Partial Least Squares Regression

PLS combines features of principal components analysis and multiple regression. It first extracts a set of latent factors that explain as much of the covariance as possible between the independent and dependent variables. Then a regression step predicts values of the dependent variables using the decomposition of the independent variables.

Tables. Proportion of variance explained (by latent factor), latent factor weights, latent factor loadings, independent variable importance in projection (VIP), and regression parameter estimates (by dependent variable) are all produced by default.

Charts. Variable importance in projection (VIP), factor scores, factor weights for the first three latent factors, and distance to the model are all produced from the Options tab.

Partial Least Squares Regression Data Considerations

Measurement level. The dependent and independent (predictor) variables can be scale, nominal, or ordinal. The procedure assumes that the appropriate measurement level has been assigned to all variables, although you can temporarily change the measurement level for a variable by right-clicking the variable in the source variable list and selecting a measurement level from the pop-up menu. Categorical (nominal or ordinal) variables are treated equivalently by the procedure.

Categorical variable coding. The procedure temporarily recodes categorical dependent variables using one-of-c coding for the duration of the procedure. If there are c categories of a variable, then the variable is stored as c vectors, with the first category denoted (1,0,...,0), the next category (0,1,0,...,0), ..., and the final category (0,0,...,0,1). Categorical dependent variables are represented using dummy coding; that is, simply omit the indicator corresponding to the reference category.

Frequency weights. Weight values are rounded to the nearest whole number before use. Cases with missing weights or weights less than 0.5 are not used in the analyses.

Missing values. User- and system-missing values are treated as invalid.

Rescaling. All model variables are centered and standardized, including indicator variables representing categorical variables.

To Obtain Partial Least Squares Regression

From the menus choose:

Analyze > Regression > Partial Least Squares...

1. Select at least one dependent variable.
2. Select at least one independent variable.

Optionally, you can:

• Specify a reference category for categorical (nominal or ordinal) dependent variables.
• Specify a variable to be used as a unique identifier for casewise output and saved datasets.
• Specify an upper limit on the number of latent factors to be extracted.