# MFA

Last modified at 2/2/2021 3:32 PM by Maren Johnson

## Multiple Factor Analysis

Multiple Factor Analysis (MFA) is a statistical technique based on PCA used to analyze multiple sets of data pertaining to the same set of products. Although all the variables could be combined into one large data set and analyzed by PCA, one group of products may exert more influence on the construction of the product space than other sets of variables. MFA solves this problem by giving equal weighting to each defined group of variables.

During the first step of MFA, a PCA is performed on each group of variables. Then the groups are normalized by dividing all the variables within a group by the first eigen value for that group. All the variables are then combined into a single data set and a global PCA is run.

## Applications

There are many uses to which MFA is well suited. It can be applied to a variety of data sources, provided that all the variables within each group are either quantitative or qualitative (not both). However MFA can be used to combine a group of quantitative variable with a group of qualitative variables. Applications of MFA include:

• analysis of Projective Mapping data
• comparison of panels describing the same products
• combination of descriptive and chemical data
• comparison of product spaces obtained by different descriptive techniques