{ "id": "eppk0jc20k", "slug": "serial-mediation-analysis", "title": "Serial mediation analysis", "updated": "2026-10-15", "topic_path": [ { "id": "physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical" }, { "id": "physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math" }, { "id": "physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics" }, { "id": "physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference" }, { "id": "physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/topics/physical.math.statistics.stats_statistical_inference.regression-analysis" } ], "geo": [ { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Non-geographic · 1946 to 2000: Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t1946", "label": "Non-geographic · 1946 to 2000", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946" }, { "id": "geo.nongeo.t1946.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical" }, { "id": "geo.nongeo.t1946.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math" }, { "id": "geo.nongeo.t1946.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference", "label": "Statistical inference, estimation, sampling, and testing", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference" }, { "id": "geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis", "label": "Regression analysis", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t1946.physical.math.statistics.stats_statistical_inference.regression-analysis" } ] }, { "id": "geo.nongeo.t2001.physical.math.statistics", "label": "Non-geographic · 2001 to 2020: Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical.math.statistics", "path": [ { "id": "geo.nongeo", "label": "Non-geographic", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo" }, { "id": "geo.nongeo.t2001", "label": "Non-geographic · 2001 to 2020", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001" }, { "id": "geo.nongeo.t2001.physical", "label": "Physical world and mathematics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical" }, { "id": "geo.nongeo.t2001.physical.math", "label": "Mathematics and statistics", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical.math" }, { "id": "geo.nongeo.t2001.physical.math.statistics", "label": "Statistics and probability", "api_url": "https://www.edgepedia.org/api/v1/geo/geo.nongeo.t2001.physical.math.statistics" } ] } ], "excerpt": "Serial mediation analysis is a statistical method testing whether an effect passes through two or more mediators in a specified causal order, such as X → M1 → M2 → Y.", "snippet": "Serial mediation analysis is a statistical method testing whether an effect passes through two or more mediators in a specified causal order, such as X → M1 → M2 → Y.", "node": "physical.math.statistics.stats_statistical_inference.regression-analysis", "markdown": "# Serial mediation analysis\n\nSerial mediation analysis is a statistical method in mediation analysis that tests whether the effect of an independent variable X on an outcome Y is transmitted through a sequence of two or more mediators arranged in a specified causal order, such as X → M1 → M2 → Y.[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html) It answers a question a single-mediator model cannot: whether the effect passes through one mediator and then through another, in sequence. The method estimates a set of regression equations, computes indirect effects as products of path coefficients, and tests them with bootstrap confidence intervals.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf)\n\n| Key fact | Detail |\n|---|---|\n| Defining quantity | The serial indirect effect through two mediators is the product of three paths, \\( a_{1} \\cdot d_{21} \\cdot b_{2} \\), alongside two single-mediator indirect effects[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html) |\n| Estimation | Three (or four) OLS regressions: X → M1; X and M1 → M2; X, M1, and M2 → Y; optionally X → Y for the total effect[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) |\n| Standard software | PROCESS Model 6 (SPSS, SAS, R), default 95% confidence interval, and 5,000 bootstrap resamples[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) |\n| Inference | Percentile bootstrap confidence interval; the interval excluding zero is the test, with no separate p-value in PROCESS[3](https://casrai.org/guides/hayes-process-macro-model-numbers-reporting) |\n| Model size | Custom PROCESS models allow up to 6 mediators in parallel, serial, or blended form[4](https://journals.sagepub.com/doi/full/10.1177/0002764219859633) |\n| Main caveat | Cross-sectional data with poorly defined temporal ordering often yields biased, misleading mediation estimates[5](https://link.springer.com/content/pdf/10.1007/s10742-024-00327-4.pdf) |\n\n## How it works\n\nThe building block is the product of coefficients. In a parallel multiple-mediator model, the indirect effect through mediator \\( j \\) is the product of the effect of X on \\( M_{j} \\) and the effect of \\( M_{j} \\) on Y; a serial model extends this by modeling each mediator as causally influencing later mediators in the chain.