Robust Regression - Example: BUPA Liver Data

Example: BUPA Liver Data

The BUPA liver data have been studied by various authors, including Breiman (2001). The data can be found via the classic data sets page and there is some discussion in the article on the Box-Cox transformation. A plot of the logs of ALT versus the logs of γGT appears below. The two regression lines are those estimated by ordinary least squares (OLS) and by robust MM-estimation. The analysis was performed in R using software made available by Venables and Ripley (2002).

The two regression lines appear to be very similar (and this is not unusual in a data set of this size). However, the advantage of the robust approach comes to light when the estimates of residual scale are considered. For ordinary least squares, the estimate of scale is 0.420, compared to 0.373 for the robust method. Thus, the relative efficiency of ordinary least squares to MM-estimation in this example is 1.266. This inefficiency leads to loss of power in hypothesis tests, and to unnecessarily wide confidence intervals on estimated parameters.