#SmartPLS4 Series 31 - Explanatory Power (R Square and F Square) and Q Square

Model explanatory power in SmartPLS is assessed through three linked metrics: R square (insample explanatory power), F square (effect size of specific predictors), and Q square (out-of-sample predictive relevance). R square quantifies how much variance in each endogenous (dependent) latent construct is explained by its incoming paths. In the example used, perceived organizational support (POS) has an R square of 0.482, meaning 48.2% of POS variance is explained by its predictor(s). Organizational performance (OP) has an R square of 0.627, so 62.7% of OP variance is accounted for by the set of exogenous constructs pointing into OP (IM, POS, OC, CC, and ISQ in the diagram). Internal marketing (ISQ) has an R square of 0.462, indicating 46.2% of ISQ variance explained by IM. Constructs with no incoming arrows—such as IM in the described model—do not receive an R square because their variance is not explained within the model.

Thresholds help interpret whether those explained variances are adequate. Miller (1992) suggested R square values for endogenous constructs should be at least 0.10 to be considered adequate. Cohen (1988) provides effect-size style benchmarks for R square: 0.26 is substantial, 0.13 is moderate, and 0.02 is weak. A marketing-focused rule of thumb cited in the session points to higher expectations—around 0.75 for substantial, 0.33 for moderate, and 0.19 for weak—reflecting stricter standards in that literature. The practical takeaway is that each endogenous construct’s R square should be reported and interpreted using the appropriate benchmark.

F square then answers a different question: how much does each predictor matter? F square measures the change in R square when an exogenous variable is removed from the model. If removing a predictor causes little change, its contribution is small; if removing it substantially lowers R square, the predictor has a meaningful effect. Cohen’s guidelines are used for interpretation: F square of 0.02 indicates a small effect, 0.15 a medium effect, and 0.35 a large effect. In the example, removing POS, OC, or CC does not significantly change OP’s R square, while removing IM does—because IM is doing most of the explanatory work for the dependent constructs it points to. The same logic applies to mediators like PS and outcomes like ISQ, where IM is the primary driver.

Finally, Q square evaluates predictive relevance, not explained variance. Q square is expected to be greater than zero; values above zero indicate that the model reconstructs the endogenous constructs well enough to have predictive relevance. The session notes that SmartPLS4 uses PLS predict (replacing the older blindfolding approach in this context) to obtain Q square results. Interpretation follows common benchmarks: Q square values around 0.02–0.15 indicate weak predictive relevance, 0.15–0.35 moderate, and above 0.35 strong. Reporting guidance ties everything together: present R square and F square for each endogenous outcome (and summarize overall R square if needed), then add Q square values (e.g., OP’s Q square is shown as 0.561) to demonstrate predictive relevance. Together, these metrics provide a complete picture of explanatory power and prediction quality in a structural model.