The chiropractic clinical competency examination uses groups of items that are integrated by a common case vignette. The nature of the vignette items violates the assumption of local independence for items nested within a vignette. This study examines via simulation a new algorithmic approach for addressing the local independence violation problem using a two-level alternating directions testlet model. Parameter values for item difficulty, discrimination, test-taker ability, and test-taker secondary abilities associated with a particular testlet are generated and parameter recovery through Markov Chain Monte Carlo Bayesian methods and generalized maximum likelihood estimation methods are compared. To aid with the complex computational efforts, the novel so-called TensorFlow platform is used. Both estimation methods provided satisfactory parameter recovery, although the Bayesian methods were found to be somewhat superior in recovering item discrimination parameters. The practical significance of the results are discussed in relation to obtaining accurate estimates of item, test, ability parameters, and measurement reliability information.