Efficiency and bias of estimators and sampling designs for determining length-weight relationships of fish

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Abstract
The parameters of the allometric equation used to describe the length–weight relationship in fish are usually estimated by linear regression of log-transformed data. Simulation of length–weight regressions showed that for sample sizes commonly encountered in fisheries research, estimates of the intercept are biased high. In contrast with this, estimates of mean weight-at-length are biased low. As a result, different bias-correction factors are necessary to adjust for transformation bias. When the objective is to estimate the intercept of the length–weight equation, two existing methods correct for transformation bias. The appropriate bias-correction factor for mean weight-at-length, however, is exp(σ2/2) where σ2is the residual variance of the regression. As an alternative to the log-transformation method, the properties of nonlinear least-squares regression were explored. Estimates obtained with nonlinear regression are less efficient, but are relatively robust to departures from the assumed error structure. Simulation of several sampling designs showed that greater precision without loss of accuracy is obtained as subsampling is concentrated toward the extremes of the length distribution.

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