Homogeneity versus Parsimony in Markov Manpower Models: A Hidden Markov Chain Approach
Everestus O. Ossai *
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Precious N. Ezra
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Felix O. Ohanuba
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
Martin N. Eze
Department of Statistics, University of Nigeria, Nsukka, Nigeria.
*Author to whom correspondence should be addressed.
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.
Keywords: Statistical manpower planning, hidden Markov model, homogeneity, parsimony
How to Cite
Downloads
References
Seal HL. The mathematics of a population composed of k stationary strata each recruited from the stratum below and supported at the lower level by a uniform number of annual entrants. Biometrika. 1945;33:226-230.
Bartholomew DJ, Forbes AF, McClean SI. Statistical techniques for manpower planning. 2nd ed. Chichester: Wiley; 1991.
De Feyter T. Modelling heterogeneity in manpower planning: Dividing the personnel system into more homogeneous subgroups. Appl Stoch Models Bus Ind. 2006;22(4):321–334.
Guerry MA. Hidden heterogeneity in manpower systems: A Markov-switching model approach. European Journal of Operational Research. 2011;210(1):106-113.
DOI: 10.1016/j.ejor.2010.10.039
Rombaut E, Guerry MA. Decision trees as a classification technique in manpower planning. In: The 16th conference of the applied stochastic models and data analysis international society. 2015;863–877.
Davies GS. A note on a continuous time Markov manpower model. Journal of Applied Probability. 1985;22:932-938.
DOI: https://doi.org/10.2307/3213961
Ugwuowo FI, McClean S I. Modelling heterogeneity in a manpower system: A review. Applied Stochastic Models in Business and Industry. 2000;16(2):99–110.
DOI: 10.1002/1526-4025(200004/06)16:2<99::AID-ASMB385>3.0.CO;2-3
Udom, AU, Ebedoro UG. On multinomial hidden Markov model for hierarchical manpower systems. Communications in Statistics – Theory and Methods; 2019.
Available:https://doi.org/10.1080/03610926.2019.1650185
Seasholtz MB, Kowalski B. The parsimony principle applied to multivariate calibration. Analytica Chimica Acta. 1993;277(2):165-177.
Available:https://doi.org/10.1016/0003-2670(93)80430-S
Guerry MA, De Feyter T. Markovian approaches in modelling workforce systems. Journal of Current Issues in Finance, Business and Economics. 2009;2(4):1–20.
Blumen I, Kogan M, McCarthy PJ. The industrial mobility of labour as a probability process. Ithaca, New York: Cornell University Press; 1955.
Spilerman S. Extensions of the Mover-Stayer model. American Journal of Sociology. 1972;78(3):599–626.
DOI:10.1086/225366
Visser I, Raijmakers ME, Molenaar PC. Fitting hidden Markov models to psychological data. Scientific Programming. 2002;10(3):185–99.
DOI: 10.1155/2002/874560.
Shirley KE, Small DS, Lynch KG, Maisto SA, Oslin DW. Hidden Markov models for alcoholism treatment trial data. The Annals of Applied Statistics. 2010;4(1):366–95.
DOI: 10.1214/09-AOAS282
Maruotti A, Punzo A, Bagnato L. Hidden Markov and semi-Markov models with multivariate leptokurtic-normal components for robust modelling of daily returns series. Journal of Financial Econometrics. 2019;17(1):91–117.
DOI: 10.1093/jjfinec/nby019
Can CE, Ergun G, Soyer R. Bayesian analysis of proportions via a hidden Markov model. Methodology and Computing in Applied Probability; 2022.
Available:https://doi.org/10.1007/s11009-022-09971-0
MacDonald IL, Zucchini W. Hidden Markov and other models for discrete-valued time series. London:Chapman & Hall; 1997.
Rabiner LR. A tutorial on hidden Markov model and selected applications in speech recognition. Proceedings of the IEEE. 1989;77(2):257–86.
DOI: 10.1109/5.18626
Bartholomew DJ. Stochastic models for social processes. 3rd ed. Chichester: Wiley; 1982.
Perneger TV. How to use likelihood ratios to interpret evidence from randomized trials. Journal of Clinical Epidemiology. 2021;136:235-242.
DOI: https://doi.org/10.1016/j.jclinepi.2021.04.010
De Rochemonteix M, Napolioni V, Sanyal N, Belloy ME, Caporaso NE, Landi MT, et al. A likelihood ratio test for gene-environment interaction based on the trend effect of genotype under an additive risk model using the gene-environment independence assumption. American Journal of Epidemiology. 2021;190 (1):129–141.
Available:https://doi.org/10.1093/aje/kwaa132
Portet S. A primer on model selection using the Akaike Information Criterion. Infectious Disease Modelling. 2020;5:111-128.
DOI: 10.1016/j.idm.2019.12.010