Different estimation procedures have been developed for the unidimensional three-parameter item response theory (IRT) model. These techniques include the marginal maximum likelihood estimation, the fully Bayesian estimation using Markov chain Monte Carlo simulation techniques, and the Metropolis-Hastings Robbin-Monro estimation. With each technique, a prior can be specified to reflect prior belief on each model parameter. Previous studies evaluating the fully Bayesian estimation procedure for this model suggests that the model can be viewed as a mixture model, and it suffers from a non-convergence problem unless strong informative priors are specified for the item slope and intercept parameters. This study focused on comparing the three estimation methods for the three-parameter logistic (3PL) model in parameter estimation using Monte Carlo simulations. In particular, sample sizes, test lengths, prior specifications and actual item parameters were manipulated to reflect various test situations. The results suggest that: 1) all three estimation methods performed differently under different simulation conditions, 2) the three methods performed better when the actual parameters are close to their prior mean or mode than when the actual parameters are close to their boundary values, 3) a relatively more informative prior had to be specified for item parameters to ensure convergence with each of the three methods and the item parameters were more accurately estimated. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]