Distortion Diagnostics for Covariate-adjusted Regression: Graphical Techniques Based on Local Linear Modeling

Abstract: Linear regression models are often useful tools for exploring the relationship between a response and a set of explanatory (predictor) variables. When both the observed response and the predictor variables are contaminated/distorted by unknown functions of an observable confounder, inferring the underlying relationship between the latent (unobserved) variables is more challenging. Recently, S¸entürk and Müller (2005) proposed the method of covariate-adjusted regression (CAR) analysis for this distorted data setting. In this paper, we describe graphical techniques for assessing departures from or violations of specific assumptions regarding the type and form of the data distortion. The type of data distortion consists of multiplicative, additive or no-distortion. The form of the distortion encompasses a class of general smooth distorting functions. However, common confounding adjustment methods in regression analysis implicitly make distortion assumptions, such as assuming additive or multiplicative linear distortions. We illustrate graphical detection of departures from such assumptions on the distortion. The graphical diagnostic techniques are illustrated with numerical and real data examples. The proposed graphical assessment of distortion assumptions is feasible due to the CAR estimation method, which utilizes a local regression technique to estimate a set of transformed distorting functions (S¸entürk and Nguyen, 2006). Key words: Covariate-adjusted regression, distortion, graphical diagnostics, local regression modeling, multiplicative effect, varying-coefficient models. 472 D.V. Nguyen and and Damla S¸entürk 1