Multiple Factor Analysis (MFA)

Multiple factor analysis (MFA) weights each block of variables by the inverse of its first eigenvalue and then performs a global principal component analysis of the concatenated blocks.

다중요인분석(MFA)은 변수 블록마다 첫 고유값의 역수로 가중한 뒤, 이어 붙인 블록 전체에 주성분분석을 수행하는 기법입니다.

How can I analyze sensory, chemical and consumer measurements of the same products together without one block dominating?

같은 제품에 대한 관능, 화학, 소비자 측정치를 한 블록이 지배하지 않도록 함께 분석하려면 어떻게 하나요?

Multiple factor analysis balances several blocks of variables measured on the same individuals by dividing each block by its first eigenvalue, then finds common dimensions across all blocks. It reports the global factor map, the position of each block on the axes, partial points per block and RV and Lg coefficients that show how similar the blocks are.

When to use Multiple Factor Analysis (MFA)

• The same individuals are described by several groups of variables
• Blocks differ in size or variance and must be balanced
• You want to compare the structure of blocks with RV coefficients

When to use something else

• There is only one set of variables: use Principal Component Analysis
• Configurations come from several assessors on the same attributes and need rotation: use Generalized Procrustes Analysis (GPA)

Assumptions and requirements

• All blocks are measured on the same individuals (rows with missing values are dropped)
• Quantitative variables; standardized within block when scale is true
• Enough individuals relative to variables for stable axes

What the analysis reports

• Global eigenvalues and percentage of inertia
• Block weights (1 / first eigenvalue), block coordinates and contributions
• RV and Lg coefficients between blocks
• Partial points per block and the global factor map

How to report it

A multiple factor analysis of [J] blocks ([p] variables, N = [n]) yielded a first dimension with eigenvalue [value] ([value]% of inertia); the RV coefficient between [block A] and [block B] was [value].

Related methods

• Principal Component Analysis
• Generalized Procrustes Analysis (GPA)
• Canonical Correlation Analysis

Run Multiple Factor Analysis (MFA) on Quorant