Comparing The Two-and Three-parameter Logistic Models In The Item Response Theory

Selection of an appropriate item response model is critical in the measurement of latent examinee ability.Logistic models are widely used because of its unique advantage in the item response theory.The one-,two-and three-parameter logistic(1PL,2PL and 3PL)models are nested,and as such can be compared using likelihood ratio(LR)tests.The null hypothesis in the LR test for selection among the 2PL and 3PL models sets the guessing parameters to their lower bounds of 0.This violates one of the assumptions of the LR test and renders the usual reference distribution inappropriate for the comparison.A review of the current literature revealed that this problem is not well understood in the educational measurement field.Ignoring this issue can lead to selection of an ov erly simplified model,with implications for the ability estimates.In order to solve the problem in the nonstandard case and provide an appropriate method of selecting the most parsimonious models,the paper,(Christy Brown,Jonathan Templin & Allan Cohen(2014)),studied the problem of an appropriate distribution when using LR test to select item response models.Simulation results show that the nature of the problem,using an inappropriate distribution can lead to a first type of error below the nominal level ? and a loss of power.The appropriate distribution under a special circumstance is given,but that for general cases are unknown.Considering the need in practical application,and basing on the appropriate distribution under the special circumstance,a method to deal with nonstandard cases is put forword,but this method is very cumbersome.In this paper,from the perspective of local independence assumptions,LR tests are used to compare the 2PL and 3PL models,and the estimation processes of the item's parameters are derived again to simplify the original method and propose a method simpler and more easy to perform.When implementing the improved method,the process is simpler and more convenient than the original method,the number of test is greatly reduced,and the simulation result is not bad.Finally,do some discussion about the improved method.