Overcoming Unidentifiability in Linear Functional Relationship Model Using Balanced Replicated Data

Abstract

This paper proposes a balanced replicated linear functional relationship model (LFRM) to overcome the unidentifiability issue present in the unreplicated LFRM, where both the predictor and response variables are measured with errors. In the unreplicated LFRM, parameter estimation relies on the restrictive assumption of a known ratio of error variances, denoted as . This study demonstrates that by transforming unreplicated data into balanced groups, all parameters namely the intercept, slope, incidental parameters, and two error variances, can be independently estimated using the Maximum Likelihood Estimation (MLE) method. A simulation study was conducted to evaluate the performance of the proposed model. To illustrate the practical application of the balanced replicated LFRM, a fat mass measurement dataset is used. The results demonstrate robustness, as the error variances are estimated without prior assumptions. This novel approach eliminates the need for  based assumptions, offering an unbiased and consistent solution for LFRM parameter estimation.