Likelihood Ratio Search Procedure for Optimum Number of States in a Hidden Markov Manpower Model
Everestus O. Ossai *
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Mbanefo S. Madukaife
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper aims at obtaining the optimum number of states for a hidden Markov manpower model, which, hitherto, has been chosen arbitrarily. A search procedure that attains this optimum number after a few steps across a series of N hidden Markov manpower models is proposed. The likelihood ratio statistic is employed to conduct pairwise model comparison tests on the N hidden Markov manpower models ordered according to their level of parsimony. The illustration shows the usefulness of the procedure in choosing the right number of states for a hidden Markov manpower model to avoid wrong specification of such models. The proposed procedure can be useful in other areas of research, such as in biological, medical and social sciences, where application of hidden Markov model may require the determination of number of hidden states based on unobserved data with latent heterogeneity. The procedure has a straightforward formulation and its application in other areas requires mainly the adaptation of the model specifications for the new area’s system dynamics.
Keywords: Statistical manpower planning, heterogeneity, hidden Markov model, number of states, likelihood ratio test