Automated Path Tracing for General Linear Models

Abstract

Monte Carlo simulations in statistics are computer experiments involving random sampling from known probability distributions to study properties of statistical methods. As the relations among variables become increasingly complex, the method of generating data under imposed model and distributional conditions becomes progressively more complicated. In this article, we algebraically derive a kernel for calculating direct causal effects in a path model for the univariate general linear model (GLM), specifically discussing regression models and extensions such as analysis of variance. A rationale is provided for decisions made for dealing with multiple unknown parameters and predictor correlation, where all unknown parameters are assumed to be equal. Separate from the methodological value is the real world application involving solving for a full correlation matrix, sample size, and power analysis in a GLM framework.