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

Abstract

Takada’s group developed a method for estimating the yearly transition matrix by calculating the mth 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.

Structural Changes in the Romanian Economy Reflected through Corine Land Cover Datasets

“…(6) The recent progress in the use of the transition probability matrix for assessing economic convergence phenomena [36] at different scales suggests that, when dealing with time-dependent anomalies of evolution, using this transition matrix approach is a sound way to investigate trends. As the land-use dynamics are not convergent on a steady state, implementing more sophisticated analysis, such as half-life indicators of the CLC categories, is not recommended because the possible Markov chains will not necessarily act in an ergodic state [37]. This is the reason why, in order to encompass as much as possible of the land-use dynamics, the CLC categories aggregated at pseudo-LAU1 scale were classified, for t 0 = 2006 and t 1 = 2018.…”

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

“…Finally, it should be emphasized that perhaps the most important feature of the RBM procedure is its simplicity and speed. As noted by [8], the TAM procedure is not feasible for problems with a large number of years and/or land cover classes. For example, our original intent was to use the NLCD data with 15 classes over 10 years.…”

“…For example, our original intent was to use the NLCD data with 15 classes over 10 years. Using the timing information provided by [8], it would take over 43 years to compute each of the annualized transition matrices. For the RBM procedure, it takes less than a second.…”

“…Takada et al [6] also indicate that it is possible that more than one stochastic annual transition matrix may be found, or indeed that none will be found. In a follow-up study, Hasegawa et al [8] found that only 11% of 62 cases examined produced stochastic matrices. However, they showed that by forcing small negative transitions to be 0, it was possible to increase this number to 87%.…”

“…That said, the biggest issue is the computational burden of the procedure used. Hasegawa et al [8] cite an example of solving a case with 10 classes over 24 years requiring over 1000 days for computation.…”