Multivariate Linear Path Models

Path analysis is useful to explain the interrelationships among sets of observed variables in a causal chain. However, path analysis has been underutilized in health science and epidemiology research, because of its restrictive requirement of a complete causal ordering of variables. In order to solve this problem, we suggest the use of multivariate path models and derive a multivariate ”Calculus of Coefficients (COC)”, which results in a partitioning of the matrix of total effects into a sum of the matrix of direct effects and all matrices of indirect effects through intermediate outcome vectors. The multivariate COC derived in this study extends the classical univariate path model and associated results to the multivariate case, where vectors of outcome variables replace single variables in the causal chain. A general methodology for inferences is developed by utilizing bootstrap methods and union-intersection tests. The methods are applied to data from the Western New York Health Study to describe the direct and indirect effects of health behaviors such as diet, smoking, drinking, and exercise on an index of risk factors called the Cardio-Metabolic Risk Index (CMRI). With its less restrictive assumption on causal ordering and its simplicity of the method for general inferences , the suggested model can be a powerful tool for examining the interrelationship among quantitative variables from the types of studies commonly undertaken in epidemiology or health science research.