assign uniform [0,1] distribution.
	ItemParamPriorBeta4 (RealVector &param)
	Class construction from a parameter vector.
	ItemParamPriorBeta4 (Real a, Real b, Real l, Real u)
	Class construction from four individual parameter values.
virtual int	NumParameters ()
	Returns number of prior beta distribution parameters for the IRT parameter.
virtual bool	ZeroDensity (Real p)
	Returns true if density at p is zero.
virtual Real	NearestNonZero (Real x)
	If density of x is zero, then this function will return the value closest to x that has a non-zero density.
virtual Real	LogDensity (Real p)
	Only computes part of the log of the density that depends on the parameter.
virtual Real	DerivLogDensity1 (Real p)
	First derivative of log density.
virtual Real	DerivLogDensity2 (Real p)
	Second derivative of log density.
virtual std::string	DistributionName () const
	Returns string containing name of distribution used for prior.

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Detailed Description

Class representing a four-parameter beta prior distribution of item parameters in Bayes modal estimation.

Definition at line 35 of file ItemParamPriorBeta4.h.

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Constructor & Destructor Documentation

etirm::ItemParamPriorBeta4::ItemParamPriorBeta4

(

)

Default constructor - assign uniform [0,1] distribution.

Definition at line 74 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters.

                                           :
    ItemParamPrior(4)
  {

    mParameters[0] = 1.0;
    mParameters[1] = 1.0;
    mParameters[2] = 0.0;
    mParameters[3] = 1.0;
  }

etirm::ItemParamPriorBeta4::ItemParamPriorBeta4

(

RealVector &

param

)

Class construction from a parameter vector.

Definition at line 44 of file ItemParamPriorBeta4.cpp.

                                                            :
    ItemParamPrior(param)
  {
  }

etirm::ItemParamPriorBeta4::ItemParamPriorBeta4	(	Real	a,
		Real	b,
		Real	l,
		Real	u
	)

Class construction from four individual parameter values.

Definition at line 53 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters.

                                                                         :
    ItemParamPrior(4)
  {
    // check for valid parameters
    if (a <= 0.0 || b <= 0.0)
      throw RuntimeError("Invalid shape parameter for beta dist",
          "ItemParamPriorBeta4::ItemParamPriorBeta4");
    if (l >= u)
      throw RuntimeError("Invalid upper or lower limit for beta dist",
          "ItemParamPriorBeta4::ItemParamPriorBeta4");

    mParameters[0] = a;
    mParameters[1] = b;
    mParameters[2] = l;
    mParameters[3] = u;
  }

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Member Function Documentation

virtual int etirm::ItemParamPriorBeta4::NumParameters

(

)

[inline, virtual]

Returns number of prior beta distribution parameters for the IRT parameter.

Implements etirm::ItemParamPrior.

Definition at line 44 of file ItemParamPriorBeta4.h.

    {
      return 4;
    }

virtual bool etirm::ItemParamPriorBeta4::ZeroDensity

(

Real

p

)

[inline, virtual]

Returns true if density at p is zero.

Reimplemented from etirm::ItemParamPrior.

Definition at line 50 of file ItemParamPriorBeta4.h.

References etirm::ItemParamPrior::mParameters.

Referenced by DerivLogDensity1(), DerivLogDensity2(), and LogDensity().

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Real etirm::ItemParamPriorBeta4::NearestNonZero

(

Real

x

)

[virtual]

If density of x is zero, then this function will return the value closest to x that has a non-zero density.

Reimplemented from etirm::ItemParamPrior.

Definition at line 86 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters.

  {
    // Density at lower and upper limits has zero
    // density, so return a value that is offset
    // from the lower and upper limits by the following amount
    const Real offset = 0.001;

    if (x <= mParameters[2])
    {
      return mParameters[2]+offset;
    }
    else if (x >= mParameters[3])
    {
      return mParameters[3]-offset;
    }
    else
    {
      return x;
    }
  }

Real etirm::ItemParamPriorBeta4::LogDensity

(

Real

p

)

[virtual]

Only computes part of the log of the density that depends on the parameter.

Parameters:

[in]

p

Argument of log density function (an item parameter value)

Implements etirm::ItemParamPrior.

Definition at line 113 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters, and ZeroDensity().

  {

    /* Check for value outside limits of distribution */
    if (ItemParamPriorBeta4::ZeroDensity(p))
    {
      {
        return std::log(0.0);
      }
    }

    Real value = (mParameters[0] - 1.0) * std::log(p - mParameters[2]);

    value += (mParameters[1] - 1.0) * std::log(mParameters[3] - p);

    return value;
  }

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Real etirm::ItemParamPriorBeta4::DerivLogDensity1

(

Real

p

)

[virtual]

First derivative of log density.

Only computes part of the log of the density that depends on the parameter

Implements etirm::ItemParamPrior.

Definition at line 137 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters, and ZeroDensity().

  {
    /* Outside limits of distribution density does not change,
     so derivative is zero */
    if (ItemParamPriorBeta4::ZeroDensity(p))
      return 0.0;

    Real value = (mParameters[0] - 1.0) / (p - mParameters[2]);
    value -= (mParameters[1] - 1.0) / (mParameters[3] - p);

    return value;
  }

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Real etirm::ItemParamPriorBeta4::DerivLogDensity2

(

Real

p

)

[virtual]

Second derivative of log density.

Only computes part of the log of the density that depends on the parameter.

Implements etirm::ItemParamPrior.

Definition at line 156 of file ItemParamPriorBeta4.cpp.

References etirm::ItemParamPrior::mParameters, and ZeroDensity().

  {
    /* Outside limits of distribution density does not change,
     so derivative is zero */
    if (ItemParamPriorBeta4::ZeroDensity(p))
      return 0.0;

    Real denom = p - mParameters[2];
    Real value = (1.0 - mParameters[0]);
    value /= denom*denom;
    denom = mParameters[3] - p;
    value -= (mParameters[1] - 1.0) / (denom*denom);

    return value;
  }

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virtual std::string etirm::ItemParamPriorBeta4::DistributionName

(

)

const [inline, virtual]

Returns string containing name of distribution used for prior.

Implements etirm::ItemParamPrior.

Definition at line 68 of file ItemParamPriorBeta4.h.

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

• C:/programs/etirm/src/ItemParamPriorBeta4.h
• C:/programs/etirm/src/ItemParamPriorBeta4.cpp

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