Homogeneity versus Parsimony in Markov Manpower Models: A Hidden Markov Chain Approach

Abstract

We aim at tackling the problem of inadequate specification of a Markov manpower model in this paper, by formulating a procedure for validating the inclusion or non-inclusion of some transition parameters in the model. The mover-stayer principle and its extensions are employed to incorporate hidden classes in the model to achieve more homogeneity and this is compared with the model without the hidden classes, which is more parsimonious, using Likelihood ratio statistic, Akaike Information Criterion and Bayesian Information Criterion. The illustration shows a case of manpower data where, up to a certain level of hidden states, homogeneity is more important than parsimony.

Likelihood Ratio Search Procedure for Optimum Number of States in a Hidden Markov Manpower Model

“…The formulation of HMM for manpower systems, HMMM in the current paper, has been done in a number of works in this area; see [2,4,5]. Here we specify and highlight important components of HMMM relevant to the current aim.…”

“…; what hidden states stand for depend on the type of HMMM. Ossai et al [5] introduced the model type HMM to represent a HMM for a manpower system with hidden states in each observable class, where the states are described according to the personnel's ability to move to other observable classes. In the current work we represent a HMMM with hidden states per observable class by HMMM .…”

“…HMM has been applied in the area of statistical manpower planning, see, for example, [2,4,5]. A manpower system is a system of personnel groups on the basis of existing ranks or carders of personnel in the system, where members of a group have the potential of moving to other groups according to some probability distribution [6][7][8].…”

“…Udom and Ebedoro [2] increased the number of hidden states in a manpower system to three to represent the class of 'movers', 'mediocres' and 'stayers'. Ossai et al [5], in an attempt to check whether the property of parsimony or homogeneity is more important in a manpower system, increased the number of hidden classes to five, representing the class of 'high movers', 'movers', 'above mediocres', 'mediocres' and 'stayers', with the values of probabilities of moving to other observable classes decreasing in this order. The authors' choices of the number of hidden classes in these cases are not guided by any rule nor are there any check whether they are the best choices to make.…”

“…The authors' choices of the number of hidden classes in these cases are not guided by any rule nor are there any check whether they are the best choices to make. Again, all the authors, with the exception of [5], compared only their new HMMM with the CMMM and concluded on the superiority of their HMMM based on this. However, Udom and Ebedoro [2] emphasize the need to search for the optimum number of hidden states to be included in a HMMM.…”