Research Document - 2003/057

Local Influence Diagnostics for the Retrospective Problem in Sequential Population Analysis

By Cadigan, N.G. and Farrell, P.J.

Abstract

The retrospective problem involves systematic differences in sequential population analysis (SPA) estimates of stock size or some other quantity in a reference year. The differences occur as successively more data are used for estimation, and appear to be structural biases that result from a mis-specification of  the SPA. In some cases the retrospective problem is so severe that the SPA is considered to be too unreliable for stock assessment purposes. This was the case in the 2002 assessment of the fall spawning herring stock in the southern Gulf of St. Lawrence (4T fall herring; see LeBlanc, MacDougall, and Poirier, 2002). There are many possible causes of retrospective patterns, and it is usually difficult in practice to determine which causes are more likely. In this paper we show how to use local influence diagnostics to investigate whether small changes or perturbations to SPA input components such as catches or natural mortalities can remove or reduce retrospective patterns. The plausibility of the perturbations can be used to assess the likelihood that the component is the source of the retrospective pattern. We apply these local influence diagnostics to the 4T fall herring SPA. We show that reasonable changes in the SPA assumption about the relationship between catch per unit effort (CPUE)and stock size is a plausible source of the retrospective pattern. Catches, natural mortality assumptions, or the weighting of SPA residuals in estimation appear to be less plausible sources of the retrospective patterns.

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