Multiple Correspondence Analysis

Multiple correspondence analysis extends correspondence analysis to three or more categorical variables by analyzing the indicator matrix, mapping categories that co-occur across respondents close together.

다중대응분석은 지시행렬을 분석해 세 개 이상의 범주형 변수로 대응분석을 확장하며, 응답자들 사이에서 함께 나타나는 범주를 가까이 배치합니다.

I have ten multiple-choice survey questions; how can I find the main dimensions that structure the answer patterns?

객관식 설문 문항이 열 개 있는데, 응답 패턴을 구성하는 주요 차원을 어떻게 찾을 수 있나요?

Multiple correspondence analysis performs correspondence analysis on the respondents-by-categories indicator matrix and returns coordinates for every category on a few dimensions. Because the raw indicator inertias understate the importance of the dimensions, Benzécri-adjusted inertias expressed relative to Greenacre's adjusted total inertia are reported.

When to use Multiple Correspondence Analysis

• You have three or more nominal or ordinal survey variables.
• You want a map of how answer categories co-occur.
• You need a few continuous dimensions summarizing categorical responses for later analysis.

When to use something else

• Variables are continuous; use principal component analysis instead.
• Only two categorical variables are involved; use simple correspondence analysis instead.

Assumptions and requirements

• Observations are independent.
• Variables are categorical with a modest number of categories.
• Very rare categories are merged, since they dominate the map.

What the analysis reports

• Indicator-matrix principal inertias
• Benzécri-adjusted inertias and percentages of Greenacre's adjusted total inertia
• Category masses
• Category principal coordinates

How to report it

A multiple correspondence analysis of [Q] categorical variables ([J] categories, N = [n]) showed that the first two dimensions explained [value]% and [value]% of the adjusted inertia (Benzécri adjustment, Greenacre total).

Related methods

• Correspondence Analysis
• Principal Component Analysis (PCA)
• Latent Class Analysis (LCA)

Run Multiple Correspondence Analysis on Quorant