Addressing age measurement errors in fish growth estimation from length-stratified samples

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 sampling method. The data may contain age measurement errors (MEs). We propose a methodology that accounts for both LSAS and age MEs to accurately estimate fish growth. The proposed methods use empirical proportion likelihood methodology for LSAS and the structural errors in variables methodology for age MEs. 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 that is 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. Our simulation study shows that neglecting age MEs can lead to significant bias in growth estimation, even with small but non-negligible age MEs. However, our new approach performs well regardless of the magnitude of age MEs and accurately estimates SEs of parameter estimators. Real data analysis demonstrates the effectiveness of the proposed model validation device. Computer codes to implement the methodology are provided.