Construction of a System Dynamics Model by Principal Component Analysis

In the present paper we present a method of constructing a system dynamics model. When multiple variables are given, we sum them up by principal component analysis. By utilizing the extracted principal components we construct simultaneous differential equations concerning the original variables. Our method has two characteristics. First, usual factor analysis, etc., are restricted to the estimation of the causality between the latent variables and the original variables on their functional relations. Our method can explain dynamic mutual effects among the original variables. Second, contrary to the usual constructions of system dynamics models, our method does not require to give a priori the latent variable (i.e., it is time in usual system dynamics models.) and minimizes subjective judgemrnt in determining the parameters of the model. In the latter half of the paper we give an example of an application of our method to actual data and discuss the implications of the model given by the interpretation of the obtained simultaneous differential equations.