README.md

Chapter 8: Extensions of the Multiple Regression Model

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Atkinson,A.C., Riani,M., Corbellini,A., Perrotta D., and Todorov,V. (2024), "Applied Robust Statistics through the Monitoring Approach: Applications in Regression", Heidelberg: Springer Nature.

Abstract

The chapter explores five extensions to the regression model considered in earlier chapters. Section 8.1 introduces the use of prior knowledge in regression analysis, including the construction of prior distributions from fictitious observations. In section 8.2 Bayesian regression is combined with the FS. Section 8.3 provides analyses of successive annual sets of trade data, in which the prior distribution is updated annually. Heteroskedastic regression is introduced in section 8.4. The analysis of trade data makes clear the importance of avoiding models in which the variance goes to zero as $x$ does. Section 8.5 extends the analysis of trade data to data from several regression lines. The number of groups is estimated in section 8.5.2 from an FS which starts the search many times from random points. Regression clustering (section 8.5.3) involves the choice of parameters and, for robustness, a choice of trimming level. The monitoring approach in section 8.5.4 identifies solutions which do not depend on arbitrary choices of these hyper-parameters. The fourth extension, in section 8.6, is to use monitoring to provide a robust model for short term economic time series that may have strong annual trends. The final extension, in section 8.7, is to regression in which the explanatory variables are the components of a composition.

Code to reproduce Figures and Tables in this Chapter

For each chapter of the book we have given for each file the original source .m file and the corresponding .ipynb file. The .m file (after installing FSDA) can be run on your MATLAB desktop or in MATLAB Online (please see the button Open in MATLAB Online below). The .ipynb is given in order to show you the output of the code. In order to run the .ipynb files inside jupiter notebook follow the instructions in the file ipynbRunInstructions.md.

FileName	Description	Open in MATLAB on line	Jupiter notebook
comp_FishMorph.m	Fish Morphology data. This file creates Figures 8.36-8.39		[ipynb]
comp_ValueAdded_AddedT.m	Value added data: monitoring tstat This file creates Figure 8.34		[ipynb]
comp_ValueAdded_Ini.R	Value added data: tolerance ellipses and ternary diagrams This file creates Figure 8.33	Open
comp_ValueAdded_MMreg.R	Value added data: MM-regression This file creates Figure 8.35, Table 8.3 and Table 8.4	Open
facemasks.m	Facemasks data Facemasks: 352 imports of FFP2 and FFP3 masks (product 6307909810) into the European Union extracted in a day of November. This file creates Figures 8.19-8.20, 8.22, 8.26-8.29.		[ipynb]
facemasks_BIC.R	Facemask data: BIC traditional analsys This file creates Figures 8.24 and 8.25	Open
facemasksInteractive.m	Facemasks data: interactive part. This file creates Figures 8.21 and 8.23		[ipynb]
HousePrice.m	Windsor House Price data. This file creates Figures 8.1-8.7.		[ipynb]
InternationalTrade1.m	Heteroskedasticity: International Trade Data 2. This file creates Figures 8.12-8.15.		[ipynb]
InternationalTrade2.m	Heteroskedasticity: International Trade Data 2. This file creates Figures 8.16 and 8.18. File which creates Figure 8.17 is called InterenationalTrade2Interactive.m		[ipynb]
InternationalTrade2Interactive.m	Heteroskedasticity: International Trade Data 2 (interactive plot). This file creates Figure 8.17. File which creates Figures 8.16 and 8.18 is called InternationalTrade2.m		[ipynb]
timeseries_analysis.m	Robust monitoring of time series This file creates Figures 8.30-8.32.		[ipynb]
Lobster2002_2004.m	Lobster dataset years 2002-2004. This file creates Figures 8.8-8.11.		[ipynb]