Moderation Analysis

When the coefficient is not a constant

Satisfaction drives loyalty — about 0.50 in the structural lesson. But does it drive loyalty equally for a customer who can walk away tomorrow and one who is locked into a contract?

That is moderation. A mediator transmits an effect; a moderator changes its strength. Formally, the CUSA → CUSL coefficient stops being a constant and becomes a line: a base effect plus an interaction weight times the moderator.

Building the interaction term

library(seminr)

corp_rep_mm_mod <- constructs(
  composite("COMP", multi_items("comp_", 1:3)),
  composite("LIKE", multi_items("like_", 1:3)),
  composite("CUSA", single_item("cusa")),
  composite("SC",   multi_items("switch_", 1:4)),
  composite("CUSL", multi_items("cusl_", 1:3)),
  interaction_term(iv = "CUSA", moderator = "SC", method = two_stage))

corp_rep_sm_mod <- relationships(
  paths(from = c("COMP", "LIKE"),          to = c("CUSA", "CUSL")),
  paths(from = c("CUSA", "SC", "CUSA*SC"), to = c("CUSL")))

There are three ways to build the term. Product-indicator multiplies all indicator pairs — only defensible with reflective measures. Orthogonalization fixes multicollinearity but complicates interpretation. Two-stage uses construct scores from a first-stage model: it works with any measurement mode — including our single-item CUSA — and has the best statistical power. Default to two-stage.

Note that SC enters the structural model twice: as a direct predictor of loyalty and inside the interaction term. You must always include the moderator’s main effect. R² for loyalty ticks up from 0.56 to 0.57.

Is the interaction significant?

set.seed(123)
corp_rep_boot_mod <- bootstrap_model(corp_rep_pls_model_mod, nboot = 1000)
summary(corp_rep_boot_mod, alpha = 0.05)$bootstrapped_paths |> round(3)

The interaction is −0.071, CI −0.136 to −0.009 — excludes zero, significant. The negative sign says: the higher the switching costs, the weaker the satisfaction-to-loyalty link.

SC’s own direct effect is not significant. That is fine, and it stays in the model regardless.

Effect size — use the right benchmark

corp_rep_summary_mod$fSquare

Interaction f² is 0.014. Against Cohen’s usual 0.02 / 0.15 / 0.35 that looks negligible — but interaction effects are systematically small, and judging them by Cohen’s benchmarks understates every moderation ever published.

Use Kenny’s (2018) benchmarks for moderation: 0.005 small, 0.01 medium, 0.025 large. By those, 0.014 is a solid medium effect. Cite the right benchmark, or a reviewer will do it for you.

Simple slopes — the figure for your paper

slope_analysis(moderated_model = corp_rep_pls_model_mod,
               dv = "CUSL", moderator = "SC", iv = "CUSA",
               leg_place = "bottomright")

Note this takes the estimated model, not the bootstrap object.

Three lines: satisfaction → loyalty at low, mean, and high switching costs. At low SC the slope is steepest, around 0.54; at high SC it flattens to roughly 0.40. All three remain positive — satisfaction always helps, it simply buys less loyalty when customers are already captive.

Managerially: in high-switching-cost segments (contracts, ecosystems) satisfaction investments return less loyalty, because loyalty is partly involuntary. In low-switching-cost segments satisfaction is your main defence.

Categorical moderation is multigroup analysis

Here is why the textbook puts MGA in the moderation chapter. We just moderated with a continuous variable. A moderator can equally be categorical — a group. Same question, group instead of scale.

table(corp_rep_data$servicetype)   # 125 vs 219

set.seed(123)
corp_rep_mga <- estimate_pls_mga(corp_rep_pls_model,
                                 corp_rep_data$servicetype == 1,
                                 nboot = 1000)
corp_rep_mga

Henseler’s MGA p-value is one-sided. A path differs at the 5% level when p < .05 (group 1’s path is larger) or p > .95 (group 2’s is larger). Reading it as a conventional two-sided p is a common and consequential error.

Three of five paths differ across service types. Competence buys loyalty only in group 1; likeability matters roughly twice as much in group 2; satisfaction converts to loyalty more in group 1. The pooled model averaged all three differences away.

One caveat before you trust any of this: measurement invariance. Run MICOM (Henseler, Ringle & Sarstedt, 2016) before comparing groups, or apparent path differences may just be measurement differences. MICOM is beyond the workbook’s scope, but the obligation is not optional.

R practice — use version control. Even a solo analysis deserves a Git history. “Which version produced Table 3?” should never be a guess.

Going further

Chapter 7 of Hair et al. (2026) covers both moderation and multigroup analysis. That completes the core series — the seminrExtras lesson introduces the advanced toolkit beyond the textbook.