Mcperturb: A New 5-step Multicollinearity Diagnostic Method Developed Based on Existing Methods

The ordinary least squares method is used to estimate unknown parameters of a multiple linear regression (MLR) model. This method produces an idealistic solution if regressors (X column vectors) are linearly independent. In an MLR model, multicollinearity arises when two or more regressors depart from linear independence, thus, providing the model with redundant information and causing problems in the MLR parameter estimation. The degree of multicollinearity directly reflects the amount of redundancy and interdependence among regressors and affects the inaccuracy of the MLR inference. Several detection methods exist and are commonly used to diagnose multicollinearity. These diagnostic methods often produce a measure that reflects the degree of multicollinearity present in the overall model or among individual regressors. However, these diagnostic methods generally fail to break down complex multicollinearity relationships among the regressors. There is also a lack of a methodology that combines perturbation analysis with the available diagnostic measures. In addition, several observational strategies are often overlooked and underutilized for diagnosing multicollinearity. Therefore, we develop a new method using R, mcperturb, based on existing methods and publicly available body dimension data. The mcperturb encompasses several multicollinearity observational strategies and employs a new 5-step perturbation-based approach. This method can identify the regressors that may be the main source of the multicollinearity problem. The output files from the mcperturb method provide a comprehendible opportunity to observe the relatedness between two or more variables at a deeper level than the currently available multicollinearity diagnostic methods.