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A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling

Author

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  • J. Ronald Eastman

    (Clark Labs, Clark University, Worcester, MA 01610, USA)

  • Jiena He

    (Clark Labs, Clark University, Worcester, MA 01610, USA)

Abstract

Land change models commonly model the expected quantity of change as a Markov chain. Markov transition probabilities can be estimated by tabulating the relative frequency of change for all transitions between two dates. To estimate the appropriate transition probability matrix for any future date requires the determination of an annualized matrix through eigendecomposition followed by matrix powering. However, the technique yields multiple solutions, commonly with imaginary parts and negative transitions, and possibly with no non-negative real stochastic matrix solution. In addition, the computational burden of the procedure makes it infeasible for practical use with large problems. This paper describes a Regression-Based Markov (RBM) approximation technique based on quadratic regression of individual transitions that is shown to always yield stochastic matrices, with very low error characteristics. Using land cover data for the 48 conterminous US states, median errors in probability for the five states with the highest rates of transition were found to be less than 0.00001 and the maximum error of 0.006 was of the same order of magnitude experienced by the commonly used compromise of forcing small negative transitions estimated by eigendecomposition to 0. Additionally, the technique can solve land change modeling problems of any size with extremely high computational efficiency.

Suggested Citation

  • J. Ronald Eastman & Jiena He, 2020. "A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling," Land, MDPI, vol. 9(11), pages 1-12, October.
  • Handle: RePEc:gam:jlands:v:9:y:2020:i:11:p:407-:d:434501
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    References listed on IDEAS

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    1. Jagpreet Chhatwal & Suren Jayasuriya & Elamin H. Elbasha, 2016. "Changing Cycle Lengths in State-Transition Models," Medical Decision Making, , vol. 36(8), pages 952-964, November.
    2. Shigeaki F. Hasegawa & Takenori Takada, 2019. "Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics," Sustainability, MDPI, vol. 11(22), pages 1-11, November.
    3. Charlotte Shade & Peleg Kremer, 2019. "Predicting Land Use Changes in Philadelphia Following Green Infrastructure Policies," Land, MDPI, vol. 8(2), pages 1-19, February.
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    Cited by:

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    2. Jessica Strzempko & Robert Gilmore Pontius, 2023. "The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix," Land, MDPI, vol. 12(7), pages 1-18, July.
    3. Kiziridis, Diogenis A. & Mastrogianni, Anna & Pleniou, Magdalini & Tsiftsis, Spyros & Xystrakis, Fotios & Tsiripidis, Ioannis, 2023. "Improving the predictive performance of CLUE-S by extending demand to land transitions: The trans-CLUE-S model," Ecological Modelling, Elsevier, vol. 478(C).
    4. Diogenis A. Kiziridis & Anna Mastrogianni & Magdalini Pleniou & Spyros Tsiftsis & Fotios Xystrakis & Ioannis Tsiripidis, 2023. "Simulating Future Land Use and Cover of a Mediterranean Mountainous Area: The Effect of Socioeconomic Demands and Climatic Changes," Land, MDPI, vol. 12(1), pages 1-23, January.
    5. Luoman Pu & Jiuchun Yang & Lingxue Yu & Changsheng Xiong & Fengqin Yan & Yubo Zhang & Shuwen Zhang, 2021. "Simulating Land-Use Changes and Predicting Maize Potential Yields in Northeast China for 2050," IJERPH, MDPI, vol. 18(3), pages 1-21, January.

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