Sensitivity to model misspecification of the Von Bertanlanffy grown model with measurement error in age

Abstract

The Von Bertalanffy growth function (VonB) specifies the length of a fish as a function of its age. However, in practice, age is measured with error. We study the structural errors-in-variables (SEV) approach to account for measurement error (ME) in age. Cope and Punt (2007) also proposed this approach for fish growth data. They assumed unobserved age had a simple Gamma distribution. In this study, we investigate whether SEV VonB parameter estimators are robust to the Gamma approximation of true unobserved ages. By robust we mean lack of bias due to ME and model misspecification. Our results demonstrate that this method is not robust. We propose a flexible parametric Normal mixture distribution for the unobserved true ages to reduce this bias when estimating the length-age relationship with a VonB model. We investigate the performance of this approach in comparison to the Gamma age model through extensive simulation studies and a real-life data set.