[4](https://journals.sagepub.com/doi/full/10.1177/0002764219859633) With two mediators, the model contains three indirect effects: \\( a_{1} \\cdot b_{1} \\) through M1 alone, \\( a_{2} \\cdot b_{2} \\) through M2 alone, and the serial chain \\( a_{1} \\cdot d_{21} \\cdot b_{2} \\), whose sum is the total indirect effect; the total effect decomposes as \\( c = c' + \\sum_{i=1}^{k} a_{i} \\cdot b_{i} \\).[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html) A tutorial using PROCESS notation writes the same decomposition as \\( e = d + a_{1} \\cdot c_{1} + a_{2} \\cdot c_{2} + a_{1} \\cdot b_{2} \\cdot c_{2} \\), with three primary indirect effects (\\( a_{1} \\cdot c_{1} \\), \\( a_{2} \\cdot c_{2} \\), and the serial product) and two secondary ones (\\( a_{1} \\cdot b_{2} \\) and \\( b_{2} \\cdot c_{2} \\)).[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) Conceptually, with two causally ordered mediators there are three distinct indirect effects, one strictly through M1, one strictly through M2, and one through both, and identifying these path-specific effects requires strong assumptions.[5](https://link.springer.com/content/pdf/10.1007/s10742-024-00327-4.pdf) The ordering of the mediators is specified by the analyst; the model treats X as causing M1, which in turn causes M2, and so forth, concluding with Y.[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html)\n\n## How it is done\n\nThe practitioner specifies the causal order of the mediators, then estimates the model equation by equation. For two mediators, the three regressions are M1 on X (giving \\( a_{1} \\)); M2 on X and M1 (giving \\( a_{2} \\) and \\( b_{2} \\)); and Y on X, M1, and M2 (giving the direct effect and the mediator-to-outcome coefficients), with an optional fourth regression of Y on X for the total effect.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf)\n\nInference is by bootstrap. Percentile bootstrap confidence limits are the \\( (.5\\alpha)k \\)th and \\( 1 + (1 - .5\\alpha)k \\)th sorted values of the resampled indirect effects, and resampling should be repeated at least 1,000 times.[6](https://www.quantpsy.org/pubs/preacher_hayes_2008b.pdf) Current practice uses the 2.5th and 97.5th percentiles of at least 1,000, preferably more, bootstrap estimates, and the percentile bootstrap interval has become the standard for inference about indirect effects.[7](https://diarium.usal.es/jigartua/files/2012/07/Igartua-Hayes-TSJP-2021-Mediation-Moderation-Conditional-Process-Analysis.pdf) In PROCESS, serial mediation with two mediators is model number 6, with a default 95% confidence interval and 5,000 bootstrap replications; a fixed seed is recommended for reproducibility, and the number of resamples should be raised for more complex models or if interval bounds shift between reruns.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) • [3](https://casrai.org/guides/hayes-process-macro-model-numbers-reporting) There is no separate p-value for the indirect effect under the bootstrap approach; the interval excluding zero is the test.[3](https://casrai.org/guides/hayes-process-macro-model-numbers-reporting) In Mplus, the analysis specifies 5,000 bootstrap samples and returns p-values for indirect effects, which PROCESS does not.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) In R, the manymome package fits the same three regressions with lm(), combines them with lm2list(), and bootstraps the indirect effects; its author recommends at least 5,000 or even 10,000 bootstrap samples because results may be unstable when the indirect effect is close to zero.[8](https://blogonresearch.github.io/posts/manymome_serial_mediation/index.html)\n\n## Origin\n\n Its components have a documented lineage. MacKinnon, Lockwood, and Williams published confidence limits for the indirect effect using distribution-of-the-product and resampling methods in 2004 in Multivariate Behavioral Research.