## 7.1 **What is MFA?**

**Purpose:**

Multiple Factor Analysis (MFA) is is a statistical technique that takes root in PCA (or MCA if dealing with qualitative data). In term of data formats, MFA is similar to DISTATIS in that it can be used to analyze both observations and variables where we can see the difference between observations and variables per the a-priori design (pre-assign group). The new difference lies in how the data is processed before being fed to the mpMFA() function. MFA takes three or more data tables of the same set of observations. In our example, we have ratings data from 3 or more Panelists on the same set of products.

**Essential Steps:**

1. Find the Weights by taking the inverse of the first eigen values of each group of variables (cols in each “cell data tables”). Weight is similar for all attributes rated by the same Panelist.

2. Normalize the each “cell data table” by applying the Weights on them.

3. Combine all “cell data tables” as the “Grand table” (concatenate all cells).

3. Perform PCA on the “Grand table” (all individual data tables of each Panelist’ ratings on the same set of Products).

**Author’s Notes:**

So far, I think MFA is the most complete analysis technique in that in can shows all of the insights found in PCA and PLSC for for the observations while also able to compare the differences between Panelists in a lot more details as compared to PCA and PLSC (using just rows factor scores with color groupings). MFA is a weighted factorial analysis. Thus, it is important to show the weights associated with each Panelist before even doing the analysis. MFA implicitly assumes a balance (same number of rows and cols) between these “cell data tables”. Note: weighting of the MFA, makes the maximum axial inertia of each group equal to 1.

**Note on the package ‘MExPosition’**: The package we need MExPosition is not currently on CRAN but can be found here: https://cran.r-project.org/src/contrib/Archive/MExPosition/ . Then we have to install it manually. The version used is MExPosition_2.0.3.tar.gz. How to install custom package in GUI: Packages tab -> Install -> use the dropdown list of install from: and choose Package archive files -> select the tar.gz file.