Understanding market characteristics from aggregated brand switching data by the method of spectral decomposition

Abstract

This paper discusses a technique called spectral decomposition which can be effectively used to gain insights into interbrand/product competition. The technique is based on singular value decomposition of a transition matrix. If the assumption of stationary first-order Markov process is made for brand switching, the first component of the spectral decomposition gives us the steady state solution and the magnitude of the second eigenvalue determines the speed at which the steady state solution is reached. This technique is compared to a more popular technique, correspondence analysis. The results show that spectral decomposition provides similar insights as correspondence analysis, but has the additional advantage of providing a clue to the time required to reach steady state equilibrium. This information could be important when a new brand is launched.