[9](https://doi.org/10.1207/s15327906mbr3901_4) Taylor, MacKinnon, and Tein addressed tests of the three-path mediated effect, the serial indirect effect of a chain, in 2007 in Organizational Research Methods.[10](https://doi.org/10.1177/1094428107300344) Preacher and Hayes provided SPSS and SAS macros for asymptotic and resampling strategies for assessing and comparing indirect effects in multiple-mediator models in 2008 in Behavior Research Methods.[6](https://www.quantpsy.org/pubs/preacher_hayes_2008b.pdf) The PROCESS framework, which implements serial mediation as Model 6, is associated with Hayes's 2013 regression-based treatment of mediation, moderation, and conditional process analysis.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf)\n\n## Variants\n\nSerial versus parallel: in a parallel multiple-mediator model, mediators are allowed to correlate but not to causally influence one another; in the serial model they are linked in a causal chain.[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html) With more than three mediators, a model can blend parallel and serial processes depending on which paths between mediators are estimated and which are fixed to zero by exclusion.[1](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html) Moderated serial mediation combines the chain with moderators of the indirect effect.[11](https://pmc.ncbi.nlm.nih.gov/articles/PMC4530978/) [Estimation](https://www.edgepedia.org/estimation) also differs by platform: PROCESS fits each equation as a separate OLS regression and bootstraps products of coefficients, whereas a full SEM package such as Mplus estimates every path simultaneously, which matters with correlated errors, latent variables, or multiple outcomes.[3](https://casrai.org/guides/hayes-process-macro-model-numbers-reporting) Bayesian implementations are expanding: BayesGmed implements Bayesian causal mediation analysis with the g-formula in Stan and supports probabilistic sensitivity analysis with bias parameters as prior information.[12](https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0287037)\n\n## Applications\n\nA representative applied study in health communication surveyed 1,377 adults after an 8-month flu vaccine campaign grounded in the Health Belief Model; perceived barriers and benefits formed a serial mediation chain, and the indirect effect of exposure on behavior through perceived barriers and threat was moderated by self-efficacy, a combined serial and moderated mediation result.[11](https://pmc.ncbi.nlm.nih.gov/articles/PMC4530978/)\n\n## Limitations and alternatives\n\nThe causal ordering of mediators is an assumption of the model, not a test result, and the absence of a significant M1–M2 relation in a fitted serial model could instead suggest a parallel mediation or a single-mediator indirect effect.[2](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf) Cross-sectional designs are the central practical weakness: mediation analysis with cross-sectional data in which temporal ordering is not well-defined often produces biased, misleading results, and treating a post-treatment confounder like a baseline confounder biases estimates of the direct effect.[5](https://link.springer.com/content/pdf/10.1007/s10742-024-00327-4.pdf) A significant indirect effect based on cross-sectional data is now widely understood to be not particularly meaningful; longitudinal models that explicitly incorporate time strengthen causal inference.[13](https://www2.psych.ubc.ca/~schaller/528Readings/Preacher2015.pdf)\n\nFrom the causal mediation perspective, the second part of sequential ignorability, ignorability of the mediator given treatment and pretreatment covariates, is a strong and untestable assumption, and sensitivity analyses quantify robustness to its violation.[14](https://imai.fas.harvard.edu/research/files/BaronKenny.pdf) Strong statistical dependence between causally related mediators implies sequential ignorability is likely violated.[15](https://imai.fas.harvard.edu/research/files/medsens.pdf) Some path-specific effects, including X → M1 → M2 → Y, are not identifiable even under sequential ignorability because they involve cross-world potential outcomes, and no sensitivity analysis method is available for violation of the extended sequential ignorability assumption in the multi-stage setting.