XLSTAT: Factorial analysis of mixed data (PCAmix) in Excel

Background

Factorial analysis of mixed data (PCAmix) analyzes tables with both quantitative and qualitative variables.

It studies variable correlations, derives uncorrelated factors as linear combinations of initial variables, and visualizes observations in 2D or 3D space. Developed by Chavent et al. (2014), PCAmix combines PCA and MCA to reduce data dimension, explore variable relationships, and assess similarities among observations.

 

Dataset for Example

This attached dataset is an extract of data collected by  Centre de recherche INRA d’Angers, France.

Experts have been asked to rate 21 wines according to different sensorial descriptors (14 quantitative variables).

We also have two qualitative variables about the wine origin and the nature of the soil.

 

Setting Up

• Open XLSTAT.

• Click on the Analyzing data menu and select the PCAmix feature.

• Once you've clicked on the button, the PCAmix dialog box appears.

In the General tab:

• Select columns D-P in the Observations/quantitative variables field and columns B-C in the Observations/qualitative variables field.

• The Variable labels option is left activated as the first row of the table contains the name of the variables.

• Select column A in the  Observations labels field. 

In the Outputs tab:

• Choose to display all available results for variables and observations.

In the Charts/Observations tab:

• Choose to color observations according to a group variable which is simply a recoding of the quantitative variable “Global quality”. This coloration will allow us to distinguish groups of observations.

• All other options are left by default

In the Colors tab:

• Define the colors used for the display of the results.

• Click on the OK button to launch the computations.

• Select F1 and F2 Axes:

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The initial results show descriptive statistics of selected variables, followed by a table of non-zero eigenvalues and their corresponding percentage of inertia.

Coordinates, squared cosines, contributions, and loadings for variables and categories are displayed, along with similar data for observations. Before assessing proximity, check that contributions or squared cosines are high on relevant axes. The following charts aid in interpreting relationships among variables, observations, and axes.

The first three charts illustrate variable relationships with factorial axes:  
- Axis 1 is negatively correlated with variables like Fruity, Aroma, and Overall Quality, indicating wines with high variable values have negative scores on this axis.  
- Axis 2 is positively correlated with Odor/Intensity and Spice, and negatively with Flower; wines with high Axis 2 scores have strong odor and spice but low floral qualities.  
- Soil is linked to Axis 2, with Env4 wines scoring high there.  

Based on these axes and observation positions, we can identify wine characteristics.

The color coding shows that top wines (blue) have negative Axis 1 scores and low secondary scores, mid-range wines (center) are less appreciated, and less favored wines (green) with high scores on either axis. Spicy wines, for example, tend to be less appreciated.  

An Agglomerative Hierarchical Clustering (AHC) can be launched via the button below the principal coordinates table, with an arrow for quick navigation if many variables are present.

By clicking on this button, the AHC dialog box is then automatically configured and you just have to click on the OK button to launch the analysis.

Click here to see how to interpret the results of the AHC analysis.