Accounting for age measurement errors in fish growth model estimation using length-stratified age sampling data

Fish growth models are crucial for fisheries stock assessments and are commonly estimated using fish length-at-age data. This data is widely collected using length-stratified age sampling (LSAS), a cost-effective two-phase response-selective method. The data may contain age measurement errors. We propose a methodology that remarkably reduces the bias in the estimation of fish growth for LSAS data with age measurement errors. The proposed methods use empirical proportion likelihood methodology for LSAS and the structural errors in variables methodology for age measurement errors. We provide a measure of uncertainty for parameter estimates and standardized residuals for model validation. To model the age distribution, we employ a continuation ratio-logit model consistent with the random nature of the true age distribution. We also apply a discretization approach for age and length distributions, which significantly improves computational efficiency and is consistent with the discrete age and length data typically encountered in practice. The simulation study shows that neglecting age measurement errors can lead to significant bias in growth estimation, even with small but nonnegligible age measurement errors. However, our new approach performs well regardless of the magnitude of age measurement errors and accurately estimates standard errors of parameter estimates. Real data analysis demonstrates the effectiveness of the proposed model validation device. Computer codes to implement the methodology are provided.