A Comparison of Bayesian Estimation Techniques in a Multidimensional Two-Parameter Partial Credit Item Response Model

Bayesian estimation methods have shown better performance than the traditional Marginal Maximum Likelihood (MML) estimation method for parameter estimation in relatively simple item response models. However, extant literature is lacking on the investigation of Bayesian parameter estimation approaches for a multidimensional two parameter partial credit (M2PPC) model, therefore this simulation study investigated the performance of two Bayesian Markov Chain Monte Carlo (MCMC) algorithms: Gibbs Sampler and Hamiltonian Monte Carlo-No-U-Turn-Sampler (HMC-NUTS) for M2PPC models\u27 parameter estimation. It compared the estimation accuracy and computing speed in different combinations of situations, including prior choices, test lengths, and the relationships between dimensions. The datasets were generated based on the distributions from existing literature, and the conditions were fully crossed. It ended up with 36 conditions: Bayesian MCMC algorithms (Gibbs sampler and HMC-NUTS), prior choices (Matched Prior, Vague Prior and Hierarchical Prior), test lengths (15 and 30), and the relationships between dimensions (low = .2, medium = .5, and high = .8). Root Mean Squared Errors (RMSE) and Bias for each of the recovered parameter in all the conditions were calculated. Sets of four-way ANOVAs were conducted to check the contribution of the four factors--Bayesian algorithm, prior choice, test length, and interdimensional correlation--to the total variance in RMSE and Bias. The computational speed was also recorded for each of the estimations. The first finding is that when considering the computational speed and estimation accuracy, the results of parameter recovery of the M2PPC model show that Gibbs Sampler and HMC-NUTS performed similarly in all the simulated conditions. The second finding is concerning test length. The precision of item parameter estimates increased as the test length decreased, but the accuracy of person parameter estimates increased as the test length increased in all the simulated conditions for both Gibbs Sampler and HMC-NUTS. Test length had no consistent impact on Bias for either item parameter or person parameter estimates. The third finding is that different interdimensional correlations did not influence the recovery of item parameters but affected the precision of the estimation of person parameters. The accuracy of the person parameter recovery increased as the interdimensional correlation increased in all the different conditions for both Gibbs Sampler and HMC-NUTS. The results of analyses of variance (ANOVAs) supported the previous conclusions. This dissertation study concluded with limitations and recommendations for future work