Partial Least Squares (PLS)
The Partial Least Squares (PLS) regression is a predictive technique, which aims to produce fast, accurate, and quantitative predictions. It is particularly useful when predictor variables are highly correlated or when the number of variables exceeds the number of samples. PLS combines features of principal components analysis and multiple regressions. It first extracts a set of latent factors that explain as much of the covariance as possible between the independent and dependent variables. .
In this chapter, letfs set gWhiskeyh and gCheeseh as dependent variables (Y) and investigate the relation between dependent variables (Y) and independent variables (X).
Go back to sheet DataSheet1 and then click gMultibase_2015h and gOpen_Formh in Add-ins menu.
Click gVariablesh tab and select gWhiskeyh and gCheeseh in the list. Then click gSet Variable Yh button. Multibase recognizes whiskey and cheese as dependent variables (Y) and they will be displayed with (Y) . Then click gNexth button in Method and Preparation dialog box.
Sheets Multibase_Preparation will be generated. The dependent variables (Y) will be displayed with brown cell color as below.
Click gMultibase_2015h and gOpen_Formh in Add-ins menu again. PLS dialog box will open and click "Done" without any changes..
Two new sheets, Multibase_Result and Multibase_PLS will be generated. In the sheet Multibase_PLS, two scatter plots will be shown. One is the relation between whiskey and X variables, and the other is the correlation between cheese and X variables. X axis (Estimated) shows Y values calculated by X variables using PLS model, and Y axis (Measured) shows observed Y values. You can understand that whiskey consumption shows good correlation with independent variables, beer, chocolate, coffee and wine, because square of correlation factor is 0.615. On the other hands, the correlation between cheese and independent variables is not so good.
Variable Importance (VIP) shows the contributions of X variables to this model. You can see that beer and wine contributions are higher than chocolate and coffee, which means that whiskey consumption correlates highly with beer and wine.
2-3-1 Marunouchi Chiyoda Tokyo Japan