Diagnostics to detect differences in Robust fits of linear models

How much do influential data points affect the resulting estimates? To which fitted values do they make a difference? We propose diagnostics which help answer these questions by measuring the difference in fits between a highly efficient estimate and a highly robust estimate. The diagnostics are intended to expose the critical few observations that make a difference in the analysis. Further analyses may depend on how much weight these points should have, after closer inspection by the investigator.