PLS Results - Summary Tab

Partial Least Squares (PLS)

Select the Summary tab of the PLS Results dialog box to access the options described here. Note that in some cases there are two sets of buttons with identical descriptions; in this case, click the left buttons to display results in a spreadsheet, click the right buttons to display results in a graph. For details about the computations performed during the PLS analysis, see Computational Approach or the Partial Least Squares (PLS) Index.

Summary. Click the Summary buttons to display your results with the R-squared and increase in R-squared values for the components extracted in the analysis. Specifically, the spreadsheet will show 1) the averaged R-squared values and increase in average R-squared values for the predictor (X) variables, 2) the averaged R-squared values and increase in average R-squared values for the dependent (response or Y) variables, and 3) the R-squared values for each dependent (response) variable (if more than one dependent (response) variable was selected for the analysis). Unlike in STATISTICA General Linear Model (GLM) or Multiple Regression, these R-squared values are computed relative to the sums of squared deviations from the origin (0.0) for the centered (de-meaned) predictor or and dependent (response) variable. So these results will not be identical to those computed in, for example, GLM or Multiple Regression.

Note: statistics for verification (cross-validation) samples. If you explicitly specified a training (analysis) sample via the Cross-validation button on the PLS Quick Specs dialog box - Options tab, or via the SAMPLE keyword in a PLS syntax program, and the data file includes observations in the cross-validation (verification) sample, then the Summary spreadsheet and graph will include two additional elements: First, in the spreadsheet the line (i.e., respective Number of components, see PLS Results) that produces the smallest PRESS statistic will be highlighted, and second, the PRESS statistic for the respective number of components will be shown in the last column of the spreadsheet. In the summary graph, the number of components that yielded the smallest PRESS statistic will be indicated by a vertical line.

Weights for X. Click the Weights for X button to display a spreadsheet (left button) or a line graph (right button) of the W (predictor) weights for each component.

Loadings. Click the Loadings button to display a spreadsheet or a line graph of the factor loadings (P; see also Computational Approach). The line graph will provide a quick summary for identifying the "important" predictors for particular components.

Regr. Coeffs. Click the Regr. Coeffs button to display a spreadsheet or a line graph of the regression coefficients (B; see Computational Approach) for each predictor and for each dependent (response) variable. The line graph will provide a quick summary for identifying the "important" predictors for particular dependent (response) variables.

Scaled Coeffs. Click the Scaled Coeffs button to display a spreadsheet or a line graph of the standardized regression coefficients (Beta) for each predictor and for each dependent (response) variable. The line graph will provide a quick summary for identifying the "important" predictors for particular dependent (response) variables.

Weights for Y. Click the Weights for Y button to display a spreadsheet or a line graph of the Q normalized weights (loadings) for each component.

Descriptive stats. Click the Descriptive stats button to display a spreadsheet with the means and standard deviations of each predictor and response variable. These values are used for centering and scaling those variables. For more information about centering and scaling in PLS, refer to Geladi and Kowalsky(1986) or see the Introductory Overview.

Design terms. Click the Design terms button to display a spreadsheet of all the labels for each column in the design matrix (see the Introductory Overview); this spreadsheet is useful to unambiguously identify how the categorical predictors in the design where coded, that is, how the model was parameterized, and how, consequently, the parameter estimates can be interpreted. The GLM Introductory Overview discusses in detail the overparameterized and sigma-restricted parameterization for categorical predictors variables and effects, and how each parameterization can yield completely different parameter estimates (even though the overall model fit is usually invariant to the method of parameterization).

If in the current analysis the categorical predictors variables were coded according to the sigma-restricted parameterization, then this spreadsheet will show the two levels of the respective factors that were contrasted in each column of the design matrix; if the overparameterized model was used, then the spreadsheet will show the relationship of each level of the categorical predictors to the columns in the design matrix (and, hence, the respective parameter estimates).

Scatterplot of selected results. The options under Scatterplot of selected results are used to create a scatterplot of various results statistics such as Weights, Loadings, Regression coefficients, or the X column numbers for a selected component or response variable. First select the respective statistic to plot in the Y and X drop-down lists; then click the Plot of the selected items button to display the scatterplot. For additional details about the available statistics, see the Introductory Overview.

Y. Select the values to be plotted on the y-axis of the scatterplot in the Y drop-down list.

X. Select the values to be plotted on the x-axis of the scatterplot in the X drop-down list.

Plot of the selected items. Click the Plot of the selected items button to display the scatterplot of the selected Y and X values. The ellipse shown in the scatterplot allows you to more easily spot outliers or unusual observations in the scatterplot. The ellipse is computed from the respective values in the plot, so that the horizontal and vertical distances of the ellipse from the origin (coordinate {0,0}) is equal to 3 times the standard deviation of the values plotted along the respective axis.

Regr. coeffs. by number of components. The options under Regr. coeffs. by number of components will display a spreadsheet or a line graph of the Regression coefficients (see above) for each dependent variable, for different Numbers of components (see PLS Results).

Table of results. Click the Table of results button to display a spreadsheet that will show the values of the regression coefficients (see above) for each dependent (response) variable, and for different numbers of components.

Response. Select the dependent (response) variable to be used in the Plot (see below).

Plot. Click the Plot button to display a line-plot that is used to visualize the change in the regression coefficients over the numbers of components, for a selected dependent variable (see Response above).