Estimating discards conditional on landings and other factors

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Discards have historically been estimated using design based inference. Here we pursue a modelling approach using the data collected by the Scottish observer programme over the period 1980-2003. We assume that, on any trip, discarding either occurs or it doesn't, and when it does, the number of discards has a gamma distribution. This leads to a Bernoulli mixture of a degenerate distribution at zero and a gamma distribution, also known as a zero-inflated gamma. We use a two stage method involving generalized linear modelling at each stage to fit the zero-inflated gamma distribution with landings, gear, area fished, quarter (season) and year as explanatory variables. We fit this model to the numbers of haddock discarded at age 2 in ICES sub-area IV.