Research On The Relationships Between Jeffreys Modal And Weighted Likelihood Estimation Of Latent Trait Under Three Models

This paper focuses on two estimators of latent trait with item response theory models-the weighted likelihood estimator and the Bayesian modal estimator.For the Bayesian modal estimator,Jeffreys' prior distribution is considered,and the corresponding estimator is referred to as the Jeffreys modal(JM)estimator.This paper studies the relationships between two estimators under three models: the mixed-type model composed of both dichotomously three-parameter logistic model and polytomously the generalized partial credit model,the four-parameter logistic model and the two-parameter extension logistic model.The results show that(a)Under the mixed-type model,the JM estimator returns larger estimates than the WL estimator.(b)Under the four-parameter logistic model,a general condition between the parameter d and ability level is derived to ensure the JM estimator larger than the WL estimator.(c)Under the two-parameter extension logistic model,it is found that the JM estimator is larger than the weighted likelihood estimator.