Added variable plots for linear regression with censored data

Abstract

In linear regression the structure of the hat matrix plays an important part in regression diagnostics. In this note we investigate the properties of the hat matrix for regression with censored responses in the presence of one or more explanatory variables observed without censoring. The censored points in the scatterplot are renovated to positions had they been observed without censoring in a renovation process based on Buckley-James censored regression estimators. This allows natural links to be established with the structure of ordinary least squares estimators. In particular, we show that the renovated hat matrix may be partitioned in a manner which assists in deciding whether further explanatory variables should be added to the linear model. The added variable plot for regression with censored data is developed as a diagnostic tool for this decision process.