Analysis of Dermatological Symptoms, Credit Approval Data and Multi-Dimensional Poverty Measurement

Introduction

This repository contains R-code and data sets corresponding to the "Robust Statistical Comparison of Random Variables with Locally Varying Scale of Measurement" article written by C. Jansen, G. Schollmeyer, H. Blocher, J. Rodemann and T. Augustin. We apply the introduced tests on three examples: dermatological symptoms, credit approval data, and multi-dimensional poverty measurement.

The structure of the repository is as follows:

• File poverty_permutation_tests.R is a multi-dimensional poverty analysis.
• File credit_permutation_tests.R analyzes the credit approval data.
• File derma_permutation_tests.R analyzes the dermatological symptoms data.
• Folder R/ contains the needed functions (permutation test, sampling, definition of the constraint matrix etc) for the analysis.
• Folder data/ contains the data sets corresponding to the dermatological symptoms and credit approval data analysis. The data set used for the multi-dimensional poverty measurement is freely accessible, but only after registration at the following online portal (accessed: 08.02.2023). Please ensure that the downloaded data set is in data/ file.
• File _setup_session.R installs all (except for gurobi) needed R-packages.

The code was tested with

• R version 4.2.1
• R version 4.2.2

on

• Linux Ubuntu 20.04.5
• Windows 10

Setup

First, please install all necessary R-packages:

• For the computation of the linear programs, we used the R interface of gurobi optimizer, see here (accessed: 08.02.2023). This is a commercial solver that offers a free academic licenses which can be found here (accessed: 08.02.2023). To install this package, please follow the instructions there. A documentation can be found here (page 643ff) (accessed: 08.02.2023).
• Afterwards, please install all dependencies by sourcing the file _setup_session.R and source the files

Then download the following files and save them in a folder named 'R':

• constraints_r1_r2.R
• sample_permutation_test.R

Afterwards, please download the data sets and save them in a folder named 'data':

• dermatology.data
• credit.data
• the data set corresponding to the poverty analysis is freely accessible, but only after registration at the following online portal (accessed: 08.02.2023). Please download the file ZA5240_v2-2-0.sav (5.31MB) there.

In order to reproduce the papers' key results (and visualizations thereof) further download these scripts and save in respective folder:

• poverty_permutation_tests.R (estimated runtime: 4 days)
• credit_permutation_tests.R (estimated runtime: 4 days)
• derma_permutation_tests.R (estimated runtime: 4 days)

Running these three files sources the files in 'R/' and reproduces our result. Note that the folder 'R/', 'data/' and the three xxx_permutation_tests.R files must be in the same folder structure. Also make sure that the working directory of the R session links in the same folder.

References to the data sets:

• poverty analysis data: GESIS. Allgemeine Bevölkerungsumfrage der Sozialwissenschaften Allbus 2014. GESIS Datenarchiv, Köln. ZA5240 Datenfile Version 2.2.0, https://doi.org/10.4232/1.13141, 2018
• credit approval data: G Demiroz, HA Govenir, and N Ilter. Learning differential diagnosis of eryhemato-squamous diseases using voting feature intervals. Artificial Intelligence in Medicine, 13(3):147–165, 1998
• dermatological symptoms data: D. Dua and C. Graff. UCI machine learning repository, 2017. http://archive.ics.uci.edu/ml.