Why Did SmartPLS 4 Remove Blindfolding and Q²?

SmartPLS states explicitly in its official documentation that the Blindfolding algorithm was removed from SmartPLS 4 because it never truly assessed predictive ability on new data, rather than because of a technical fault. This article explains how Blindfolding works, why it remains an in-sample assessment, and how to move to PLSpredict and CVPAT without misrepresenting the history of the once-familiar Q² index.

PLS-SEM & METHODOLOGICAL UPDATESPrepared by Lê Minh7 min

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Prediction needs observations held out from estimation

Split observations
Set folds and repetitions
Fit
Use the training observations
Evaluate
RMSE, MAE and Q²predict
Benchmark
Read IA, LM and CVPAT in their roles

Conceptual diagram. Use consistent data splits when comparing prediction benchmarks.

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

1. What Are Blindfolding and Stone–Geisser Q²?

The Q² reported by generations of PLS-SEM theses originates in two independent papers published in 1974: Stone (1974) and Geisser (1974). Both proposed cross-validation-based model-selection criteria, later collectively called Stone–Geisser Q² in PLS-SEM research. In SmartPLS, Blindfolding calculates this index using the sum of squared prediction errors for systematically omitted data points.

The standard formula presented in most PLS-SEM textbooks is Q² = 1 − SSE/SSO, where SSE is the sum of squared prediction errors for omitted points and SSO is the sum of squares of those observed values themselves. An endogenous variable with Q² above 0 is considered to have predictive relevance: the model predicts better than simply using the sample mean.

Predictive relevance, briefly

Q² > 0 asks whether omitting some endogenous-variable data and predicting them using the remaining model yields better predictions than guessing with the sample mean. This criterion retains historical value and mathematical validity; the issue concerns which question it answers, as explained below.

2. How Blindfolding Works: Why It Remains “In Sample”

Blindfolding uses an omission distance (D), recommended from 5 to 12 and defaulting to 7 in SmartPLS. In the first round, it starts at the first data point, omits every Dth point of the focal endogenous variable’s indicators, treats them as missing, and re-estimates the PLS model on the remaining data to predict the omitted points. The second round starts at the second position, and so on. The number of rounds always equals D, so every data point is omitted and predicted exactly once.

Q² = 1 − SSE / SSO

Crucially, Blindfolding omits individual indicator data points rather than entire observations or respondents. Each round still estimates the model using almost the entire sample structure, missing only a small amount of one variable’s information. The model therefore never truly encounters a completely unseen observation; it temporarily hides a few points and predicts them within a familiar context.

Exact wording from SmartPLS documentation

“The blindfolding method does not provide an out-of-sample assessment of predictive power.” SmartPLS explicitly confirms that Blindfolding provides no out-of-sample assessment, although its Q² has often been interpreted as predictive-ability evidence over the years.

3. SmartPLS 4 Has Officially Removed Blindfolding

The official SmartPLS documentation states: “We have discontinued support for blindfolding in SmartPLS 4 and removed the algorithm.” This explicitly confirms removal rather than offering an ambiguous announcement. The algorithm is no longer available in version 4’s Calculate menu, although it remains in older SmartPLS versions.

7Default Blindfolding omission distance D in SmartPLS, with a recommended range of 5-12

DThe number of Blindfolding rounds always equals omission distance D; each point is omitted and predicted exactly once

0Number of Blindfolding algorithm entries in SmartPLS 4’s calculation menu, according to official documentation

SmartPLS itself explains the replacement: “the PLSpredict procedure and the cross-validated predictive ability test (CVPAT) provide the results” needed for a genuine out-of-sample assessment. Unlike Blindfolding, PLSpredict (Shmueli et al., 2019) uses observation-level k-fold cross-validation: entire observations are excluded from training, the model is fully re-estimated without them, and only then used for prediction. CVPAT, introduced by Liengaard et al. (2021), with practical guidance added by Sharma et al. (2022), adds a formal statistical test of these results. Detailed workflows for both tools, a practical case, and interpretation of Q²predict, RMSE, MAE, and CVPAT appear in a separate SmartPLS Lê Minh guide.

4. Distinguishing Q² (Blindfolding) and Q²predict (PLSpredict)

Both indices contain Q² in their names, but measure different things. Do not use them interchangeably or directly compare their numerical values.

Table 1
Criterion	Q² (Blindfolding)	Q²predict (PLSpredict)
Original purpose	Predictive relevance within the estimated sample	Assessing predictive ability on out-of-sample observations
How data are omitted	Individual data points, periodically according to D	Entire observations, through k-fold cross-validation
Does the model “see” omitted observations during estimation?	Yes; almost the entire sample structure remains	No; test-fold observations are completely excluded from training
Is there a comparison benchmark?	No	Yes, comparison with a linear regression model (LM)
In SmartPLS 4	Removed	Fully supported

The indices share Q² in their names but arise from different mechanisms. Do not present Q²predict as a “new version of Blindfolding Q²,” or vice versa.

5. Were Older Theses Wrong to Use Blindfolding Q²?

No. Thousands of PLS-SEM studies published over more than a decade used Blindfolding Q², and it remains mathematically valid for its intended question: in-sample predictive relevance. The problem lies in interpreting Q² > 0 as evidence of prediction on new data, exceeding what the algorithm actually assesses.

For purely explanatory studies testing paths, R², and f², removal of Blindfolding from SmartPLS 4 has little effect because these criteria stand independently. Studies explicitly claiming predictive ability, or submitted to journals increasingly expecting out-of-sample assessment, need PLSpredict and CVPAT. For example, Jumani’s (2026) study of Islamic-brand consumers in Thailand does not mention Blindfolding, proceeding directly from structural-model assessment (R², f²) to PLSpredict and CVPAT in line with the current workflow.

