Monte Carlo evaluation of a nonlinear regression estimator for aggregated length–weight data

Abstract

Parameters of fish length–weight relationships (W = aLb) are usually estimated by applying linear regression to log-transformed length and weight values, but measuring individual weights is time-consuming and expensive. Often, length and weight data are available as sets of length measurements and aggregated sample weights, and the aggregate average weight of a sample can be expressed as the average of the weights predicted for the individual fish lengths. This study evaluated the feasibility of applying nonlinear regression to aggregated length–weight data. Experiments with simulated random length–weight data demonstrated that the estimates of parameter b appear to be unbiased and the estimates of a are right-skewed and biased. Further, the estimates of ln(a) and b are almost perfectly correlated. The precision and accuracy of the estimates were greatly influenced by the number of aggregate samples but were relatively unaffected by the number of fish in each sample. An additional experiment showed that the residuals from the regression can be used to detect small changes in the length–weight parameters.