XLSTAT: Partial Least Squares Discriminant Analysis (PLSDA)

 

Dataset for Example

The attached data are from [Fisher M. (1936). The Use of Multiple Measurements in Taxonomic Problems. Annals of Eugenics, 7, 179 -188] and correspond to 150 Iris flowers, described by four variables (sepal length, sepal width, petal length, petal width) and their species. Three different species have been included in this study: setosa, versicolor and virginica.

The goal is to determine if the four variables can differentiate species and to visualize group separation on a 2D map using Partial Least Squares, which handles multicollinearity, missing data, and small sample sizes.

 

Setting Up

• Open XLSTAT.

• Click on the Modeling data menu and select the PLS Regression feature.

• Once you have clicked the button, the Partial Least Squares regression dialog box is displayed.

In the General tab:

• In the Dependent variable(s) field, select with the mouse the species.

• In Quantitative variable(s) field, select the explanatory variables, that are in our case the physical descriptors of the iris.

• The method to be used is PLS-DA for Partial Least Squares Discriminant Analysis.

• In the Options tab of the dialog box, make sure that Automatic is activated.

• Last, in the Charts tab, the Colored labels option has been activated in order to make the reading of the charts easier.

• Click on the OK button to launch the computations.

• The results are displayed on a new Excel sheet.

 

Interpreting the Results

The initial results show classic PLS regression between variables and species (responses). Following tables display basic statistics and correlations, with dependent variables in blue and explanatory variables in black, then present the PLS regression specifics.

The Q² index assesses model fit and prediction quality across the three species.

With 4 components, Q² remains low, indicating variable fit quality per species.

The R²Y and R²X values are near 1, showing the 4 components well summarize both explanatory and response variables.

The first correlations map visualizes these relationships on the first two components.

The correlation plot visualizes species and explanatory variables.

After the PLS regression, discriminant analysis results are shown.

The classification table assigns observations to the group with the highest function value; notes two reclassifications. These results may reflect measurement errors, unusual flower growth, imprecise classification criteria, or missing information.

The chart shows observations on the t axes, confirming that species are well discriminated along these factor axes derived from the original variables.

The confusion matrix shows that 85% of observations were correctly classified, calculated as the ratio of well-classified observations to the total.