Statistical Models for the Analysis of Ageing Error

Abstract

We present statistical models for estimating the true age distribution of a population, based on multiple readings from individual fish. There are two steps to this process. The first involves estimating a classification matrix that defines the probability of assigning an age a to a fish when its true age is b. Since true age is unknown, we require an assumption related to ageing error bias; we assume that the true age is the most probable value for the observed age. True age proportions, or alternatively, true ages of fish in the sample are then estimated in the second step. Our methods allow us either to conduct both steps simultaneously or to estimate true age proportions from a previously estimated classification matrix. We illustrate our methods with data on walleye pollock (Theragra chalcogramma). We recommend that multiple independent readings be obtained for a subset of structures in future ageing studies and that ageing error be considered in subsequent analyses. Sample sizes must be increased with increasing ageing error to achieve a specified precision in estimates of true age proportions.