Solving Probabilistic Discrete Event Systems with Moore–Penrose Generalized Inverse Matrix Method to Extract Longitudinal Characteristics from Cross-Sectional Survey Data

Abstract

A novel probabilistic discrete event systems (PDES) model was established by the research group of Chen and Lin to quantify smoking behavior progression across multiple stages with cross-sectional survey data. Despite the success of the research, this PDES model requires extra some exogenous equations to be obtained and solved. However, exogenous equations are often difficult if not impossible to obtain. Even if additional exogenous equations are obtained, data used to generate such equations are often error-prone. We have found that Moore–Penrose (M–P) generalized inverse matrix theory can provide a powerful approach to solve an admissible linear-equation system when the inverse of the coefficient matrix does not exist. In this chapter, we report our work to systemize the PDES modeling in characterizing health risk behaviors with multiple progression stages. By applying the M–P theory, our research demonstrates that the PDES model can be solved without additional exogenous equations. Furthermore, the estimated results with this new approach are scientifically stronger than the original method. For practical application, we demonstrate the M–P Approach using the open-source R software with real data from 2000 National Survey of Drug Use and Health. The removal of the need of extra data enhances the feasibility of this novel and powerful PDES method in investigating human behaviors, particularly, health related behaviors for disease prevention and health promotion.