Project

Non-traditional regression models in transport modelling

Goal: The project is devoted to developing of non-traditional regression models, namely Markov-modulated linear regression for analysis of traffic flow and adjacent transport tasks and find algorithms for their parameter estimation for big data

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Project log

Nadezda Spiridovska
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Participated in the conference
10th International Workshop on Simulation and Statistics, 2 – 6 September 2019, Salzburg, Austria.
 
Nadezda Spiridovska
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Abstract
Markov-modulated linear regression was firstly proposed by professor Alexander Andronov. This model is a special case of the Markov additive process (Y, J), where component J is called Markov, and component Y is additive and described by a linear regression. The component J is a continuous-time homogeneous irreducible Markov chain with the known transition intensities between the states. Usually this Markov component is called the external environment or background process. Unknown regression coefficients depend on external environment state, but regressors remain constant.
This research considers the case, when the Markov property is not satisfied, namely, the sojourn time in each state is not exponentially distributed. Estimation procedure for unknown model parameters is described when it’s possible to represent transition intensities as a convolution of exponential densities [3].
An efficiency of such an approach is evaluated by a simulation.
Acknowledgement: this work is funded by the post-doctoral research aid programme of the Republic of Latvia (No. 1.1.1.2/VIAA/1/16/075).
 
Nadezda Spiridovska
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First version of R package named MMLR is published on CRAN.
Description: A set of tools for fitting Markov-modulated linear regression, where responses Y(t) are time-additive, and model operates in the external environment, which is described as a continuous time Markov chain with finite state space. Model is proposed by Alexander Andronov (2012) <arXiv:1901.09600v1> algorithm of parameters estimation is based on eigenvalues and eigenvectors decomposition. Also, package will provide (now is not available) a set of data simulation tools for Markov-modulated linear regression (for academical/research purposes).
Work continues on increasing the number of features and the package expanding.
References
Andronov, A., Spiridovska, N. Markov-Modulated Linear Regression.
In proceedings’ book: International conference on Statistical Models and Methods for Reliability and Survival Analysis and Their Validation (S2MRSA),
2012, pp.24–28. Bordeaux, France (arXiv:1901.09600v1)
Andronov A. Parameter statistical estimates of Markov-modulated linear regression,
in: Statistical Methods of Parameter Estimation and Hypothesis Testing 24, Perm State University, Perm, Russia, 2012, pp. 163–180. (Russian).
Acknowledgement
This work was financially supported by the specific support objective activity 1.1.1.2. “Post-doctoral Research Aid” (Project id. N. 1.1.1.2/16/I/001) of the Republic of Latvia, funded by the European Regional Development Fund. Nadezda Spiridovska research project No. 1.1.1.2/VIAA/1/16/075 “Non-traditional regression models in transport modelling”.
 
Nadezda Spiridovska
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Abstract titled "Public Transport Passenger Flow Analysis and Prediction using Alternating Markov-Modulated Linear Regression" by Nadezda Spiridovska and Irina Yatskiv .
 
Nadezda Spiridovska
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Abstract named " On a parametrical estimation for a convolution of exponential densities" Alexander Andronov , Diana Santalova.
Broad application of the continuous time Markov chain is caused by exponential distribution properties. The usage of non-exponential distributions lead to considerable analytical difficulties. It is temptingly a using an approximation of arbitrary non-negative density by a convolution of exponential densities.
Two aspects of the problem are considered. Firstly, an approximation of fixed non-negative density. Secondly, the parametrical estimation of the convolution on the basis of given statistical data.
Different approaches to such approximation and estimation are considered: the method of the moments, maximum likelihood method, using of Laplace transform of the density. The latter is the least known approach and it proved one’s worth as applicable method in the paper [3]. An empirical analysis of different approach has been performed using the simulation.
The efficiency of the considered approach is illustrated by the task of the queuing theory.
Nadezda Spiridovska research project No. 1.1.1.2/VIAA/1/16/075.
 
Nadezda Spiridovska
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Thanks to the project (No. 1.1.1.2/VIAA/1/16/075 ), I improve my language skills as well.
 
Nadezda Spiridovska
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Participating in the 4th Conference on Sustainable Urban Mobility (CSUM2018). Excellent organization, hospitable people. Gathering new ideas for my research, sharing knowledge. (Project no.1.1.1.2/VIAA/1/16/075 funded by ERDF.)
 
Nadezda Spiridovska
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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.
Nadezda Spiridovska
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The project is devoted to developing of non-traditional regression models, namely Markov-modulated linear regression for analysis of traffic flow and adjacent transport tasks and find algorithms for their parameter estimation for big data