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A STUDY ON MULTICOLLINEARITY DIAGNOSTICS AND A FEW LINEAR ESTIMATORS
Keywords:
Adjust operator, generalized inverse, linear models, Moore Penrose inverse, multicollinearity, Sweep operator.DOI:
https://doi.org/10.17654/0972361723050Abstract
In this paper, the studies done by Goodnight [1] and Wetherill et al. [2] on Adjust operator and Sweep operator are revisited. The operators considered by the authors have been reinvented so as to exploit the operators in retrieving information about nature of correlation between regressors and all the persisting near linear dependencies among the regressors in a linear regression model. Thus, an effective and all encompassing multicollinearity diagnostic technique has been developed. The proposed diagnostic technique is illustrated in a live data followed by implementation of some estimation procedures in linear regression. A generalized inverse proposed by Goodnight [1] is studied with a view to using it in linear regression analysis in the data in which persisting multicollinearity conditions, diagnosed by the proposed diagnostic technique, are taken into account. Similarly, a pseudo inverse is also constructed using singular value decomposition (SVD) and then used it in linear regression in the data. The results of the linear estimation procedures are discussed comparatively with a reference to ordinary least squares (OLS) technique. The paper has shown why an effective and comprehensive diagnostic technique is a prerequisite to suitable and efficacious estimation procedure.
Received: June 25, 2023
Accepted: August 2, 2023
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