Applications Of Bayesian Statistical Inference In Educational And Psychological Measurement Under The Framework Of Item Response Theory

Within the framework of item response theory,a new and flexible general three parameter logistic model with response time(G3PLT)is proposed in this paper.The advantage of the new model is that it can combine time effect,ability and item difficul-ty to influence the correct response probability.In contrast to the traditional response time model in the educational psychology study,the time effect in our new model will directly affect the correct response probability rather than linking the response time and correct response probability through hierarchical modeling method as shown in van der Linden(2007)[121]'s model,using the latent and speed parameters are used as intermediate bridges.In addition,Metropolis-Hastings within Gibbs sampling al-gorithm is employed to estimate the model parameters.Based on the Markov chain Monte Carlo(MCMC)output,two Bayesian model assessment methods are investi-gated concerning the goodness of fit between models.Finally,two simulation studies and a real data analysis are given to further illustrate the advantages of our model over the traditional three parameter logistic modelIn the second study,a new two-parameter logistic testlet response theory model is proposed by introducing testlet discrimination parameters to model the local depen-dence among items within a common testlet.In addition,a highly effective Bayesian sampling algorithm based on auxiliary variables is proposed to estimate the testlet ef-fect models.The new algorithm not only avoids the Metropolis-Hastings algorithm boring adjustment the turning parameters to achieve an appropriate acceptance prob-ability but also overcomes the dependence of the Gibbs sampling algorithm on the conjugate prior distribution.Compared with the traditional Bayesian estimation meth-ods,the advantages of the new algorithm are analyzed from the various types of prior distributions.Based on the Markov chain Monte Carlo(MCMC)output,two Bayesian model assessment methods are investigated concerning the goodness of fit between models.Finally,three simulation studies and an empirical example analysis are given to further illustrate the advantages of the new testlet effect model and the effectiveness of the Bayesian sampling algorithmMissing responses generally exist in educational and psychological assessments The statistical inference will lead to serious deviation if the missing responses are not properly modeled in the framework of a non-ignorable missing mechanism.In this current study,it is studied whether the different missing mechanism(ignorable missing and non-ignorable missing)models are appropriate to analyze the missing response data from the perspective of parameter estimation and model assessment.In terms of parameter estimation,we use the slice-Metropolis-Hastings algorithm to estimate the parameters in the model.Based on the Markov Chain Monte Carlo samples from the posterior distributions,the deviance information criterion(DIC)and the logarithm of the pseudo marginal likelihood(LPML)are employed to compare the different missing mechanism models.Four simulation studies are conducted and a detailed analysis of PISA science data is carried out to further illustrate the proposed methodology.