A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling
Clark Labs, Clark University, Worcester, MA 01610, USA
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Land 2020, 9(11), 407; https://doi.org/10.3390/land9110407
Received: 9 September 2020 / Revised: 22 October 2020 / Accepted: 23 October 2020 / Published: 25 October 2020
(This article belongs to the Special Issue Land Change Modelling)
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.
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MDPI and ACS Style
Eastman, J.R.; He, J. A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling. Land 2020, 9, 407. https://doi.org/10.3390/land9110407
AMA Style
Eastman JR, He J. A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling. Land. 2020; 9(11):407. https://doi.org/10.3390/land9110407
Chicago/Turabian StyleEastman, J. R., and Jiena He. 2020. "A Regression-Based Procedure for Markov Transition Probability Estimation in Land Change Modeling" Land 9, no. 11: 407. https://doi.org/10.3390/land9110407
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