Multiple factor analysis (MFA) is an analytical method that is closely related to principal components analysis (PCA). However, MFA differs from PCA in that it combines measurements from more than one table. Such tables are sometimes called sub-tables or sub-matrices. Each sub-table has the same number of rows, which represent the items or products being tested. In JMP, sub-tables are represented as groups of columns in a single data table. Each column group is called a block. Note the following about blocks:
• The number of columns in a block can vary. For example, in sensory analysis, a block represents a panelist. Some panelists might rate fewer attributes of a product than other panelists.
• Each block of columns can represent different measurements entirely. MFA scales each block to enable global analysis of all measurements.
The primary goal of MFA is to find groupings of products (rows in a data table) that are similar. A secondary goal is to identify outlier panelists. An outlier panelist results are so different from the rest of the group that they change the study results. Supplementary variables can be used investigate why items group together.
You can use MFA to analyze studies where items are measured on the same or different attributes by different instruments, individuals, or under different circumstances. MFA is frequently used in sensory analysis to account for different measurements among panelists. Traditional sensory analysis can entail hours of up-front training to ensure that panelists’ measurements are consistent with each other. For example, consider a juice product with sensory measurements described as “fruity”, “sweet”, and “refreshing”. In traditional sensory analysis, each panelist would have to be trained and tested to make sure reporting on distinct sensory measurements was consistent across panelists. MFA enables the researcher to perform a PCA-like analysis with untrained panelists.
When you use MFA, the same items are measured each time and the measurements can be arranged into internally consistent groups or blocks. For sensory analysis, the rows are the items measured, and the columns are the sensory aspects recorded by each panelist (there is a block for each panelist). Missing observations are replaced by the column mean.
For more information about multiple factor analysis, see Abdi et al. (2013).