Resolving the Lord's Paradox

TL;DR

This paper clarifies Lord's paradox by demonstrating that it is not a paradox when regression parameters are correctly interpreted as predictive or causal under certain conditions, emphasizing the importance of residual modeling.

Contribution

It provides a novel explanation of Lord's paradox using regression models and introduces a method to derive super-models from sub-models based on residual analysis.

Findings

Lord's paradox is resolved through proper interpretation of regression parameters.

Residuals can be modeled with additional predictors to derive super-models.

The approach clarifies misconceptions about the paradox in statistical modeling.

Abstract

An explanation to Lord's paradox using ordinary least square regression models is given. It is not a paradox at all, if the regression parameters are interpreted as predictive or as causal with stricter conditions and be aware of laws of averages. We use derivation of a super-model from a given sub-model, when its residuals can be modelled with other potential predictors as a solution.