2015/03/09 by Brian Knaeble, Knaeble, Brian, Seth Dutter +1
Mathematics · #62-07 (Primary) #62J99 #93B35 (Secondary) #Advanced Statistical Methods and Models #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference
paper · pdf · doi:10.48550/arxiv.1503.02722
openalex publication_date 2015/03/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When a linear model is adjusted to control for additional explanatory variables the sign of a fitted coefficient may reverse. Here these reversals are studied using coefficients of determination. The resulting theory can be used to determine directions of unique effects in the presence of substantial model uncertainty. This process is called model-independent estimation when the estimates are invariant across changes to the model structure. When a single covariate is added, the reversal region can be understood geometrically as an elliptical cone of two nappes with an axis of symmetry relating to a best-possible condition for a reversal using a single coefficient of determination. When a set of covariates are added to a model with a single explanatory variable, model-independent estimation can be implemented using subject matter knowledge. More general theory with partial coefficients is applicable to analysis of large data sets. Applications are demonstrated with dietary health data from the United Nations. Necessary conditions for Simpson's paradox are derived.