Influence diagnostics in nonlinear regression

Research in nonlinear models has flourished significantly in recent years. One aspect that only recently has been studied is that of influence diagnostics, that is, the detection of observations that have an unduly large effect on the analysis (estimates, fitted values, etc.). Ross [1987] proposes influence measures that are based on the likelihood distance. In this thesis, measures equivalent to the well-known diagnostics DFFITS and DFBETAS [Belsley et al., 1980] are constructed for the nonlinear case. Unfortunately, the only way to obtain exact values for these diagnostics is to delete one observation at a time and refit the nonlinear model to the remaining data. Three approximations that require only one fit and some secondary calculations are explored, and their closeness to the "true" influence is analyzed by using some examples.