A macroscopic structure was analyzed for a system comprising multiple elements in which the dynamics is affected by their distribution. First, a nonlinear Boltzmann equation, which has an integration term with respect to the distribution of the elements, was derived. Next, the moment vector equation (MVE) for the Boltzmann equation was derived. The average probability density function (pdf) in a steady state was derived using eigen analysis of the coefficient matrix of the MVE. The macroscopic structure of the system and the mechanism that provides the average pdf and the transient response were then analyzed using eigen analysis. Evaluation of the average pdf and transient response showed that using eigen analysis is effective for analyzing not only the transient and stationary properties of the system but also the macroscopic structure and the mechanism providing the properties.