# General PLS Models

Performs Partial Least Squares analyses with a list of continuous dependent variables, and lists of continuous and categorical predictor variables arranged into an ANCOVA-like design.

Estimation and Design

Analysis syntax. Analysis syntax string for general Partial Least Squares models. You can specify here the complete syntax, as, for example, copied form a Statistica analysis. Set this string to empty, or just PLS; to create the syntax from the specific options specified below.

Detail of computed results reported. Specifies the level of computed results reported. If Minimal results is requested, Statistica will report summary statistics for the components and the regression coefficients; if All results is requested, summary plots, weights, and other statistics will be reported. Residual (observational) statistics can be requested as a separate option.

PLS method. Select the algorithm (method) that is to be used to compute the PLS components; the default is PLS. If PLS is specified, a standard PLS analysis using the NIPALS algorithm (Rannar, Lindgren, Geladi, and Wold, 1994) will be performed; if you specify SIMPLS, the factor scores will be computed via the SIMPLS algorithm (de Jong, 1993).

Max number of components. Specifies the maximum number of components to be extracted; the default value is 120.

Delta for R-square; 1.E-. Specifies the negative exponent for a base-10 constant delta (delta = 10^-RDelta); the default value is 12. Delta is used by the program as a criterion for determining whether to stop extracting additional PLS components.

Design. Required; specify the ANCOVA-like design for the categorical and continuous predictors.

Use the syntax:
DESIGN = Design specifications

Example 1.
DESIGN = GROUP | GENDER | TIME | PAID; {makes a full factorial design}

Example 2.
DESIGN = SEQUENCE + PERSON(SEQUENCE) + TREATMNT + SEQUENCE*TREATMNT;

Example 3.
DESIGN = MULLET | SHEEPSHD | CROAKER @2; {Makes factorial design to degree 2}

Example 4.
DESIGN = TEMPERAT | MULLET | SHEEPSHD | CROAKER - TEMPERAT; {Removes main effect for TEMPERAT from factorial design}

Example 5.
DESIGN = BLOCK + DEGREES + DEGREES*DEGREES + TIME + TIME*TIME + TIME*DEGREES;

Parameterization of effects. Parameterization for coding the ANCOVA-like design vectors for categorical predictor effects. Specify either the sigma-restricted model or the overparameterized model; sigma restricted parameterization is the default.

Intercept. Specifies whether the intercept (constant) is to be included in the model (i.e., a parameter is to be estimated for the intercept); the default is INTERCEPT=INCLUDE.

Auto scaling. Each column in the predictor design matrix X and matrix of dependent (response) variables Y will be divided by its respective standard deviation, and all computations will be performed on these scaled matrices X and Y. Note that the coefficients that are computed when the AUTOSCALE option is set are not the same as the standardized regression coefficients, as, for example, computed via multiple regression. For more information about auto-scaling, refer to Geladi and Kowalski(1986).

Residuals and Observational Statistics

Residual analysis. Creates predicted and residual values, and factor scores for each observation.

Normal probability plot. Creates a normal probability plot of residuals.

Parameters for Estimation

Delta for eigenvalues; 1.E-. Specifies the negative exponent for a base-10 constant delta (delta = 10^-Edelta); the default value is 12. Delta is used for checking the convergence of the iterative computation of eigenvectors for each PLS component.

Maximum number of iterations. Specifies the maximum number of iterations for the iterative computation of eigenvectors for each PLS component. The default value is 200. PLS uses an iterative power method (see Golub and van Loan, 1996) to compute the eigenvector of Y'XX'Y for each component.

Generates data source, if N for input less than. Generates a data source for further analyses with other Data Miner nodes if the input data source has fewer than k observations, as specified in this edit field; note that parameter k (number of observations) will be evaluated against the number of observations in the input data source, not the number of valid or selected observations.