Use of a Log-Linear Model with the EM Algorithm to Correct Estimates of Stock Composition and to Convert Length to Age

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Abstract
The EM (expectation‐maximization) algorithm was used to develop a general procedure for finding maximum likelihood estimates of population proportions when some observations cannot be assigned unambiguously to a population category. The method can be used to estimate the age composition of fish from length frequencies, to adjust biased estimates of age composition (e.g., scale ages that tend to be too low), and to correct biased estimates of unit stock composition. To implement the method, two samples are obtained. In the first sample, the items are cross‐classified by their actual identity and by a second (possibly error‐prone) surrogate classifying variable. In the second sample, the items are classified by only the surrogate variable. The information in the two samples is then used to estimate the population proportions in the second sample.

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