A Review of Graphical Approaches to Common Statistical Analyses: The Omnipresence of Latent Variables in Statistics

We provide a comprehensive review of simple and advanced statistical analyses using an intuitive visual approach explicitly modeling Latent Variables (LV). This method can better illuminate what is assumed in each analytical method and what is actually estimated, by translating the causal relationships embedded in the graphical models in equation form. We recommend the graphical display rooted in the century old path analysis, that details all parameters of each statistical model, and suggest labeling that clarifies what is given vs. what is estimated. We link in the process classical and modern analyses under the encompassing broader umbrella of Generalized Latent Variable Modeling, and demonstrate that LVs are omnipresent in all statistical approaches, yet until directly 'seeing' them in visual graphical displays, they are unnecessarily overlooked. The advantages of directly modeling LVs are shown with examples of analyses from the ActiveS intervention designed to increase physical activity.