Worked reporting example

The example below shows how to report a synthetic trial-level mediation analysis without overstating the estimand. Replace every bracketed value with the output from the actual fitted model and retain the scale language appropriate to the selected families.

Study-method wording

We analyzed repeated trial-level observations using a hierarchical mediation model with participants as the clustering unit. The trial-varying exposure and gaze mediator were decomposed before modeling into within-participant deviations and participant means. The gaze mediator was modeled with a Gaussian likelihood and the binary override outcome with a Bernoulli-logit likelihood. Trials with missing outcomes or mediator values were not recoded as zero. The predeclared quality_eligible policy restricted the inferential dataset to rows meeting the gaze-quality rule while preserving excluded-row provenance. Participant random intercepts were included in both submodels, with a participant-varying exposure→mediator slope where supported by the design. Weakly informative priors were specified before sampling.

Diagnostic wording

Four chains were sampled for 1,000 post-warmup draws per chain after 1,000 warmup iterations using seed 2026. The largest R-hat was [1.00x], the minimum bulk ESS was [value], and the fit produced [0] divergences and [0] maximum-tree-depth hits. Posterior predictive checks were inspected for both the mediator and outcome submodels. Because all critical convergence checks passed, posterior indirect-effect summaries were extracted. [If any critical diagnostic fails, replace this sentence with a transparent failure statement and do not report the blocked indirect effect as valid.]

Result wording for a binary outcome

The within-participant coefficient-product indirect effect (a_W × b_W) was [posterior mean/median], with a 95% credible interval of [[lower], [upper]]. This estimand is on the model's linear-predictor product scale. It should not be interpreted as a percentage-point natural indirect effect on outcome probability. The direct within-participant path (c'_W) was [estimate, interval]. Between-participant exposure paths were [estimated / not estimable because X_between was constant in the balanced within-subject design].

Interpretation wording

The result is consistent with a trial-level pathway in which within-person variation in the exposure is associated with variation in the gaze mediator and, conditional on the exposure path, with the binary decision outcome. The hierarchical model separates this within-person pattern from stable between-person differences. Causal mediation language requires additional assumptions about temporal ordering and confounding; the coefficient-product estimate alone does not establish a natural indirect effect.

Limitation wording

The gaze mediator is an operational process measure and does not by itself establish the latent psychological construct often associated with that measure. In addition, the complete-case/quality-eligible estimand is conditional on the declared observation rule, and informative gaze loss could bias the fitted pathway. Sensitivity analyses compared [prior scales / likelihoods / missingness policies / random-slope structures], with [brief description of material or negligible changes].

Compact results table

Quantity	Posterior summary	Scale / note
a_W	[estimate, 95% CrI]	mediator-model scale
b_W	[estimate, 95% CrI]	outcome linear-predictor scale
within indirect a_W × b_W	[estimate, 95% CrI]	linear-predictor product scale
within direct c'_W	[estimate, 95% CrI]	outcome linear-predictor scale
between indirect a_B × b_B	[estimate or not estimable]	report only when both paths are data-supported
max R-hat	[value]	convergence diagnostic
min bulk ESS	[value]	convergence diagnostic
divergences	[value]	should be reported explicitly
tree-depth hits	[value]	report when backend supplies it

Programmatic report helper

Use report_multilevel_gaze_mediation() for a structured model summary, but treat the returned text/table as a starting point for the manuscript rather than a substitute for design-specific interpretation. Effect extractors remain convergence-gated by default.

Related functions:

• summarise_multilevel_mediation()
• estimate_within_indirect_effect()
• estimate_between_indirect_effect()
• posterior_direct_effect()
• posterior_total_effect()
• check_mediation_convergence()
• posterior_predictive_check_mediation()
• plot_indirect_effect_distribution()
• report_multilevel_gaze_mediation()