Application Of Birnbaum Information In Educational And Mental Measurement

This thesis mainly analyzes the application of Birnbaum information on the educational or mental measurement models. The method of this thesis will be based on many test scores of the same characteristics. Applying Birnbaum information, reasonable weights will be reasoned out to make the best combination of the scores be an estimation of the people's quantity or characteristics. The combination will be a good estimation which obtains the greatest information of the quantity. The main results on the parametric models of this thesis are got with the test scores satisfying exponential distribution family. The important models we considered in this thesis include parametric models and nonparametric models. Supposing the form of the function h is known but l is unknown, Birnbaum information will be used in dealingwith some mathematical models. The parametric models we considered in this thesis include X = h(T) + e which is a general parametric change of the true score function. Linear model X - Z'β+ e and generalized linear model X = h(Z'β) + e are also considered in this thesis. The nonparametric models we considered in this thesis include simple X = l(T) + e and the single-indexed model X = l(Z'β) + e.This thesis begins from the introduction of the history and the development of mental measurement or educational measurement. And then we introduce some importantmodels in classical test theory (CTT) or item response theory (IRT) and we discuss the corresponding criterion in evaluating the goodness of estimations which involves Birnbaum information function.After that, the preparation of knowledge in this thesis is discussed which includesthe sources of Birnbaum information function. The notation of the test informationand its properties and applications are also introduced in this thesis. The corresponding conclusion ever got about best combination on the model X = T + e is also mentioned in the thesis.The important results in this thesis are some theories and conclusions of parametricmodels, including their proof and corresponding estimation of parameters. We obtain the best combination of different models by applying Birnbaum informationfunction under important parametric changes of the true score model. The estimation methods on general nonparametric model and the single-indexed model are also proposed.The method used in this thesis which is named the best combination can obtain the greatest information. And this method will be widely used because it breaks the limitation of the theory in CTT and IRT.