Multiple Correspondence Analysis (MCA) in R Studio: Full Code, Visualizations, and Interpretation

Learn how to perform Multiple Correspondence Analysis (MCA) in R Studio using full code, biplots, and categorical data. This in-depth tutorial is perfect for ecologists, biological scientists, and statisticians who want to explore multivariate relationships among categorical variables using one of the most intuitive methods—MCA.

What is Multiple Correspondence Analysis?

Multiple Correspondence Analysis (MCA) is an exploratory multivariate technique designed to analyze patterns in categorical data. It helps simplify large datasets with many categories by projecting them into fewer dimensions, allowing researchers to:

• Identify patterns among categories.
• Visualize associations among variables and individuals.
• Group similar observations based on categorical profiles.

Conceptual diagram explaining MCA (e.g., arrows showing category grouping)

Why Use MCA?

Key Advantages of MCA 

• Works exclusively with categorical variables.
• Detects latent structures in multidimensional data.
• Provides biplots that display both variables and individuals.
• Offers insights into which categories contribute most to the structure.

Common Use Cases 

• Ecology: Classifying species by environmental traits.
• Social Sciences: Survey data exploration.
• Healthcare: Patient profiling by categorical health attributes.

MCA vs PCA vs CA: What’s the Difference? 

Comparison Venn diagram of PCA, CA, and MCA

Installing Required R Packages 

Install the necessary libraries using the following commands

Code Block

install.packages("FactoMineR")

install.packages("factoextra")

These packages will allow you to perform MCA (FactoMineR) and create publication-quality visualizations (factoextra).

Loading Libraries in R

Once installed, load the libraries:

library(FactoMineR)

library(factoextra)

Pro Tip: Use suppressPackageStartupMessages() to avoid clutter in your R console.

Creating the Dataset for MCA 

We will simulate an ecological dataset of 10 plant species with attributes such as:

• Habitat
• Leaf Type
• Root System
• Flower Color
• Pollination

Sample Data

data <- data.frame(

  Species = c("Plant_A", "Plant_B", "Plant_C", "Plant_D", "Plant_E", 

              "Plant_F", "Plant_G", "Plant_H", "Plant_I", "Plant_J"),

  Habitat = c("Forest", "Grassland", "Wetland", "Desert", "Forest",

              "Grassland", "Wetland", "Desert", "Forest", "Grassland"),

  Leaf_Type = c("Broad", "Narrow", "Broad", "Needle", "Broad",

                "Narrow", "Broad", "Needle", "Broad", "Narrow"),

  Root_System = c("Taproot", "Fibrous", "Fibrous", "Taproot", "Fibrous",

                  "Fibrous", "Taproot", "Taproot", "Taproot", "Fibrous"),

  Flower_Color = c("White", "Yellow", "Purple", "White", "Yellow",

                   "Yellow", "Purple", "White", "Purple", "Yellow"),

  Pollination = c("Insect", "Wind", "Water", "Insect", "Wind",

                  "Insect", "Water", "Wind", "Insect", "Wind")

)

Preparing the Data for MCA

Step 1: Convert Categorical Variables

All categorical variables should be factors:

data[, 2:6] <- lapply(data[, 2:6], as.factor)

Step 2: Inspect the Structure

str(data)

Performing MCA in R Studio

We perform MCA excluding the Species column, which acts as an identifier (supplementary qualitative variable).

Code Block

mca_result <- MCA(data, quali.sup = 1, graph = FALSE)

• quali.sup = 1: Treats Species as supplementary.
• graph = FALSE: Suppresses the default plots.

Scree Plot: Eigenvalues of MCA Dimensions

Eigenvalues tell us how much variation is captured by each dimension. Create a scree plot:

fviz_screeplot(mca_result, addlabels = TRUE)

Coordinates of Individuals and Variables

 Individuals (Plants)

mca_result$ind$coord

These coordinates represent each plant species in reduced dimensional space.

Variables (Traits)

mca_result$var$coord

Biplot of MCA: Individuals + Variable Categories

Create a joint representation of plants and traits.

fviz_mca_biplot(

  mca_result,

  repel = TRUE,

  label = "all",

  ggtheme = theme_minimal(),

  title = "MCA Biplot of Plant Species and Traits"

)

Color-coded biplot with overlapping traits and species

 Analyzing Variable Contributions to Dimensions 

Top Contributors to Dimension 1

fviz_contrib(mca_result, choice = "var", axes = 1, top = 10)

Dimension 1

Top Contributors to Dimension 2

fviz_contrib(mca_result, choice = "var", axes = 2, top = 10)

Bar plots showing variable contribution to each dimension

Interpreting the Biplot

Summary & Key Insights

• MCA is a powerful visual technique for categorical data.
• Easy to implement using FactoMineR and factoextra.
• Produces intuitive plots and interpretable summaries.
• Helpful in any field dealing with complex category-based datasets.

Conclusion 

In this detailed guide, we explored how to run Multiple Correspondence Analysis (MCA) in R Studio, from:

• Creating and preparing datasets,
• Running the analysis using MCA(),
• Visualizing results using scree plots and biplots,
• Interpreting the significance of variables and their contributions.

Whether you're an ecologist, data analyst, or a student, MCA offers an intuitive path to understanding complex categorical data. Master it, and it will become a mainstay in your data analysis toolkit.