The Use of Modern Robust Regression Analysis with Graphics: An Example from Marketing

M. Riani

{}^{1}

A.C. Atkinson

{}^{2}

G. Morelli

{}^{3}

A. Corbellini

{}^{4}

${}^{1}$

Department of Economics and Management, University of Parma, Parma, Italy [mriani@unipr.it]
${}^{2}$

The London School of Economics, London WC2A 2AE, UK [a.c.atkinson@lse.ac.uk]
${}^{3}$

Department of Economics and Management, University of Parma, Parma, Italy [gianluca.morelli@unipr.it]
${}^{4}$

Department of Economics and Management, University of Parma, Parma, Italy [aldo.corbellini@unipr.it]

Keywords: Box-Cox transformation – Generalized Additive Model (GAM) – Forward Search – AVAS

Some robust methods, such as least squares regression, may fail to capture certain features of the data. In this study, we collected data from 1171 consumers and then used graphical monitoring and modern robust statistical methods to determine loyalty determinants and find patterns in the dataset. This research aims to improve the model reliability and significantly enhance model interpretability through the use of Forward Search, robust transformations, and non-parametric adjustments. The work also presents some important features of the FSDA toolbox, which is freely available on GitHub.

References

Atkinson and Riani [2000] A. C. Atkinson and M. Riani. Robust Diagnostic Regression Analysis. Springer–Verlag, New York, 2000.
Rousseeuw and Leroy [1987] P. J. Rousseeuw and A. M. Leroy. Robust Regression and Outlier Detection. Wiley, New York, 1987.
Tibshirani [1988] R. Tibshirani. Estimating transformations for regression via additivity and variance stabilization. Journal of the American Statistical Association, 83:394–405, 1988.