Weighted Grouping Estimation Method for Fitting Multiple Structural Regression Model when all Variables are Subject to Errors

Abstract

The Measurement Error Model (MEM) is employed to fit the relationship between two or more variables when all variables are subject to measurement errors. In the specific case of only two variables, this model is referred to as the Error in Variables model. This paper proposes two new estimation methods for a multiple structural measurement error model, applicable when all variables are subject to errors. The proposed methods, the Repetitive Weighted Grouping and the Iterative Weighted Grouping, are extensions of the Wald estimation method. To evaluate the performance of these new estimators compared to classical estimators-namely, the Maximum Likelihood Estimator (MLE) and the Method of Moments (MOM), a Monte Carlo experiment was conducted. The simulation results showed that the proposed estimators outperform the classical estimators in terms of root mean square error and bias. Additionally, real data analysis was performed to assess the relationships between national GDP, unemployment rate, and human development index using the proposed estimation methods. The results reveal that, based on mean square error (MSE), the proposed methods with r =3 and r =4 yield more accurate estimators than other methods in weight case 1, while the proposed method with r =4 proves more accurate in weight case 2. Furthermore, the proposed procedures demonstrate greater efficient than MLE and MOM in fitting the model.