6. Responding When Reviewers Ask About Q²

Reviewers familiar with older workflows may ask why a Blindfolding Q² table is absent. Explain that this reflects software and methodological changes rather than an omission.

Example explanation

The model’s predictive ability was assessed using PLSpredict and the Cross-Validated Predictive Ability Test (CVPAT), rather than Stone–Geisser Q² calculated through Blindfolding. SmartPLS removed Blindfolding from version 4 because it provides only in-sample assessment and does not adequately represent predictive ability on out-of-sample observations. PLSpredict (Shmueli et al., 2019) and CVPAT (Sharma et al., 2022) use k-fold cross-validation, allowing assessment on observations entirely excluded from estimation.

Step 1: Identify the study’s objective

If the study aims only at explanation and theory testing, predictive assessment need not be added; R², f², and path coefficients suffice.

Step 2: If SmartPLS 3 with Blindfolding was previously used

Older Q² results are not incorrect, but should be called in-sample predictive relevance rather than out-of-sample predictive ability.

Step 3: Run PLSpredict and CVPAT in SmartPLS 4

Use the appropriate k-fold cross-validation workflow and Q²predict, RMSE, MAE, and CVPAT results as out-of-sample predictive evidence.

Step 4: Prepare an explanation for reviewers

Adapt the explanation above to the study’s specific model structure.

7. Common Transition Errors

Table 2
Common wording	Why it is incorrect	Better wording
“PLSpredict Q²predict directly replaces Blindfolding Q², and the values can be compared.”	They use different sample-splitting mechanisms and do not measure the same quantity.	Present Q²predict as a distinct index, without tying it to previously reported Blindfolding Q² values.
“Earlier studies using Blindfolding Q² have methodological errors.”	Blindfolding is mathematically valid for its intended question; overinterpretation is the issue.	Acknowledge its historical role as an in-sample predictive-relevance criterion distinct from out-of-sample prediction assessment.
“SmartPLS 4 can no longer assess predictive ability.”	SmartPLS 4 replaces the tools with PLSpredict and CVPAT rather than abandoning prediction assessment.	Identify PLSpredict and CVPAT as the current tools instead of implying prediction assessment is absent.

Identify whether the study emphasizes explanation or makes predictive claims.
For SmartPLS 3 with Blindfolding, correctly call the result in-sample predictive relevance.
For SmartPLS 4, replace Blindfolding with PLSpredict and CVPAT for prediction assessment.
Do not directly compare Blindfolding Q² and Q²predict as equivalent quantities.
Prepare a short explanation for reviewers about the absent Blindfolding table.

Conclusion

SmartPLS removed Blindfolding from version 4 because its mechanism—omitting individual data points while estimating on almost the entire sample—cannot answer the question of prediction on unseen observations, rather than because Q² is incorrect. This methodologically justified change is explicitly acknowledged in SmartPLS technical documentation.

Previously published Blindfolding Q² retains its historical value when correctly named. For current manuscripts requiring predictive claims, PLSpredict and CVPAT are more appropriate. A concise explanation citing official SmartPLS documentation is sufficient to answer reviewers’ questions about the absence of Blindfolding in a SmartPLS 4 article.

References

Q² origins and official SmartPLS documentation

Stone, M. (1974). Cross-validatory choice and assessment of statistical predictions. Journal of the Royal Statistical Society: Series B, 36(2), 111-147. https://doi.org/10.1111/j.2517-6161.1974.tb00994.x
Geisser, S. (1974). A predictive approach to the random effect model. Biometrika, 61(1), 101-107.
SmartPLS (n.d.). Blindfolding. SmartPLS Documentation. Accessed 04/11/2026. https://smartpls.com/documentation/algorithms-and-techniques/resampling-and-inference/blindfolding/

Sources on PLSpredict, CVPAT, and the illustration

Shmueli, G., Ray, S., Estrada, J.M.V. and Chatla, S.B. (2019). Predictive model assessment in PLS-SEM: Guidelines for using PLSpredict. European Journal of Marketing, 53(11), 2322-2347. https://doi.org/10.1108/EJM-02-2019-0189
Liengaard, B.D., Sharma, P.N., Hult, G.T.M., Jensen, M.B., Sarstedt, M., Hair, J.F. and Ringle, C.M. (2021). Prediction: Coveted, yet forsaken? Introducing a cross-validated predictive ability test in partial least squares path modeling. Decision Sciences, 52(2), 362-392. https://doi.org/10.1111/deci.12445
Sharma, P.N., Liengaard, B.D., Hair, J.F., Sarstedt, M. and Ringle, C.M. (2022). Predictive model assessment and selection in composite-based modeling using PLS-SEM: Extensions and guidelines for using CVPAT. European Journal of Marketing, 57(6), 1662-1677. https://doi.org/10.1108/EJM-08-2020-0636
Hair, J.F., Hult, G.T.M., Ringle, C.M. and Sarstedt, M. (2022). A Primer on Partial Least Squares Structural Equation Modeling (PLS-SEM) (3rd ed.). Sage.
Jumani, Z.A. (2026). Predictive validation of an extended TPB model in Islamic branding: PLSpredict and CVPAT evidence from Muslim and non-Muslim Thai consumers. Journal of Islamic Marketing, ahead-of-print. https://doi.org/10.1108/JIMA-09-2025-0574

Academic note: The quotations from SmartPLS documentation were taken from its official Blindfolding page, accessed 04/11/2026; SmartPLS may update the page over time. Whether PLSpredict and CVPAT reporting is required still depends on the study’s specific objectives and journal or committee requirements.