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Public Member Functions |
| | ICRF_PCM (int ncat, Response firstResp, Real a=1.0) |
| Real | ICRF (Response r, const RealVector ¶m, Real theta) const |
| | Computes probability of a response in response category 'r' for latent variable value theta.
|
| Real | OpenICRF (Response r, const RealVector ¶m, Real theta) const |
| | Returns value of ICRF in open interval (0,1).
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| void | ICRFDeriv1 (Response r, const RealVector ¶m, Real theta, RealVector &deriv) |
| | Computes value of first derivative of ICRF (gradient).
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| bool | GradientDefined () const |
| | Function indicating that gradient (ICCDeriv1) is defined.
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| bool | HessianDefined () const |
| | Function indicating that Hessian is not defined.
|
| void | Scale (Real slope, Real intercept, RealVector ¶m) |
| | Compute linear transformation of item parameters onto a new IRT scale.
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| int | NumParameters () const |
| | Returns number of estimated parameters.
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| int | NumAllParameters () const |
| | Returns number of fixed (a) and estimated (b1, b2, ...) parameters.
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| int | NumRespCat () const |
| | Returns number of response categories.
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| std::string | Name () const |
| | Return name of model.
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| IRTModel | Model () const |
| | Return model type from enum defined in etirmtypes.h.
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| void | GetAllParameters (const RealVector &estParam, RealVector &allParam) const |
| | Takes estimate parameters (b1, b2, ...) as input, outputs allParam, the vector made up of fixed parameter a, and the estimated parameters b1, b2, ...
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| template<class I> |
| void | SetAllParameters (I begin_param, I end_param, RealVector &estParam) |
| | Set a, b1, b2, ... parameters.
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Private Member Functions |
| void | ExpZ (const RealVector ¶m, Real theta) |
| | Computes mDenom, mDenom2, and elements of mExpz.
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Private Attributes |
| int | mNumCat |
| | number of response categories
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| int | mNumParameters |
| | number of estimated parameters in model
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| Real | mA |
| | slope parameter
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| Response | mFirstResponse |
| | Response associated with first response category.
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| RealVector | mExpz |
| Real | mDenom |
| | denominator of ICRF
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| Real | mDenom2 |
| | Square of mDenom.
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Computes probability of a response in response category 'r' for latent variable value theta.
Returns value of item characteristic response function (ICRF) for response r, parameters in vector param (b1, b2, ...), and theta value.
ICRF_PCM::ICRF
- Parameters:
-
| [in] | r | Response category, where a response in the first response category is mFirstResponse, the response in the second response category is mFirstResponse+1, etc. |
| [in] | param | Vector containing item parameters. |
| [in] | theta | Latent variable value for which probability is calculated. |
Definition at line 58 of file ICRF_PCM.cpp.
References mA, mFirstResponse, and mNumCat.
Referenced by OpenICRF().
00059 {
00060
00061 Real z = 0.0;
00062 Real num = (r == mFirstResponse) ? 1.0 : -1.0;
00063 Real sum = 1.0;
00064 Real a = mA;
00065 Response ir = mFirstResponse+1;
00066 RealVector::const_iterator ip = param.begin();
00067 for (int i = mNumCat-1; i--; ++ir, ++ip)
00068 {
00069 z += a * (theta - *ip);
00070 Real ez = std::exp(z);
00071 if (ir == r) num = ez;
00072
00073 sum += ez;
00074 }
00075
00076 return num/sum;
00077
00078 }
Returns value of ICRF in open interval (0,1).
Computes probability of a correct response for latent variable value theta, where probability must be in the open interval (0, 1). This function can be used when the logarithm of the probability or logit of the probability needs to be taken.
OpenICRF
Definition at line 90 of file ICRF_PCM.cpp.
References ICRF().
00091 {
00092
00093 double prob = ICRF(r, param, theta);
00094
00095
00096 if (prob <= 0.0)
00097 {
00098 prob = std::numeric_limits<Real>::min();
00099 }
00100 else if (prob >= 1.0)
00101 {
00102 prob = 1.0 - std::numeric_limits<Real>::epsilon();
00103 }
00104
00105 return prob;
00106 }
Computes value of first derivative of ICRF (gradient).
Computes first derivatives of ICRF with respect to all parameters.
ICRFDeriv1
Returns derivative with respect to item parameters in vector deriv.
The derivative is obtained by computing the derivative of the numerator and denominator of the ICRF probability separately, and using the formula for the derivative of a quotient of functions.
Definition at line 149 of file ICRF_PCM.cpp.
References ExpZ(), mA, mDenom, mDenom2, mExpz, mFirstResponse, and mNumCat.
00150 {
00151 ExpZ(param, theta);
00152
00153 Real probnum = mExpz[r - mFirstResponse];
00154 Real a = mA;
00155
00156
00157
00158
00159 RealVector::const_iterator ie = mExpz.begin()+mNumCat-1;
00160 RealVector::iterator id = deriv.begin() + mNumCat-2;
00161 Real dderiv = 0.0;
00162 Real nderiv = -a * probnum;
00163 Response ir = mFirstResponse + mNumCat - 1;
00164 for (int i = mNumCat-1; i--; --ir, --ie, --id)
00165 {
00166 dderiv += -a * *ie;
00167
00168 if (ir <= r) *id = nderiv * mDenom;
00169 else *id = 0.0;
00170 *id -= probnum * dderiv;
00171 *id /= mDenom2;
00172 }
00173
00174 }
Takes estimate parameters (b1, b2, ...) as input, outputs allParam, the vector made up of fixed parameter a, and the estimated parameters b1, b2, ...
Copy fixed a parameter and estimated b parameters from estParam into allParam. Set a, b1, b2, ... parameters, where a is fixed, and b1, b2, ... are estimated.
GetAllParameters
Definition at line 198 of file ICRF_PCM.cpp.
References mA, and mNumParameters.
00199 {
00200 if (estParam.size() != mNumParameters || allParam.size() != mNumParameters+1)
00201 {
00202 throw InvalidArgument("Invalid number of parameters", "ICRF_PCM::GetAllParameters");
00203 }
00204
00205 allParam[0] = mA;
00206 RealVector::iterator ia = allParam.begin() + 1;
00207 RealVector::const_iterator ie = estParam.begin();
00208 for (int i = mNumParameters; i--; ++ia, ++ie)
00209 {
00210 *ia = *ie;
00211 }
00212 }
| void etirm::ICRF_PCM::ExpZ |
( |
const RealVector & |
param, |
|
|
Real |
theta | |
|
) |
| | [private] |
Computes mDenom, mDenom2, and elements of mExpz.
Computes the terms exp(sum_{k=1}^i z_k), i = 1, mNumCat-1, where z_k = a * (theta - b_k), a = mA, b_k = param[k-1]. These terms are stored in the data member mExpz. Also store values in data members mDenom and mDenom2.
ExpZ
Definition at line 115 of file ICRF_PCM.cpp.
References mA, mDenom, mDenom2, mExpz, and mNumCat.
Referenced by ICRFDeriv1().
00116 {
00117 Real a = mA;
00118
00119
00120 mExpz[0] = 1.0;
00121 mDenom = 1.0;
00122 RealVector::iterator ie = mExpz.begin()+1;
00123 RealVector::const_iterator ip = param.begin();
00124 Real num = 0.0;
00125 for (int i = mNumCat-1; i--; ++ip, ++ie)
00126 {
00127 num += a * (theta - *ip);
00128 *ie = std::exp(num);
00129 mDenom += *ie;
00130 }
00131
00132 mDenom2 = mDenom * mDenom;
00133 }
