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

The Measurement Error Model (MEM) is employed tot fithe relationship between two or more variables when all variables are subject to measurement errors. In thespecific case of only two variables, this model isreferred to as the Error in Variables model. This paper proposes wot new estimation methods for a multiple struct ural measurement error model, applicable when all variables are subject to errors. The proposed methods,e thRepetitive Weighted Grouping and the Iterative Weighted Grouping, are extensions of the Wald estimation methodo. T 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. eTh simulation results showed that the proposed estimators outperform the classical estimators in terms rootf mean square error and bias. Additionally, real data analysis was performed to assess the relationships betwen national GDP, unemployment rate, and human development indexusing the proposed estimation methods. The resultsreveal that, based on mean square error (MSE), the proposed methods with r =3 and r =4 yield more accurate esimators 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 eategr efficient than MLE and MOM in fitting the model.