Partial Least Squares

by G. David Garson

Partial least squares (PLS) analysis is an alternative to OLS regression, canonical correlation, or structural equation modeling (SEM) of systems of independent and response variables. In fact, PLS is sometimes called "component-based SEM," in contrast to "covariance-based SEM," which is the usual type and which is implemented by Amos, LISREL, EQS and other major software packages. On the response side, PLS can relate the set of independent variables to multiple dependent (response) variables. On the predictor side, PLS can handle many independent variables, even when predictors display multicollinearity. PLS may be implemented as a regression model, predicting one or more dependents from a set of one or more independents; or it can be implemented as a path model, handling causal paths relating predictors as well as paths relating the predictors to the response variable(s). PLS is implemented as a regression model by SPSS and by SAS's PROC PLS. SmartPLS is the most prevalent implementation as a path model.

PLS is characterized as a technique most suitable where the research purpose is prediction or exploratory modeling. In general, covariance-based SEM is preferred when the research purpose is confirmatory modeling. PLS is less than satisfactory as an explanatory technique because it is low in power to filter out variables of minor causal importance (Tobias, 1997: 1).

The advantages of PLS include ability to model multiple dependents as well as multiple independents; ability to handle multicollinearity among the independents; robustness in the face of data noise and missing data; and creating independent latents directly on the basis of crossproducts involving the response variable(s), making for stronger predictions. Disadvantages of PLS include greater difficulty of interpreting the loadings of the independent latent variables (which are based on crossproduct relations with the response variables, not based as in common factor analysis on covariances among the manifest independents) and because the distributional properties of estimates are not known, the researcher cannot assess significance except through bootstrap induction. Overall, the mix of advantages and disadvantages means PLS is favored as a predictive technique and not as an interpretive technique, except for exploratory analysis as a prelude to an intepretive technique such as multiple linear regression or covariance-based structural equation modeling. Hinseler, Ringle, and Sinkovics (2009: 282) thus state, "PLS path modeling is recommended in an early stage of theoretical development in order to test and validate exploratory models."

Table of Contents
Overview4
Key Concepts and Terms5
Background5
Models6
Regression vs. path models6
PLS-DA models7
Mixed methods7
Reflective vs. formative models7
Confirmatory vs. exploratory models7
Inner (structural) model vs. outer (measurement) model8
Variables8
Measured factors and covariates8
Modeled factors and response variables8
Measurement level of variables10
Parameter estimates11
Cross-validation and goodness-of-fit11
PRESS and optimal number of dimensions12
PLS path modeling with SmartPLS13
Creating a PLS project and importing data13
Validating the data16
Creating the path model in SmartPLS17
Reflective vs. formative models19
Hiding the measurement model19
Estimation options in SmartPLS19
Finite mixture PLS20
Running the path model in SmartPLS20
Data metric for centered data21
Weighting scheme22
SmartPLS Output22
Path coefficients22
Bootstrapped significance23
Options26
Saving the model27
SmartPLS Output27
Model fit coeffi

97 pages, Kindle Edition

First published May 15, 2012