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Probability of Deriving a Yearly Transition Probability Matrix for Land-Use Dynamics

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  • Shigeaki F. Hasegawa

    (Institute of Low Temperature Science, Hokkaido University, N19W8, Kita-Ku, Sapporo 060-0819, Japan)

  • Takenori Takada

    (Faculty of Environmental Earth Science, Hokkaido University, N10W5, Kita-Ku, Sapporo 060-0810, Japan)

Abstract

Takada’s group developed a method for estimating the yearly transition matrix by calculating the m th power roots of a transition matrix with an interval of m years. However, the probability of obtaining a yearly transition matrix with real and positive elements is unknown. In this study, empirical verification based on transition matrices from previous land-use studies and Monte-Carlo simulations were conducted to estimate the probability of obtaining an appropriate yearly transition probability matrix. In 62 transition probability matrices of previous land-use studies, 54 (87%) could provide a positive or small-negative solution. For randomly generated matrices with differing sizes or power roots, the probability of obtaining a positive or small-negative solution is low. However, the probability is relatively large for matrices with large diagonal elements, exceeding 90% in most cases. These results indicate that Takada et al.’s method is a powerful tool for analyzing land-use dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jsusta:v:11:y:2019:i:22:p:6355-:d:286250
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    Cited by:

    1. 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.
    2. 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.
    3. René Ulloa-Espíndola & Jenny Cuyo-Cuyo & Elisa Lalama-Noboa, 2023. "Towards Rural Resilience: Assessing Future Spatial Urban Expansion and Population Growth in Quito as a Measure of Resilience," Land, MDPI, vol. 12(2), pages 1-30, January.
    4. Carlos Manjarrez-Domínguez & Mario Iván Uc-Campos & Mario Edgar Esparza-Vela & María del Rosario Baray-Guerrero & Omar Giner-Chávez & Eduardo Santellano-Estrada, 2023. "Geospatial-Temporal Dynamics of Land Use in the Juárez Valley: Urbanization and Displacement of Agriculture," Sustainability, MDPI, vol. 15(11), pages 1-20, May.

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