Moderation Analysis in PLS-SEM: Adding an Interaction Construct in AnalyVa

Moderation is the PLS-SEM technique that gets misread most often: a non-significant interaction term doesn’t mean the moderator doesn’t matter, and a significant one doesn’t automatically mean it’s large. This post picks up the four-construct model from the indicator-cleaning walkthrough, adds a moderator, and runs it through AnalyVa’s full significance pipeline — Beta, p-value, and significance-star display — so the difference between “detected” and “meaningful” stays visible the whole way through.

Adding the moderator construct

Step 1 — Build the WP construct from its indicators. Select WP1–WP3 in the sidebar the same way any other construct is built (click, shift-click, drag to canvas). AnalyVa confirms with “Created WP” and places it as a standalone construct, not yet connected to anything.

WP construct created from WP1, WP2, WP3, sitting unconnected on the canvas

Drawing the interaction paths

A moderator needs one interaction path per relationship it’s hypothesized to moderate. This model tests four: does WP change the strength of WM → WSE, WA → WSE, PFT → WSE, or CFT → WM?

Step 2 — H9: WP × WM → WSE. With the Path tool active, click WP, then click WSE. AnalyVa draws the interaction as a dashed purple line — visually distinct from the solid blue structural paths — and labels it automatically.

H9 interaction path drawn from WP to WSE, dashed purple

Step 3 — H10: WP × WA → WSE. Same click-click pattern for the second interaction term.

H10 interaction path added, two dashed purple lines now visible

Step 4 — H11: WP × PFT → WSE. A third interaction term, same pattern.

H11 interaction path added, three dashed purple lines converging on WSE

Step 5 — H12: WP × CFT → WM. The fourth interaction targets WM instead of WSE — the moderator doesn’t have to point at the same endogenous construct every time.

H12 interaction path added, all four moderation paths visible

Step 6 — Reposition WP for a readable diagram. With all four interactions drawn, drag WP to a clearer spot (top center, in this case) using the canvas’s arrow controls. All four dashed paths — H9 through H12 — now fan out clearly from WP.

WP repositioned to the top of the canvas with H9–H12 clearly visible

Running the moderated model

Step 7 — Open Run → PLS-SEM → Standard Algorithms → PLS-SEM algorithm again. The same menu used to run the base model in the earlier post — running it again re-estimates with the four new interaction terms included.

The PLS-SEM submenu reopened with the moderated model on canvas

Step 8 — Check the moderation-specific setup option, then start. The configuration dialog has the same Path/Factor/PCA weighting choice as before, plus one option that only matters for moderation models: Use SmartPLS-compatible centroid proxy for moderation products. Leaving it unchecked matches R/seminr-style path weighting; checking it matches SmartPLS’s centroid approach for building interaction terms. Pick whichever matches the software you’re benchmarking against, then click Start calculation.

The PLS-SEM algorithm dialog with the SmartPLS-compatible centroid checkbox for moderation products

Adding the moderator changes the outcome construct’s explanatory power: WSE’s R² moves from 0.335 in the unmoderated model to 0.366 here — the four interaction terms and WP’s direct effect together account for that gain.

Bootstrapping for significance

Path coefficients alone don’t tell you which moderation effects are real. That requires bootstrapping.

Step 9 — Open Run → PLS-SEM → Bootstrapping.

Run menu open with Bootstrapping highlighted, moderated model already estimated

Step 10 — Read the Beta (p) display. AnalyVa runs 5,000 bootstrap resamples (“fast parallel”) and, by default, annotates each path with its coefficient and p-value inline: -0.034 (p=0.313), -0.053 (p=0.140), -0.007 (p=0.814) — all three visible interaction terms here are non-significant at conventional thresholds.

The bootstrapped model with Beta (p) values shown inline on each path

Step 11 — Switch the Path display to Significance Stars. The dropdown at the bottom toolbar controls how path values render: Beta, Beta (p), Significance Stars, p-value, or None. Switching to Significance Stars trades exact p-values for a faster visual scan — useful once you already know roughly where the interesting cases are.

The Path display dropdown open, Significance Stars selected

Step 12 — Read the starred diagram. Every path now carries ***, **, *, or ns, with a legend at the bottom of the canvas (* p<0.05 ** p<0.01 *** p<0.001 ns p>0.05). All four interaction terms read ns. The direct paths — CFT → WSE, WM → WSE, PFT → WSE — stay solidly significant at ***.

The full model with significance stars on every path and the legend visible

Reading the moderation table

Stars on the canvas are a summary. The Results panel has the full picture.

Step 13 — Open the Moderations (Interaction Effects) table. Below the standard bootstrap output, AnalyVa groups the four interaction terms into their own table with a plain-language effect label:

Term	β	Effect
WP × WM → WSE	0.0186	Weak
WP × WA → WSE	−0.0071	Weak
WP × PFT → WSE	−0.0529	Moderate
WP × CFT → WM	−0.0337	Weak

None of the four reach a large effect size, and — cross-referencing the bootstrap table below — none reach significance either (p = 0.610, 0.814, 0.140, and 0.313 respectively). That’s a real, reportable result: this moderator doesn’t meaningfully change any of the four paths tested, at least not in this sample.

The Moderations (Interaction Effects) table with beta and Weak/Moderate labels

Step 14 — Cross-check with the full bootstrap table. Every path — structural and interaction — gets its own row with Beta, SE, t, p, and the 95% bootstrap confidence interval. Hovering any p cell surfaces a plain-language tooltip (“★★★ Highly significant (p < .001)”), which is a fast way to explain a results table to a co-author who doesn’t read t-statistics fluently.

The full bootstrap results table with a hover tooltip reading Highly significant

Step 15 — Note which paths are genuinely significant. The base structural paths (PFT → WSE, CFT → WSE, WM → WSE, WP → WSE, CFT → WM, PFT → WM, WP → WM) all clear p<.001. Only the interaction terms are the non-significant group here — a pattern worth stating explicitly in a manuscript: “the direct effects held; none of the four hypothesized moderations were supported.”

The bootstrap table with the highly-significant tooltip and non-significant interaction rows visible

Loadings and indirect effects, same run

Step 16 — Scroll to Bootstrap Loadings. The same 5,000-sample bootstrap also re-estimates every outer loading with its own SE, t, and p — every indicator here clears p<.001.

Bootstrap Loadings table listing every indicator with SE, t, and p

Step 17 — Check Bootstrap Indirect Effects for mediation. Because CFT and PFT both route through WM and WA on their way to WSE, AnalyVa also reports the indirect (mediated) effect for each path — CFT → WM → WSE, CFT → WA → WSE, PFT → WM → WSE, PFT → WA → WSE — with its own confidence interval. This comes free in the same run; no separate mediation analysis needed.

Bootstrap Indirect Effects table showing four mediation paths with confidence intervals

What to report

A null moderation result is still a result. The write-up here would state: R² for WSE improved marginally with the moderator added (0.335 → 0.366), but all four interaction terms were non-significant under 5,000-sample bootstrapping (p > 0.10 in every case), so the hypothesis that WP moderates these relationships is not supported in this sample. That’s a defensible, complete finding — and every number needed to write it came out of a single PLS-SEM run plus one bootstrap pass.