Generalized local influence with applications to fish stock cohort analysis

N. G. Cadigan and P. J. Farrell

Journal of the Royal Statistical Society Series C, 2002, vol. 51, issue 4, 469-483

Abstract: Summary. It is important to understand the influence of data and model assumptions on the results of a statistical analysis, and influence diagnostics are valuable tools for this. We consider local influence diagnostics for a statistical model that is fully parametric, and where estimation involves a fit function that is second order differentiable with respect to the parameters. Similarly to Cook, we study the local behaviour of influence graphs formed from perturbations to model components. However, the diagnostics that we develop are more general in that the type of model result that is used to assess influence is fairly arbitrary and must only be first order differentiable with respect to model parameters and the perturbations. This allows us to focus our influence analyses on important results, and to produce diagnostics that are meaningful to practitioners. The procedures that we propose are applied to sequential population analysis, a common method that is used to estimate the size of commercially exploited fish stocks. Our diagnostics reveal interesting patterns of influence that are not revealed by using Cook's likelihood displacement influence diagnostics. Our diagnostics lead to an increased understanding of how the data affect important estimates, and thereby provide information for assessing the potential effect of errors in model inputs. In addition, empirical comparisons illustrate that the local influence diagnostics proposed tend to provide a good description of global influence.

Date: 2002
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