Systemize the Probabilistic Discrete Event Systems with MoorepenroseGeneralized-inverse Matrix Theory for Cross-sectionalBehavioral Data

Journal of Biometrics & Biostatistics

article

Ding-Geng(Din) Chen¹  XinguangChen³  FengLin⁴  Y.L. Lio⁵  HarrietKitzman¹ 

[1] Center for Research, School of Nursing;Department of Biostatistics and Computational Biology, University of Rochester Medical Center;Department of Epideomiology, University of Florida;Department of Electrical and Computer Engineering, Wayne State University;Department of Mathematical Sciences, University of South Dakota

关键词: Discrete event systems;    Matrix inverse;    Moore-Penrose generalized inverse matrix;    Cross-sectional survey;    Longitudinal transition probability;   

DOI  :  10.4172/2155-6180.1000219

来源: Hilaris Publisher

【 摘 要 】

Moore-Penrose (M-P) generalized inverse matrix theory provides a powerful approach to solve an admissible linear-equation system when the inverse of the coefficient matrix does not exist. M-P matrix theory has been used in different areas to solve challenging research questions, including operations research, signal process, and system controls. In this study, we report our work to systemize a probability discrete event systems (PDES) modeling in characterizing the progression of health risk behaviors. A novel PDES model was devised by Lin and Chen to extract and investigate longitudinal properties of smoking multi-stage behavioral progression with cross-sectional survey data. Despite its success, this PDES model requires extra exogenous equations for the model to be solvable and practically implementable. However, exogenous equations are often difficult if not impossible to obtain. Even if the additional exogenous equations are derived, the data used to generate the equations are often error-prone. By applying the M-P theory, our research demonstrates that Lin and Chen’s PDES model can be solved without using exogenous equations. 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 extra data facilitate researchers to use the novel PDES method in examining human behaviors, particularly, health related behaviors for disease prevention and health promotion. Successful application of the M-P matrix theory in solving the PDES model suggests potentials of this method in system modeling to solve challenge problems for other medical and health related research.

【 授权许可】

Unknown