MFAanalyses

MFA analyses refer to analyses based on Multiple Factor Analysis (MFA), a multivariate exploratory technique that generalizes principal component analysis to data organized in separate blocks measured on the same set of individuals. MFA discovers common structure across blocks while respecting the grouping of variables, and it provides a global set of factors along with block-specific contributions.

In a typical MFA workflow, the data consist of an observation matrix and a collection of blocks, each containing variables that describe the same individuals. Variables within each block are standardized, and blocks are weighted to balance their influence in the global computation. A global analysis then extracts principal components (factors) that maximize explained variance across all blocks. Factor scores describe individuals in the reduced space, while loadings indicate variable directions, and block contributions reveal the relative influence of each block on the factors. MFA often allows supplementary rows or columns to be projected onto the global factors without altering them.

Variants of MFA include exploratory MFA, hierarchical MFA, and partial MFA, as well as extensions that handle missing data, sparse representations, or additional constraints. Some implementations support supplementary data, enabling comparisons across groups or time points. MFA is flexible for data integration, dimensionality reduction, and exploratory analysis where variables are grouped but observed on the same subjects.

Applications span social sciences, marketing, ecology, and biology, including consumer profiling, cross-domain data integration, and multi-omics studies. The method is valued for preserving block structure, providing interpretable components, and enabling assessment of the relative contribution of each data block to the global signal.

See also: Principal Component Analysis, Factor Analysis, Multiple Factor Analysis, data integration.