Research And Simulation Comparisons Of Item Parameter Estimation Based On Mixed 4PL Model With Different Prior Distributions

As a modern psychological measurement theory,item response theory has important value and wide significance in the practical application of educational quality assess-ment and the construction of psychological test question bank.Parameter estimation,as the core of item response theory,is divided into item parameter estimation and per-sonal potential trait estimation.The estimation of item parameters directly affects the estimation of individual potential trait.Recently,under the idea of mixed-type model,some researchers studied the influence of the prior distribution of project parameters on the posterior estimation under the mixed four-parameter logistic model,but only studied the case where the prior distribution of each parameter has the same mean value and different variance.Based on the assumption that the capability parameters are known and the question length and sample size are fixed,this paper explores the influence of different prior distributions of item parameters on the marginal maximum a posterior estimate of item parameters(MMAP)based on the mixed four-parameter logistic model and Expectation-Maximization algorithm(EM).For the difficulty pa-rameter b in the mixed four-parameter logistic model,since b ?(-3,+3),we take the normal distribution here.For the discrimination parameter a,due to a>0,we choose the normal distribution which the mean value is greater than 0.For the guess param-eter c and the upper asymptote parameter d,due to c ?(0,1),d ?(0,1),we take the beta distribution for c and d.It is found that when the mean of the prior distribution of parameters is closer to the mean of the selected parameter truth value,the prior distribution with abundant prior information has better effect on parameter estimation than the prior distribution with weak prior information and the uniform distribution(no prior distribution of information).When the mean of the prior distribution of the parameter deviates from the mean of the selected parameter truth value,the accuracy of parameter estimation can be improved by increasing the variance of the parameter appropriately.When the mean of parameter prior distribution deviates too much from the selected parameter truth value,the prior distribution of uniform distribution is a good choice.