Identifying influential multinomial observations by perturbation

The assessment of the influence of individual observations on the outcome of the analysis by perturbation has received a lot of attention for situations in which the observations are independent and identically distributed. However, no methods based on minor perturbations for carrying out such assessments are available in the context of multinomial models. A simultaneous perturbation scheme for the cell probabilities is proposed that leads to the definition of some new diagnostic tools for identifying influential observations. It is shown that the diagnostics derived extend and complement those based on the case deletion approach. The new diagnostics are used to explain departures from certain multinomial log-linear model assumptions. These tools are also used to give insights into genetic data for paternity.