A note on the binomial model with simplex constraints

Abstract

Liu (2000) considered maximum likelihood estimation and Bayesian estimation in a binomial model with simplex constraints using the expectationmaximization (EM) and data augmentation (DA) algorithms. By introducing latent variables Zij and Yij (to be defined later), he formulated the constrained parameter problem into a missing data problem. However, the derived DA algorithm does not work because he actually assumed that the Yij are known. Furthermore, although the final results from the derived EM algorithm are correct, his findings are based on the assumption that the Yij are observable. This note provides a correct DA algorithm. In addition, we obtained the same E-step and M-step under the assumption that the Yij are unobservable. A real example is used for illustration. © 2011 Elsevier B.V. All rights reserved.