The Flow Matrix Offers a Straightforward Alternative to the Problematic Markov Matrix

The Flow matrix is a novel method to describe and extrapolate transitions among categories. extrapolates constant transition size per unit of time on continuum with maximum one incident observation during the extrapolation. linearly until persistence category shrinks zero. has concepts mathematics that are more straightforward than Markov matrix. However, many scientists apply by default because popular software packages offer no alternative matrix, despite conceptual mathematical challenges poses. proportion interval whole-number multiples duration calibration interval. extrapolation allows at most each but repeated incidents through sequential intervals. Many extrapolations approach steady state asymptotically as approaches constant. We use case studies concerning land change illustrate characteristics matrices. both deviate from reference data validation interval, implying there reason prefer other in terms correspondence processes we analyzed. two matrices differ substantially their underlying behaviors. Scientists should consider ease interpretation for when extrapolating