Generalized local influence with applications to fish stock cohort analysis

• Published in: Applied statistics Vol. 51; no. 4; pp. 469 - 483
• Main Authors: Cadigan, N. G., Farrell, P. J.
• Format: Journal Article
• Language: English
• Published: Oxford, UK Blackwell Publishers 01.01.2002; Blackwell; Royal Statistical Society
• Series: Journal of the Royal Statistical Society Series C
• Subjects: Curvature; Exact sciences and technology; Fisheries; Global influence; Influence diagnostics; Influence graph; Linear inference, regression; Mathematical independent variables; Mathematics; Methodology; Modeling; Ocean fisheries; Parametric inference; Perturbation analysis; Population estimates; Population size; Probability and statistics; Regression analysis; Sciences and techniques of general use; Sequential methods; Sequential population analysis; Slope of a line; Statistical analysis; Statistical methods; Statistical models; Statistics; Parameter estimation; Statistical analysis; Error estimation; Parametric model; Perturbation; Statistical diagnostics; Jacobi matrix; Parametric estimation; Local influence; Influence diagram; Parametric method; Statistical regression; Sequential analysis; Sequential method; Statistical model; Influence; Population dynamics; Diagnosis; Likelihood function
• ISSN: 0035-9254; 1467-9876
• DOI: 10.1111/1467-9876.00281

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.