Multivariate Linear Errors in Variables Regression: A simulation Study of Bisector Technique on Three-Dimensional Space

Abstract

The aim of this study is to compare the performances of Type I and Type II multivariate regression techniques via Monte Carlo simulation. The earlier studies on Type II regression are all based on simple linear regression because the computations of multivariate Type II regression are more complex. This study is completed with three variables by taking each of them as a dependent variable respectively and then bisectional plane of couple of two variables are calculated. As a result of simulation study performance of Type II regression found best in all scenarios of the data sets according to MSE criteria. It’s hard to meet all assumptions of classical regression in real life. Most of the studies about regression analysis are done under some theoretical backgrounds. In this study we mainly interested in the assumption of error term that is just because of the one independent variable. In practice all of the variables in a study may include some measurement errors. In these situations one must consider the importance of Type II regression analysis.