Markov-Modulated Linear Regression: Tasks and Challenges in Transport Modelling

Nadezda Spiridovska

In: Kabashkin I., Yatskiv I., Prentkovskis O. (eds) Reliability and Statistics in Transportation and Communication. RelStat 2017. Lecture Notes in Networks and Systems, vol 36. Springer, Cham
DOI: 10.1007/978-3-319-74454-4_21
: Transport modelling, Regression models,  Markov-Chain based models, Markov-Modulated linear regression,  External environment 

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Different models and modelling techniques are used in all four stages of the classical transport model. Regression models are widely used in two of them, i.e. in trip generation modelling and transport choice modelling (modal split). Still probabilistic-statistical models generally accept that parameters (regression coefficients in our case) of the model remain unchanged throughout the period of the process of viewing the model. However in practice these parameters usually changing randomly.

Markov-Modulated linear regression brings the idea that the regression model parameters do not remain constant throughout the period of model viewing, but vary randomly with the external environment, the impact of which is described by a Markov chain with continuous time and final state set. This assumption seems quite natural, because the “external environment” is a random in every day’s sense of this word.

This study attempts to identify the advantages and disadvantages of using Markov-modulated linear regression models exactly in transport modelling, comparing with classical regression models and stochastic Markov-chain based models as well. The research gives a vision of Markov-modulated linear regression model’s place in the transportation field, describing new tasks and challenges when facing to the different circumstances such as missing data or big data.