A Comparative Study Of Two Different Item Response Theory

At present,with the in-depth study of the surveyor,the item response theory has become more mature,which the item response theory of Lord and Hamilton is the most famous.So far,IRT still has many theoretical problems to be solved.For example,it is easy to equate the unidimensional hypothesis with the assumption of local independence,unidimensional assumption does not meet the requirements of the actual test,why the local independence hypothesis add the word "local" ? Is the model just to fit the test data? Is the IRT just an empirical theory? If not,what is its theoretical basis? This article will discuss these issues around them.In recent years,the IRT scholars represented by Wenjiu Du have discussed the theoretical problems of IRT in summing up their previous experiences.In 2014,the book " Higher Item Response Theory" was published.The book uses probability theory as a mathematical tool to discuss the basic assumptions of IRT and the theoretical basis of the response model.In this book,many theorems,formulas are proved.In the book "Higher Item Response Theory",a series of concepts are defined,specifically,including sample space ?,operator sets G,item sets H,and subjects F.Du replaced unidimensional assumption,local independence assumption and model assumption with order preserving hypothesis,independence hypothesis and linear hypothesis,and he used the method of node,which is based on the two-parameter logistic model,the probability distribution function of the secondary scoring model and the multi-level scoring model is proved.More importantly,he boldly tried and applied the deductive approach to transition the IRT from empirical theory to deductive theory.In the book "higher item response theory",Du put forward three basic assumptions that are different from Lord and Hamilton,and thus get different conclusions,mainly as follows:(1)Under the preservation hypothesis,each of the subjects with the value of the ability parameters can be defined,and that is given the invariant value,and the percentile of the subjects on the test items is the same.But in Lord and Hamilton's IRT,the capability parameter is just an abstract concept,just a term that describes the potential trait and is not quantified;(2)Including the two-parameter model,the three-parameter model,the secondary scoring model and the multi-scoring model,all the item response model can be used to deduce the reasoning of the nod to get the corresponding probability distribution function,thus the item response model has a theoretical basis.However,the IRT of Lord&Hamilton are only forthe fitting of the data,lacking theoretical basis;(3)When the item parameters and capacity parameters are unknown need to be estimated at the same time,the estimated value converges to the probability value.And the item response theory of Lord&Hamilton does not have such a property.(4)Du uses the deductive method to make a reasoning argument on the item response theories' theorem and formula.It is concluded that the future development trend of IRT is a turning point.On the whole,the item response theory of Lord and Hamilton is still empirical and lacks a certain logical basis.