Data Analysis Repository

This repository contains scripts for performing two advanced statistical analysis techniques: Principal Component Analysis (PCA) and Non-Metric Multidimensional Scaling (MDS). Both techniques are used to reduce the dimensionality of data and to visualize relationships between variables or observations.

Table of Contents

• Introduction
• Principal Component Analysis (PCA)
• Non-Metric Multidimensional Scaling (MDS)
• Usage
• Dependencies
• Contributing
• License

Introduction

Dimensionality reduction techniques are essential tools in data analysis for simplifying complex datasets, improving visualization, and uncovering hidden patterns. This repository includes scripts for two widely used techniques:

1. Principal Component Analysis (PCA): PCA is a statistical technique that transforms a dataset into a set of linearly uncorrelated variables called principal components. These components capture the maximum variance in the data, allowing for dimensionality reduction while retaining most of the original information.

2. Non-Metric Multidimensional Scaling (MDS): MDS is a means of visualizing the level of similarity (or dissimilarity) of individual cases in a dataset. Non-metric MDS, in particular, preserves the rank order of the dissimilarities, making it useful for ordinal data.

Principal Component Analysis (PCA)

The pca_analysis.R script performs Principal Component Analysis on a dataset. The key steps involved in this script are:

1. Loading the Data: The script starts by loading the required packages and data. It ensures the data is in the appropriate format for PCA.

2. Data Transformation: The data is transformed from long to wide format, making it suitable for correlation analysis and PCA.

3. Handling Missing Data: Cases with missing values are dropped due to their small proportion relative to the total dataset, minimizing potential bias.

4. Correlation Matrix Calculation: A correlation matrix is calculated, excluding variables collected for descriptive purposes only.

5. PCA Construction: The script constructs the PCA model, checks the explained variance for each component, and visualizes this through a Scree plot and a Log Eigenvalue diagram.

6. Component Interpretation: The script visualizes the PCA results, including scatter plots and bar plots for participant scores on the principal components.

7. Biplot: Finally, a biplot is created to visualize the relationship between the first two principal components and the original variables.

Non-Metric Multidimensional Scaling (MDS)

The mds_analysis.R script performs Non-Metric Multidimensional Scaling on a dataset of country similarities. The key steps in this script include:

1. Loading Packages and Data: The script loads the necessary packages and the dataset for analysis.

2. Data Inspection: The dataset is checked for any coding mistakes, outliers, or missing values that could affect the analysis.

3. Similarity to Dissimilarity Conversion: The similarity data is converted into dissimilarities using the sim2diss function. This conversion is crucial for performing MDS.

4. MDS Execution: Non-Metric MDS is carried out using the isoMDS function. The stress value, an indicator of how well the MDS configuration represents the dissimilarities, is checked.

5. Visualization: The coordinates from the MDS analysis are plotted in a two-dimensional space, with additional visual aids such as vertical and horizontal reference lines.

6. Shepard Plot: A Shepard plot is generated to assess the goodness of fit, comparing the dissimilarities with the distances between points in the MDS configuration.

Usage

To run the analysis scripts:

1. Ensure that all dependencies are installed (see Dependencies below).
2. Load your dataset into the R environment.
3. Run the scripts in your R environment.

The PCA script expects a dataset formatted for PCA, while the MDS script expects a dataset of similarity measures between entities.

Dependencies

Both scripts require R and several R packages:

• tidyverse
• reshape2
• psych
• smacof
• MASS
• ggplot2
• gridExtra

Install the necessary packages using:

install.packages(c("tidyverse", "reshape2", "psych", "smacof", "MASS", "ggplot2", "gridExtra"))