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

J. Ronald Eastman and Jiena He
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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

Land, 2020, vol. 9, issue 11, 1-12

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.

Keywords: Markov chain; land change model; transition probability; quadratic regression (search for similar items in EconPapers)
JEL-codes: Q15 Q2 Q24 Q28 Q5 R14 R52 (search for similar items in EconPapers)
Date: 2020
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (5)

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