How to Report Moderated Mediation in APA 7

The mistake I see most often when reviewing moderated mediation is always the same one: the indirect effect is estimated at each level of the moderator, it comes out significant at one level and not at the other, and the paper concludes that the mediation depends on the moderator. Comparing two significance decisions is not the same as testing that they differ, and since 2015 there has been a statistic that actually tests it. Here is what APA 7 requires, how PROCESS model 7 differs from model 14, and how the table is built. The general guide is in how to report results in APA 7, and mediation without a moderator in how to report a mediation analysis.

What moderated mediation actually is

You have mediation when X influences Y through M. You have moderated mediation when the strength of that indirect path depends on a fourth variable. The indirect effect stops being a single number and becomes a function of the moderator, so the question changes from “does it mediate?” to “for whom does it mediate more?”.

That changes the whole write-up. If the indirect effect is a linear function of the moderator, that function has a slope, and the slope is what you have to test. Hayes (2015) called it the index of moderated mediation, and it is the statistic your hypothesis rests on. Everything else — the conditional effects, the tidy two-line figure — comes after it.

Do not confuse it with mediated moderation, which is a different model: there it is the product of X and the moderator that travels through M, not X itself. And do not confuse it with splitting the sample and running a separate mediation in each half. Splitting wastes power, dichotomizes a variable that is usually continuous, and above all compares nothing: you end up with two intervals that never speak to each other.

Model 7 versus model 14: where the moderator sits

In model 7 the moderator acts on the a path, from X to M. The mediator equation contains X, the moderator and their product, so the indirect effect is (a₁ + a₃W)b and the index of moderated mediation is a₃b. This is the model for hypotheses such as “job demands only produce emotional exhaustion when job control is low”: what the moderator changes is the entrance to the mechanism.

In model 14 the moderator acts on the b path, from M to Y. The outcome equation contains M, the moderator and their product, so the indirect effect is a(b₁ + b₃W) and the index is ab₃ (b₁ is the coefficient on M, b₂ the one on the moderator and b₃ the one on the product, just as a₃ carries the product in model 7). This is the model for hypotheses such as “everyone gets exhausted, but exhaustion only turns into turnover intentions when organisational support is poor”: what changes is the exit from the mechanism.

The neighbors reviewers will ask about: model 8 is model 7 plus moderation of the direct effect, model 15 is model 14 plus that same moderation, model 58 moderates the a and b paths with the same moderator, and model 59 adds the direct effect on top. Choosing between them is a theoretical decision, not a search. If you fit model 7 and model 14 and keep whichever gives an interval that misses zero, you have selected a model with the data in front of you and the index no longer means what you say it means.

In the Method section state the model number, the PROCESS version and the software: “PROCESS v4.2 for SPSS, model 14”. If you work in R with lavaan or in Mplus there is no model number, so write out both equations and define the index explicitly. How each model is set up step by step is covered in the guide to mediation and moderation with PROCESS.

The index and its bootstrap interval

The index is tested with a bootstrap confidence interval, exactly like the indirect effect in a simple mediation, and for the same reason: the product of two coefficients is not normally distributed, so there is no trustworthy standard error and therefore no p-value to give. The rule is that the interval must exclude zero. Writing “index = −0.07, p = .012” is a clear error — there is no p to be had there.

Always report three things about the bootstrap: how many resamples (5,000 is the minimum you see published, 10,000 is the sensible default today), which type of interval (percentile is what Hayes recommends; the bias-corrected interval inflates Type I error and is on its way out) and the confidence level. Add the random seed if you want the number to be reproducible: without it, two runs of the same analysis give slightly different intervals, and a reviewer who reruns your syntax will get figures that do not match yours.

Two limits worth knowing before you write the discussion. The index captures linear moderation only: if you expect a U-shaped effect, it will not find it. And if your moderator is categorical with more than two levels there is no single index but one per contrast — with three groups you have two indices, and you must say which category is the reference.

Alongside the index go the conditional indirect effects, which is where magnitude is read. The convention is to probe at the mean of the moderator and at ±1 SD, or at the 16th, 50th and 84th percentiles when the distribution is skewed. With a continuous moderator, the Johnson-Neyman technique gives the exact value at which the indirect effect stops being distinguishable from zero, and it is more informative than three points chosen by convention.

Worked example in the text (model 14)

“We estimated a moderated mediation model with PROCESS v4.2 for SPSS (model 14), using 10,000 bootstrap resamples and 95% percentile confidence intervals, in a sample of N = 250 hospital nurses. Job demands predicted emotional exhaustion, a = 0.46, SE = 0.07, t(248) = 6.57, p < .001. Emotional exhaustion predicted turnover intentions, b₁ = 0.40, SE = 0.06, t(245) = 6.67, p < .001, and that path was moderated by perceived organisational support, b₃ = −0.15, SE = 0.05, t(245) = −3.00, p = .003. The direct effect remained significant, c′ = 0.18, SE = 0.07, t(245) = 2.57, p = .011.”

“The index of moderated mediation excluded zero, index = −0.07, 95% CI [−0.13, −0.02]. The indirect effect of job demands on turnover intentions through emotional exhaustion was strongest at low support (−1 SD), effect = 0.25, 95% CI [0.15, 0.37], smaller at the mean, effect = 0.18, 95% CI [0.11, 0.27], and smallest at high support (+1 SD), effect = 0.12, 95% CI [0.04, 0.20].”

