Weighted PLS (WPLS): When a Survey Sample Does Not Represent the Population

Survey samples rarely represent their populations perfectly. When a properly constructed sampling-weight variable is available, Weighted PLS incorporates it into PLS-SEM estimation to improve population representation relative to standard unweighted PLS.

PLS-SEM & SMARTPLSPrepared by Lê Minh4 min

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Sample weights should follow the design

Population
Define the target population
Sample
Inspect composition and selection
Weights
Explain construction and application
Sensitivity
Compare weighted and unweighted results

Conceptual diagram. Weights do not automatically fix all selection or measurement bias.

Source: Lê Minh · Conceptual illustration, not software output.

1. Why a Survey Sample May Be Unrepresentative

SmartPLS documentation identifies three main causes: unequal selection probabilities across groups, differential unit nonresponse, and noncoverage, where some population groups have no opportunity to enter the sampling frame.

Any of these can bias sample estimates away from population parameters regardless of sample size, because groups are overrepresented or underrepresented relative to their population shares.

2. Weighted PLS Principles

Weighted PLS (Becker & Ismail, 2016; Cheah, Roldán, Ciavolino, Ting & Ramayah, 2021) incorporates sampling weights through weighted correlations and regressions instead of treating observations equally. With correctly constructed weights, for example through post-stratification, WPLS estimates are on average more accurate representations of population parameters than standard PLS.

3. When to Use WPLS

Two prerequisites

First, there must be grounds to suspect unequal population representation, such as complex sampling or different response rates across groups. Second, an appropriate sampling-weight variable must be available, often supplied with secondary survey datasets or constructed using an established post-stratification procedure.

Creating weights merely to run WPLS, without a validated procedure, may do more harm than good because errors in the weights affect the entire estimation.

4. Implementation in SmartPLS

Construct or identify the weight variable

Prepare a sampling weight for each observation before importing the data. Weight construction requires specialized methodological guidance rather than arbitrary decisions.

Import the data into SmartPLS

Import the dataset, including the weight variable, into the project as usual.

Run PLS or PLSc

Run PLS, PLSc, or another algorithm built on them.

Select the weight variable in the weighting tab

Choose the prepared weight variable from the list. SmartPLS automatically applies WPLS to subsequent calculations.

If an algorithm lacks a weighting tab, WPLS is unavailable for it.

5. Survey Datasets That Commonly Include Weights

International datasets commonly reused in secondary research often include sampling weights, such as the International Social Survey Programme (ISSP), European Social Survey (ESS), European Working Conditions Survey, European Company Survey (ECS), and European Quality of Life Surveys (EQLS). WPLS provides an appropriate way to incorporate their original weights in PLS-SEM.

6. WPLS Limitations

Benefits depend entirely on weight quality; incorrectly constructed weights can worsen results.
In SmartPLS, WPLS currently supports PLS, PLSc, and algorithms built on them rather than every algorithm.
Researchers must construct weights when they are absent; SmartPLS does not do this automatically.

7. Common Mistakes

Table 1
Weak practice	Why it is inappropriate	Recommended practice
"Assign observation weights intuitively and run WPLS."	Weights require established procedures, such as post-stratification, rather than arbitrary assignment.	Use supplied dataset weights or construct them following specialized sampling-weight guidance.
"Use WPLS for any SmartPLS algorithm without checking the weighting tab."	WPLS currently supports PLS, PLSc, and algorithms built on them.	Check for a weighting tab before reporting WPLS use.
"Weight origins or construction need not be reported."	Readers need this information to assess the reliability of adjusted results.	State whether weights came from the original dataset or were constructed using a specified method.

8. Checklist before Reporting

Have you explained why unequal population representation is suspected?
Have you reported the sampling weights' origin or construction?
Have you confirmed weighting-tab support for the selected PLS/PLSc algorithm?
Have you compared weighted and unweighted results to show differences?

Conclusion

Weighted PLS addresses unequal population representation due to unequal selection probabilities, differential nonresponse, or noncoverage. It applies an existing weight variable within PLS-SEM estimation rather than automatically solving the weighting problem.

Its practical value therefore depends on input weight quality. For international surveys with established weights, WPLS makes appropriate use of that information rather than ignoring it in PLS-SEM.

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. https://doi.org/10.1016/j.emj.2016.06.009
Cheah, J.-H., Roldán, J. L., Ciavolino, E., Ting, H., & Ramayah, T. (2021). Sampling weight adjustments in partial least squares structural equation modeling: Guidelines and illustrations. Total Quality Management & Business Excellence, 32(13-14), 1594-1613. https://doi.org/10.1080/14783363.2020.1754125

Academic note: This article presents WPLS principles and procedures following SmartPLS documentation and the two cited methodological sources. Consult Becker and Ismail (2016) and Cheah, Roldán, Ciavolino, Ting, and Ramayah (2021) directly when constructing weights for a dataset rather than improvising a calculation.