Rethinking OLS: Direct Estimation of Average First-Order Trends in the Conditional Mean Function

Music City Center 

A key to valid and reproducible inference is the use of a priori model specification. In such a framework, practitioners often specify simple regression models where most covariate effects are modeled linearly due to the desire for inference on estimands with simple interpretations. However, these simplified models are nearly guaranteed to be misspecified for the true model in which case standard interpretations of their parameters no longer hold. We therefore argue that this approach of starting with a model and defining target estimands from it is unideal. Instead, we advocate for starting with a model-robust estimand whose existence is based on minimal assumptions on the underlying data mechanism. As an alternative to OLS with linear covariate effects, we propose estimation of the average slopes in the conditional mean function as simple and interpretable first-order trends for summarizing continuous covariate effects. We propose a cubic B-spline-based estimator and give analytical and empirical results showing its effectiveness. We then apply our method to data from a recruitment registry for Alzheimer's disease clinical research and compare results to an OLS-based analysis.

Model-robust regression

Non-parametric regression

Robust statistical methods

Model misspecification 

WNAR