Approaches to Weighting Data Components and Addressing Concerns about Density-Dependent Catchability for Lake Erie Percid Assessments

I discuss the current approach to setting weighting factors (lambdas) for different types of information that contribute to the objective function when estimating parameters for Lake Erie percid stock assessments, and a suggested modification based on information indicating that catchability may be density dependent. This white paper was prepared in response to concerns that density dependent changes in catchability could invalidate the current approach for setting lambdas. I suspect changes in catchability are a real issue because the catchability and selectivity blocks are relatively long (all years since 1990 are in one block), but want to stress that density dependent catchability is only a big problem if the changes in catchability are not captured by changes in catchability among time blocks. My understanding of the current approach, based on previous examinations of code and recent discussions with Andy Cook, is that lambdas are set for “effort deviations” prior to the assessment and then relative values of the lambdas within other data types (harvest-at-age or survey indices-at-age) are determined by iteratively changing lambdas until the residual variability is consistent with that assumed by the lambdas. The “best” component within a type is given a lambda of 1.0, the same as the highest effort lambda. I argue that the approach I think is being used to set the relative lambda values for effort components is problematic, even if the underlying assessment assumptions about the relationship between fishing mortality and fishing effort are correct. The iterative approach is reasonable, but setting the best component of each type to 1.0 makes strong assumptions about the relative quality of effort, harvest, and survey information. I argue that a more involved iterative procedure that takes into account prior knowledge about data variability should be considered. I also argue that if there is evidence of density dependent catchability that is not captured by catchability time blocks, then down-weighting effort components is a reasonable response in the context of the current assessment model. However, the presence of such density dependence is not the only consideration for setting effort lambdas, and as an (perhaps longer term) alternative I recommend considering changes to the assessment model so that it can better allow for gradual changes in catchability. I provide some suggestions on how to estimate an overall beta for the power relationship between fishery catch rates and abundance indices, keeping in mind the use of catchability blocks in the assessments. Discussion of the current approach Estimation context and the scope of these comments The primary topic addressed in these comments is how “lambda” values, weighting different components of the objective function used in Lake Erie percid assessessment, should be determined. I specifically address questions of how the lambdas should be altered when there is evidence that fishery catchability is density dependent. As a basis for what follows, this subsection describes the estimation approach used in the percid assessments and why the current method used to specify lambda values is an issue. The stock assessment approach used for Lake Erie percids follows a standard catch-at-age modeling approach adapted from the CAGEAN program developed by Deriso, Quinn, and colleagues. This approach estimates the assessment parameters by minimizing a sum of squares objective function using AD Model Builder software. For the purposes of statistical inference, this has been equated with a likelihood based approach, with assumed lognormal distributions for data. In this context two different variants of the objective functions have been used. The first follows a “concentrated likelihood” approach and the “negative concentrated likelihood” (with additive constants dropped) minimized by AD Model builder is: ) ln( 2 log RSS k L conc = − and the second is a full “negative log likelihood” (again with additive constants dropped): RSS k LogL 2 2 1 ) ln( σ σ + = − These two forms are based on identical assumptions and lead to identical point estimates and asymptotic standard errors for the parameters. In both cases RSS represents the weighted residual sum of squares over components making up the objective function: