Estimation Of Standard Errors Of Parameters In IRT Model With Latent Variable Distribution: Parallel Bootstrap Metho

The standard error(SE)of model parameters of item response theory(IRT)is of great importance in theory development and practical application.Researchers have proposed various IRT models with estimation of latent trait distribution that based on traditional IRT model following normal distribution,collectively referred to as latent trait distribution IRT models,including DC-IRT model and EH-IRT model.Previous studies have found that these models can accurately estimate model parameters under normal or non-normal latent trait distribution,but studies focusing on model parameters SEs have not been conducted commensurably,which limits the development of these models.This dissertation proposes parallel non-parametric bootstrap(p NPB)and parallel parametric bootstrap(pPB)methods for estimating model parameters SEs of latent trait distribution IRT based on the existing methods under the cognitive diagnostic model framework.Study 1 was conducted to illustrate the necessity of studying model parameters SEs under the latent trait distribution IRT framework based on the relative fit of the models to three empirical datasets(i.e.,Generalized Anxiety Data Set,Dispositional Optimism Data Set,and Nicotine Dependence Syndrome Data Set).Results showed that(1)the relative fit of the latent trait distribution IRT models was superior to that of the IRT models following normal distribution under all indicators,and(2)the DC-IRT model was the optimal model for all empirical datasets based on the AIC,BIC,and HQ.Therefore,it was necessary to study model parameters SEs under the latent trait distribution IRT framework using the DC-IRT model as an example.Study 2 was designed to investigate the performance of the p NPB and pPB methods for estimating the model parameters SEs of the DC-IRT under ideal conditions.Different latent trait distributions,sample sizes,and bootstrap sample sizes were examined to explore the accuracy of the p NPB and pPB methods for estimating model parameters SEs of the DC-IRT.Results showed that(1)overall,p NPB and pPB methods performed well in estimating item parameters SEs,and the accuracy of estimates increased with sample size,and(2)the p NPB method performed slightly better in the parameters of latent trait distribution(i.e.,DC parameters)SEs under N(29)300,while pPB method performed poorly.The purpose of Study 3 was to investigate the robustness of the p NPB and pPB methods for estimating model parameters SEs.This study explored the performance of the p NPB and pPB methods when the latent trait distribution was incorrectly specified in the IRT model and compared them with the OIA,XPD,and Sw methods.Results showed that(1)p NPB and pPB methods performed well overall and had good robustness,and(2)p NPB method performed slightly better than pPB method.Study 4 was an empirical study aimed at demonstrating the value of p NPB and pPB methods in analyzing empirical datasets,including Generalized Anxiety Data Set,Dispositional Optimism Data Set,and Nicotine Dependence Syndrome Data Set.Results showed that p NPB and pPB methods provided similar results in item parameters SEs,but slight differences in DC parameters SEs,which were consistent with the results of the simulation studies.Developing flexible and effective SEs estimation methods in the framework of latent trait distribution IRT models has important theoretical and practical value.Based on the simulation and empirical studies,the dissertation found that p NPB and pPB methods could be used to estimate model parameters SEs for latent trait distribution IRT models,and p NPB method was slightly better than pPB method.