On multinomial hidden Markov model for hierarchical manpower systems

In this paper, a three-state multinomial hidden Markov model (HMM) is formulated to handle the problem of intra-category heterogeneity caused by latent factors for transition flows of a hierarchical manpower system. The model, which incorporates mover, mediocre and stayer latent subclasses for each personnel category, is applied in analyzing manpower data for the academic staff of a University system in Nigeria. An EM algorithm is used to estimate the probabilities of transition of members from each of the subclasses. The principles of Likelihood Ratio Test, Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) for model comparison/validation gave evidence in favor of the HMM over the classical Markov model for the system.