Understanding the Stack Overflow Post: Correlation Matrix Analysis with R

In this post, we’ll dive into a detailed explanation of how to analyze a correlation matrix using R. We’ll break down the code provided in the Stack Overflow question and explore each step in detail.

Introduction to Correlation Analysis

Correlation analysis is a statistical technique used to measure the relationship between two or more variables. In this case, we’re working with a correlation matrix generated from the adults dataset in R. The goal is to identify which pairs of variables have a strong correlation (i.e., a correlation coefficient greater than 0.2).

Step 1: Loading Required Libraries

To begin our analysis, we need to load the necessary libraries. In this case, we’re using RCurl for downloading the dataset and caret for data transformation.

# Load required libraries
library(RCurl)
library(caret)

Step 2: Downloading the Dataset

We start by downloading the adults dataset from the UCI Machine Learning Repository. We use the getURL function from RCurl to download the dataset and store it in a variable called x.

# Download the dataset
urlfile <- 'https://archive.ics.uci.edu/ml/machine-learning-databases/adult/adult.data'

x <- getURL(urlfile, ssl.verifypeer = FALSE)

Step 3: Reading and Processing the Dataset

Next, we read in the downloaded dataset using read.csv. We specify that the first row contains the header names.

# Read the dataset into a data frame
adults <- read.csv(textConnection(x), header = F)

We also change the header names to match the standard R naming convention.

# Change the header names
names(adults) <- c('Age', 'Workclass', 'FinalWeight', 'Education', 
                    'EducationNumber',
                    'MaritalStatus', 'Occupation', 'Relationship', 
                    'Race', 
                    'Sex', 'CapitalGain', 'CapitalLoss', 'HoursWeek', 
                    'NativeCountry', 'Income')

# Convert the Income column to binary (0 or 1)
adults$Income <- ifelse(adults$Income == '&lt;=50k', 0, 1)

# Transform categorical variables into numerical values
library(caret)
dmy <- dummyVars(" ~.", data = adults)
adultsTrsf <- data.frame(predict(dmy, newdata = adults))

# Check the dimension of the transformed dataset
dim(adultsTrsf)

Step 4: Creating a Correlation Matrix

We now calculate the correlation matrix using the cor function. We use the cor.prob function to generate a square matrix with row/column indices, correlation values, and p-values.

# Function to create a correlation matrix
cor.prob <- function(X, dfr = nrow(X) - 2) {
  R <- cor(X, use = "pairwise.complete.obs")
  above <- row(R) < col(R)
  r2 <- R[above]^2
  Fstat <- r2 * dfr / (1 - r2)
  R[above] <- 1 - pf(Fstat, 1, dfr)
  R[row(R) == col(R)] <- NA
  R
}

# Create a correlation matrix
cor.prob(adultsTrsf)

Step 5: Flattening the Correlation Matrix

We use the flattenSquareMatrix function to convert the correlation matrix into a square matrix with row/column indices, correlation values, and p-values.

# Function to flatten a square matrix
flattenSquareMatrix <- function(m) {
  if ((class(m) != "matrix") | (nrow(m) != ncol(m))) stop("Must be a square matrix.")
  if (!identical(rownames(m), colnames(m))) stop("Row and column names must be equal.")
  ut <- upper.tri(m)
  data.frame(i = rownames(m)[row(m)[ut]],
             j = rownames(m)[col(m)[ut]],
             cor = t(m)[ut])
}

# Flatten the correlation matrix
corMasterList <- flattenSquareMatrix(cor.prob(adultsTrsf))

Step 6: Ordering the Correlation Matrix

We sort the correlation matrix in descending order of absolute correlation values.

# Order the correlation matrix by absolute correlation value
corList <- corMasterList[order(-abs(corList$cor)),]

Step 7: Selecting Variables with High Correlation

Finally, we select variables with a high correlation (i.e., a correlation coefficient greater than 0.2) and assign them to the selectedSub variable.

# Select variables with high correlation
selectedSub <- subset(corList, (abs(cor) > 0.2 & j == 'Income'))

Conclusion

In this post, we’ve walked through a step-by-step analysis of a correlation matrix using R. We’ve discussed each component of the code and provided explanations for how to interpret the results. By following these steps, you should now be able to analyze your own correlation matrices and identify variables with high correlations.

Last modified on 2023-07-12