The Semi-Parametric Models And Statistical Methods Based On Item Response Theory

In the estimation of item response models,the normality of latent traits is frequently assumed.However,this assumption may be untenable in real testing.In contrast to the conventional three-parameter normal ogive(3PNO)model,a 3PNO model incorporating Ramsay-curve item response theory(RC-IRT),denoted as the RC-3PNO model,allows for flexible latent trait distributions.We propose a stochastic approximation expectation maximization(SAEM)algorithm to estimate the RC-3PNO model with non-normal latent trait distributions.The simulation studies of this work reveal that the SAEM algorithm produces more accurate item parameters for the RC-3PNO model than those of the 3PNO model,especially when the latent density is not normal,such as in the cases of a skewed or bimodal distribution.Three model selection criteria AIC,BIC and HQIC are used to select the optimal number of knots and the degree of the B-spline functions in the RC-3PNO model.A real data set from the PISA 2018 test is used to demonstrate the application of the proposed algorithm.RC-3PNO model is adaptive to dichotomous data sets.The methods in the second chapter is extended to the graded response model(GRM)in chapter 3,and the Markov chain Monte Carlo(MCMC)algorithm incorporated with Ramsay curve method(denoted as RC-MCMC algorithm)is given.The simulation results revealed that the item parameter estimation and the estimate of density curve g(θ)for the latent trait θ using the proposed method under different conditions is accurate.An empirical study is given to illustrate the application of the proposed model and algorithm to the Sexual Compulsivity Scale(SCS)data sets.In contrast to the response data,response time data is usually asymmetric.Up to now a large number of models using asymmetrical distributions to fit response time data have been generated in the field of psychology and education measurement,and the log-normal distribution is typically used.However there are cases in which the response time data after log-transformation is not normal.Semiparametric statistical methods give directions to involving these obstacles.Models based on semiparametric methods are not restricted to the assumption of specific distributions,and reserve the intuitive descriptions of model parameters.The proportional hazards model is a typical example.The proportional hazards model is a frequently used model in survival analysis,and the implements in fields of psychology and education measurement has increased in recent years.A piecewise constant proportional hazards latent trait model is proposed in this research based on the proportional hazards model.And the proportional hazards model can be seen as a special case of the piecewise constant proportional hazards latent trait model.Compared with traditional parametric models,the model in this research is more flexible which is not restricted to specific distribution assumptions.Furthermore,it reserves the intuitive descriptions of model parameters compared to non-parametric methods.The Gibbs sampling algorithm based on the auxiliary variables(GAAV)is given subsequently.In contrast to traditional Bayesian algorithms,the GAAV algorithm is feasible with non-conjugate distributions,and even effective when the miss-specified priors are used.The simulation studies verified the accuracy of parameter estimation using GAAV algorithm and the sensitivity to priors of the algorithm.A comparative study of the GAAV algorithm and adaptive rejection sampling for Gibbs algorithm is given.Bayesian model assessment based on the deviance information criterion(DIC)and the pseudomarignal likelihood(LPML)is presented in simulation study.Finally,the application of GAAV algorithm to PISA data sets is provided.