The Concept and Theory of Moderation Analysis in PLS-SEM

Moderation analysis in PLS-SEM is built for one core problem: relationships between two constructs often change depending on a third variable. That third variable—the moderator—can strengthen, weaken, or even reverse the direction of the relationship between an independent (exogenous) construct and a dependent (endogenous) construct. A common example given is how the link between collaborative culture and organizational performance varies with role ambiguity: high role ambiguity weakens the relationship, while low role ambiguity strengthens it.

Before testing moderation, researchers must decide what kind of moderation they expect. Some studies hypothesize that only one specific path in the model depends on the moderator; others expect that all relationships in the model vary with the moderator. That choice affects the testing strategy. In the framework described here, moderation modeling is handled through a two-stage approach, split into Stage 1 (main effects) and Stage 2 (interaction effect), which is recommended for building moderation terms in PLS-SEM.

Stage 1 estimates the main-effect model using the independent exogenous variable, the moderator, and the dependent endogenous variable—without yet including the interaction. From this stage, the method produces latent variable scores for the relevant constructs (labeled as y1, y2, and m). Those latent variable scores are then multiplied to create a single interaction term used in Stage 2. The interaction term is treated as a single-item construct measured by the product of the Stage 1 latent scores.

A key practical implication follows: measurement model evaluation for the interaction term is not required. Standard reliability and validity checks typically used for latent variables are not applied to the interaction term because it is represented as a single item derived from Stage 1. Instead, the measurement model should be assessed first for the constructs involved in the main-effects model—reliability and validity of the independent and moderator constructs—before introducing the moderation structure. The logic is that the interaction term’s measurement model assessment would be meaningless under this construction, and standard criteria do not transfer cleanly to a single-item interaction term.

Once the moderation is in place, structural model assessment focuses on how much the interaction improves explanation of the endogenous variable. The central metric is f² (f-square) for the interaction effect, which quantifies the change in R² when the interaction term is included versus excluded. The calculation uses R² included minus R² excluded, scaled by the included R²: f² = (R² included − R² excluded) / (1 − R² included). Interpretation relies on effect-size guidelines, but the transcript emphasizes that moderation effects are often small in practice. Traditional benchmarks (0.02/0.15/0.35 for small/medium/large, attributed to Cohen) are contrasted with more conservative standards suggested by Kenny (0.005/0.01/0.025), and it notes that average moderation effect sizes reported in tests can be around 0.009.

Finally, the interaction term’s operationalization matters. The transcript highlights three primary methods and points to simulation evidence (citing Chin, Marcolin, and Newsted, 2013) that the two-stage approach performs well for parameter recovery and statistical power. It also notes that two-stage is uniquely flexible when the independent construct or the moderator is specified formatively. Overall, the recommended workflow is: validate the measurement model for main effects first, then construct the interaction term via two-stage latent score multiplication, and evaluate moderation using f² and structural criteria.