RRSARMMI: Ridge Regularization for Spatial Auto-Regressive Models with Multicollinearity Issues

This repository contains the code and data necessary to reproduce the results presented in the paper "Ridge Regularization for Spatial Auto-regressive Models with Multicollinearity Issues" submitted to Advances in Statistical Analysis (AStA).

Authors: Cristina Chavez-Chong, Cécile Hardouin, Ana Karina Fermin

Table of Contents

• Introduction
• Usage
• Folder Structure
• Data
• Scripts
• Reports
• License
• Contact

Introduction

In this repository, we provide the resources necessary to reproduce the analysis and results presented in our paper "Ridge Regularization for Spatial Auto-regressive Models with Multicollinearity Issues" submitted to Advances in Statistical Analysis (AStA). The project provides two main resources:

• Two examples of our numerical experiments (RRSAR and RRSEM algorithms).
• The reproduction of the analysis of a dataset about COVID-19 in metropolitan France.

Usage

The code in this repository was built in R version 3.6.2. To use the provided scripts and functions, follow these steps:

1. Clone this GitHub repository to your local machine using the following command:

   git clone https://github.com/c0ra/RRSAR.git

2. Install Required Packages: Navigate to the project directory and run the requirements.R script to install the required R packages. Use the following command in your R console or terminal:

   source("requirements.R")

   This will install all the necessary packages automatically.
3. Explore the Scripts and Data: Explore the contents of the repository, including R Markdown files, scripts, and data files, to reproduce the analyses or adapt them to your needs.
4. Run the R Markdown Reports: Open them in RStudio or any R Markdown compatible environment and follow the instructions within each report.

Folder Structure

The repository is organized as follows:

• /data: Contains the real dataset COVID-19.
• /scripts: Includes R scripts with functions to perform SFRR, RRSAR and RRSEM estimation methods.
• /reports: Contains R Markdown files that generate analysis reports and the .pdf files with full results of our numerical experiments.

Data

The covid_data.shp is a simple features file which contains 12 variables and a geometry column type Multi Polygon. The observations are collected from the 96 French départements, which are administrative units. The full meaning of the variables is in the appendix of our paper.

The variables are:

• Department: name of the French department.

• Region: name of the French region.

• LnHosp: logarithm of hospitalization rate.

• LnPop : logarithm of population density.

• SLivR : standard of living gap.

• C3 : percentage of inhabitants in the three largest cities of the department.

• Work : rate of workers.

• Inac : inactive rate.

• A65pls : share of people aged 65 and over.

• Emer : rate of emergency services per 1000 habitants.

• FDoc : rate of doctors per 1000 habitants.

• Urban: indicator of an urban department (vs rural).

Scripts

The repository includes three scripts:

• requirements.R: Includes the preliminary code needed to install the necessary libraries.
• functions_numerical_experiments.R: Includes the code for SFRR, RRSAR and RRSEM estimation procedures for the simulation study.
• functions_covid.R: Includes the code for SFRR, RRSAR and RRSEM estimation procedures in the context of the application.

The functions_* scripts are called in the main .Rmd files to run the SFRR, RRSAR and RRSEM estimation algorithms.

Reports

The reports folder contains .html files for generated in Rmarkdown and .pdf files with the full results that are summarised in our paper.

• covid_19_application.html: Exploratory analysis performed on the COVID-19 dataset, as well as to apply RRSAR and RRSEM methodology to estimate all the parameters and to assess the importance of the covariates on the COVID-19 intensity.
• example_simulation_estimation_sar.Rmd: Instructions to generate one simulation following the SAR model structure and to estimate the model coefficients using the OLS, SAR, Ridge regression, SFRR and RRSAR procedures.
• example_simulation_estimation_sar.html: Report with instructions to generate one simulation following the SAR model structure and to estimate the model coefficients using the OLS, SAR, Ridge regression, SFRR and RRSAR procedures.
• • example_simulation_estimation_sem.Rmd: Instructions to generate one simulation following the SEM model structure and to estimate the model coefficients using the OLS, SEM, Ridge regression, SFRR and RRSAR procedures.
• example_simulation_estimation_sem.html: Report with instructions to generate one simulation following the SEM model structure and to estimate the model coefficients using the OLS, SEM, Ridge regression, SFRR and RRSAR procedures.
• complete_results_sar.pdf: Full results of our simulation study with data generated following the SAR model.
• complete_results_sem.pdf: Full results of our simulation study with data generated following the SEM model.

To reproduce specific results, run the corresponding .Rmd file. Make sure to adjust file paths and settings as needed.

License

This project is licensed under the MIT License.

Contact

If you have any questions or need further information, please contact Cristina Chavez.