Three formatting details that slip through constantly. Symbols are italicized (a, b, c′, t, p, SE, N, SD) while Greek letters stay upright. The leading zero belongs only to statistics that can exceed 1: unstandardised coefficients and the index keep it (0.46, −0.07), the p-value does not (.003). And the degrees of freedom differ between the two equations: in model 14 the mediator equation has one predictor and the outcome equation has four, which is where 248 and 245 come from.

One warning about b₁: with the product term in the model, that coefficient is not “the effect of exhaustion”, it is the effect of exhaustion when the moderator equals zero. If you mean-centered the moderator, that is the effect at the mean; if you did not center it and support is scored from 1 to 7, it is the effect at a value no participant has. Say in the Method whether you centered, because it changes what half the table means. If the raw PROCESS output is in front of you and you cannot tell which block holds the index, paste the output into the interpreter and it breaks it down in this format.

Already drafted it? Paste your Results section into Review one section: it reads it the way a reviewer would and returns the first objection, attached to the sentence that causes it.

The table

A moderated mediation table has two panels, one per equation. The upper panel is the mediator model (consequent: M), with rows for X, the moderator and the product term; the lower panel is the outcome model (consequent: Y). Each row carries the unstandardised coefficient, its SE, the confidence interval and the p-value. At the foot of each panel go the R² and the F with its degrees of freedom.

Below that, in a block of its own with its own heading, come the conditional indirect effects — one row per value of the moderator, with the effect and its bootstrap interval — closed by the row for the index of moderated mediation. That last row is the point of the whole table and is often the only number a hurried reviewer looks for, so do not bury it in a footnote.

APA formatting: horizontal rules at the top, under the headings and at the foot, no vertical rules at all, and a note giving the number of resamples, the interval type and what the moderator values represent. Do not paste the PROCESS output as it comes: those dashed tables carry columns APA does not want (LLCI and ULCI collapse into a single “95% CI [ , ]”) and they announce that nobody reread the manuscript. If you would rather have it laid out for you, the APA 7 mediation table generator produces a version ready to paste into Word.

What reviewers flag

Concluding from two significance tests. “The indirect effect was significant for women and not for men, indicating moderated mediation” indicates nothing. Two intervals, one crossing zero and one not, can overlap almost entirely. The comparison is made with the index, which is precisely why the index exists.

Not reporting the index. It belongs in the text and in the table, with its interval. Without it you have descriptive conditional effects and no test of the hypothesis your title announces.

Omitting the resamples, the interval type or the model number. It is one sentence, and without it the analysis is not reproducible: “we used PROCESS” does not say which of the ninety-odd models you ran. And if you fitted several until one worked, say so and present the preferred one as exploratory; it shows, and it gets asked about.

Probing the moderator outside the observed range. If the mean minus one standard deviation falls below the floor of your scale, that conditional effect describes people who do not exist. Check the range before you choose probe values.

Running moderated mediation on a simple-mediation sample. Product terms produce small effects and large standard errors, so an interaction needs considerably more participants than a main effect. With N = 90 and a continuous moderator, a non-significant index does not tell you the moderator is irrelevant, it tells you the study could not have seen it.

Frequently asked questions

What is the index of moderated mediation?

It is the slope of the function linking the indirect effect to the moderator, proposed by Hayes (2015). In PROCESS model 7 it equals a₃b; in model 14 it equals ab₃, with subscript 3 marking the product term in both cases. It is tested with a bootstrap confidence interval: if the interval excludes zero, the indirect effect changes linearly with the moderator. It is the only statistic that genuinely tests a moderated mediation hypothesis.

What is the difference between PROCESS model 7 and model 14?

In model 7 the moderator acts on the a path, from the independent variable to the mediator, and the index is a₃b. In model 14 the moderator acts on the b path, from the mediator to the outcome, and the index is ab₃. In short, model 7 moderates the entrance to the mechanism and model 14 moderates its exit. The choice is theoretical and must be justified in the Method section, not settled by fitting both and keeping the significant one.

How do you report moderated mediation in APA 7?

Report the index with its bootstrap interval and no p-value: index = −0.07, 95% CI [−0.13, −0.02]. Around it go the coefficients of both equations (with SE, t and p), the conditional indirect effects at specific values of the moderator, the PROCESS model number, the number of resamples and the interval type. The index keeps its leading zero because it can exceed 1.

Can you report a p-value for the index of moderated mediation?

No. The index is a product of coefficients and its sampling distribution is not normal, which is exactly why bootstrapping replaced the Sobel formula. Inference is made from the confidence interval: if it excludes zero, you have evidence of moderated mediation. A manuscript that prints a p-value next to the index is mixing two different frameworks.

How many bootstrap resamples should you request?

PROCESS defaults to 5,000 and papers are published with that, but 10,000 is the sensible default today and costs no meaningful time on a model this size. Use percentile intervals, which is what Hayes recommends; bias-corrected intervals inflate Type I error. Set the random seed as well, so that someone else can reproduce your exact figures.

Is it moderated mediation if the indirect effect is significant in only one group?

No, and this is the most common error in the whole analysis. One interval crossing zero while the other does not can be caused by differences in group size or variance rather than by any difference between the indirect effects. The difference has to be tested directly with the index of moderated mediation, in the same way an interaction is tested with a product term rather than by comparing two separate correlations.

With the index and its bootstrap interval, the conditional effects, the model number on record and a two-panel table, your moderated mediation is reported the way APA 7 asks. If the design gets heavier — two moderators, serial mediators, repeated measures, or data nested within sites — we can work through it together in my statistical consulting.