二元項目反應(yīng)函數(shù)的非參數(shù)估計.pdf

1、東南大學(xué)碩士學(xué)位論文二元項目反應(yīng)函數(shù)的非參數(shù)估計姓名：陸錢春申請學(xué)位級別：碩士專業(yè)：數(shù)學(xué)；概率論與數(shù)理統(tǒng)計指導(dǎo)教師：江其保201101AbstractMultidimensionalitemresponsetheory(MIRT)istheresultoftheconvergenceofideasfromanumberofareasinpsychologyeducation，testdevelopment，psychometrics，a

2、ndstatisticsMultidimensionalnonparametricitemresponsetheoryisoneofthepopularproblemsinIRTinrecentyearsOntheonehand，thenonparametricdescriptionisasflexibilityasneededtomodelunusualortmforseenfeatureintheclLrVebecauseoflat

3、enttraitsanditemresponsefunctions(IRFs)OntheotherhanditiseasyteducetheunnecessaryimpactandsmooththecuINeunderthenonparametricmethodoffunctionaldataanalysisInthispaperthemethodsoffunctionaldataanalysisareusedtononparametr

4、icallyestimatet、)l，0dimensionalitemresponsefunctionfordichotomouslyscoredtestdataFirstlyinordertemovethenonpositivityrestriction，theIRFistransformedbythelogisticfunctionThetransformedfunctionisthenexpandedbyBspinebasisfu

5、nctionsthecoefficientmatrixisfittedtOthedatabyanEMalgorithmSecondlyourEMalgorithmisusedtomaximizethelogarithmofmarginallikelihoodimpliedintheobserveddataDuetothenonlinearityofoBrmodel，adouble缸egralarisesintheexpectations

6、tepThisintegralistransformedintoaweightedSuminthemaximizationstep，andtherootofthepartialderivativeofthelogarithmofweightedsunlwithrespecttOthecoefficientmatrixisrequiredupdateForthesakeofalgorithmicstabilitythenonlineare

7、quationsissolvedwithdampedleastsquaresInadditionteduce也enoiseorinterferenceof也edataitselfand也eeffectsfromthedimensionselectionofthebasisfunctionaroughnesspenaltyshouldbeusedinthesmoothingofthetwodimensionalitemcharacteri

8、sticcurve(ICe)ThisisimplementedbyaddingtWOsecondorderpenaltyfactOrstotheleastsquareFinallytoevaluatethecorrectnessandeffectivenessof01／I“methodarealdatasetisfittedtObothourmodelandthetraditionalparametricmodelBycomparing