# Weighted PLS Algorithm (WPLS)

## Abstract

The weighted PLS algorithm (WPLS), as presented by Becker and Ismail (2016), is a modified version of the original PLS path modeling algorithm that incorporates sampling weights.

## Description

Applications of PLS-SEM usually focus on survey responses in management, social science, and market research studies, with researchers using their collected samples to estimate population parameters. For this purpose, the sample must represent the population. However, population members are often not equally likely to be included in the sample, which indicates that sampling units have different probabilities of being selected. Hence, sampling (post-stratification) weights should be used to obtain consistent estimates when estimating population parameters. The use of sampling weights is a possible solution to correct the results with, for example, weighted means or weighted variances, when estimating population parameters. Not only can imperfections in the sample due to unequal probabilities of selection be corrected by applying appropriate weights, but also imperfections in terms of unit nonresponse and noncoverage.

PLS-SEM is a system of regressions on standardized indicator data, and it calculates weighted composites as approximation of the conceptual latent variables in an iterative algorithm. A suitable approach to incorporating sample weighting into PLS-SEM builds on the data of the observed (or manifest) variables and a weighting variable that corrects for the unequal probability of selection and thereby ensures representativeness of the sample with regards to the population. The weighted PLS algorithm (WPLS), as presented by Becker and Ismail (2016), incorporates these weights using weighted correlations and weighted regression results when estimating the PLS path model. WPLS is a modified version of the original PLS path modeling algorithm that incorporates sampling weights. As a result, WPLS provides better average population model parameter estimates than the basic PLS algorithm when appropriate sampling weights are available (Becker and Ismail, 2016).

## WPLS Settings in SmartPLS

A requirement to use the WPLS algorithm is the availability of a weighting variable in your data set. The weighting variable is a variable in your dataset that includes the sampling weight for every observation. This weighting variable needs to be created by the researcher prior to importing the data into SmartPLS (see journal articles and other literature to obtain further information on the creation of sampling weights).

When running the PLS and PLSc algorithm as well as all other algorithms that are based on the PLS and PLSc results in SmartPLS, an option to select a weighting variable will appear.

Just select the weighting variable by using the combo box in the weighting tab that appears when running the algorithm in SmartPLS. After selecting a weighting variable, SmartPLS automatically applies WPLS. All subsequent PLS computations will draw on these sampling weights . As a result, you obtain weighted PLS results.

If the weighting tab is not available for an algorithm in SmartPLS the WPLS methods is not (yet) available for this algorithm.

## Links

## References

- Becker, J.-M. & Ismail, I. R. 2016.
**Accounting for Sampling Weights in PLS Path Modeling: Simulations and Empirical Examples**,*European Management Journal*, 34(6): 606-617.**Link to Article**