Estimation of the Von Bertalanffy growth model when ages are measured with error

The Von Bertalanffy (VB) growth function specifies the length of a fish as a function of its age. However, in practice, age is measured with error which introduces problems when estimating the VB model parameters. We study the structural errors-in-variables (SEV) approach to account for measurement error in age. In practice the gamma distribution is often used for unobserved true ages in the SEV approach. We investigate whether SEV VB parameter estimators are robust to the gamma approximation of the distribution of true ages. By robust we mean a lack of bias due to measurement error and model misspecification. Our results demonstrate that this method is not robust. We propose a flexible parametric normal mixture distribution for the true ages to reduce this bias. We investigate the performance of this approach through extensive simulation studies and a published data set. Computer code to implement the model is provided.