Research On The Impact Of Starting Values On Mcmc Parameter Estimation Of Item Response Theory

In item response theory(IRT), parameter estimation plays an important role forthe construction of item pool, examinee investigating and examinee equalityinvestigating. With the continuous development of IRT, there are different methods ofparameter estimation. But as the model becomes more and more complex, it is hardfor the parameter estimation method to deal with the complicated model that has thecomplex computation. In1990s, American statistician Albert introduced the Markovchain Monte Carlo (MCMC) method to the parameter estimation of IRT, somescholars applied it to the various models and obtained better estimation results inrecent years.The MCMC method not has special requirement for the starting value of theparameter,but the traditional method of parameter estimation requires accurateparameter starting value. However, when the parameter starting value is far differentfrom the true value, the MCMC method requires a longer chain length to iterate in theestimation process, this process consumes a large amount of time.This paper introduces the traditional parameter estimation method of startingvalue to the MCMC parameter estimates, obtaining more accurate starting value byestimation, which as the starting value of Markov chain and calculate iteratively. Bythis method, the Markov chain can quickly reach the stationary distribution, reducingthe sampling time.This paper examines2PLM and GRM, a large number of MonteCarlo simulation studies demonstrate that: For2PLM, when the sample size or testlength is large and the chain length is short, the effects of starting value is obvious,which means the more accurate starting value brings the higher estimation accuracy.For GRM, the estimated results is similar to2PLM, but the effect is more obvious.