Analyzing the Application of Regression Diagnostics in Identifying Model Misspecification and Influential Observations

Posted: Apr 01, 2015

• Theodore Moore
• Sarah Young
• James Gonzalez

Abstract

Regression analysis remains one of the most widely used statistical techniques across scientific disciplines, from economics and social sciences to engineering and healthcare. The fundamental assumption underlying regression modeling is that the specified model adequately represents the true data-generating process. However, in practice, model misspecification represents a pervasive challenge that can lead to biased estimates, incorrect inferences, and ultimately flawed decision-making. Traditional regression diagnostics have provided valuable tools for detecting violations of model assumptions, but these methods often operate in isolation and may fail to capture complex patterns of misspecification in modern datasets characterized by high dimensionality, complex relationships, and heterogeneous structures. The identification of influential observations represents another critical aspect of regression diagnostics that has received substantial attention in the statistical literature. Influential observations, defined as data points that exert disproportionate impact on parameter estimates or model predictions, can dramatically alter analytical conclusions. While numerous influence measures have been developed, including Cook's distance, DFFITS, and DFBETAS, their application in complex modeling scenarios remains challenging due to interactions between influence and misspecification. This research addresses these challenges by developing an integrated diagnostic framework that simultaneously addresses model misspecification and influential observations. Our approach represents a significant departure from traditional diagnostic practices by incorporating machine learning techniques to enhance pattern recognition in diagnostic plots and developing novel composite measures that capture the interplay between specification errors and influential points.