[16](https://pmc.ncbi.nlm.nih.gov/articles/PMC6428612/) On inference, published simulation findings disagree: one earlier review of a two-mediator model reported that bias-corrected and BCa bootstrapping performed best in power and Type I error rates in small to moderate samples,[6](https://www.quantpsy.org/pubs/preacher_hayes_2008b.pdf) while a later large-scale [Monte Carlo](https://www.edgepedia.org/monte-carlo) study of two-mediator sequential models found the popular BC bootstrap showed inflated Type I error rates and confidence interval under-coverage, recommending MC-ML, profile likelihood, and Bayesian methods for hypothesis testing, and the percentile bootstrap for confidence intervals with multivariate nonnormal data.[17](https://pmc.ncbi.nlm.nih.gov/articles/PMC6901816/)\n\n## References\n\n1. [More Than One Mediator (recoding of Hayes, 2018, Introduction to Mediation, Moderation, and Conditional Process Analysis)](https://bookdown.org/content/b472c7b3-ede5-40f0-9677-75c3704c7e5c/more-than-one-mediator.html)\n2. [Illustrations of serial mediation using PROCESS, Mplus and R (Lemardelet & Caron, 2022, The Quantitative Methods for Psychology, 18(1), 66-90)](https://www.tqmp.org/RegularArticles/vol18-1/p066/p066.pdf)\n3. [Hayes' PROCESS Macro: Model Numbers, Syntax, and Reporting](https://casrai.org/guides/hayes-process-macro-model-numbers-reporting)\n4. [Conditional Process Analysis: Concepts, Computation, and Advances in the Modeling of the Contingencies of Mechanisms](https://journals.sagepub.com/doi/full/10.1177/0002764219859633)\n5. [Practical challenges in mediation analysis: a guide for applied researchers (Health Services and Outcomes Research Methodology, 2025)](https://link.springer.com/content/pdf/10.1007/s10742-024-00327-4.pdf)\n6. [Asymptotic and resampling strategies for assessing and comparing indirect effects in multiple mediator models (Preacher & Hayes, 2008, Behavior Research Methods)](https://www.quantpsy.org/pubs/preacher_hayes_2008b.pdf)\n7. [Mediation, Moderation, and Conditional Process Analysis: Concepts, Computations, and Some Common Confusions (Igartua & Hayes)](https://diarium.usal.es/jigartua/files/2012/07/Igartua-Hayes-TSJP-2021-Mediation-Moderation-Conditional-Process-Analysis.pdf)\n8. [Serial Mediation in R: A Tutorial (manymome package)](https://blogonresearch.github.io/posts/manymome_serial_mediation/index.html)\n9. [David P. MacKinnon, Chondra M. Lockwood, Jason Williams (2004). Confidence Limits for the Indirect Effect: Distribution of the Product and Resampling Methods. Multivariate Behavioral Research.](https://doi.org/10.1207/s15327906mbr3901_4)\n10. [Aaron B. Taylor, David P. MacKinnon, Jenn-Yun Tein (2007). Tests of the Three-Path Mediated Effect. Organizational Research Methods.](https://doi.org/10.1177/1094428107300344)\n11. [The Health Belief Model as an Explanatory Framework in Communication Research: Exploring Parallel, Serial, and Moderated Mediation](https://pmc.ncbi.nlm.nih.gov/articles/PMC4530978/)\n12. [BayesGmed: An R-package for Bayesian causal mediation analysis | PLOS One](https://journals.plos.org/plosone/article?id=10.1371%2Fjournal.pone.0287037)\n13. [Advances in Mediation Analysis: A Survey and Synthesis of New Developments (Annual Review of Psychology)](https://www2.psych.ubc.ca/~schaller/528Readings/Preacher2015.pdf)\n14. [A General Approach to Causal Mediation Analysis (Imai, Keele & Tingley, 2010, Psychological Methods 15(4):309-334)](https://imai.fas.harvard.edu/research/files/BaronKenny.pdf)\n15. [Identification and sensitivity analysis for multiple causal mechanisms: revisiting the case of political campaigns (Imai & Yamamoto)](https://imai.fas.harvard.edu/research/files/medsens.pdf)\n16. [Generalized Causal Mediation and Path Analysis: Extensions and Practical Considerations](https://pmc.ncbi.nlm.nih.gov/articles/PMC6428612/)\n17. [Indirect Effects in Sequential Mediation Models: Evaluating Methods for Hypothesis Testing and Confidence Interval Formation (Monte Carlo simulation study)](https://pmc.ncbi.nlm.nih.gov/articles/PMC6901816/)\n\n---\n*Topic: Encyclopedia › Physical world and mathematics › Mathematics and statistics › Statistics and probability › Statistical inference, estimation, sampling, and testing › Regression analysis*\n\n*Initially written Sep 29, 2026 · Edited: Oct 15, 2026*\n\n*Copyright 2026 EdgeChat AI, a subsidiary of Biostate AI.*\n\nLicense: Edgepedia Community License 1.0, https://www.edgepedia.org/edgepedia/license\n", "same_as": [], "url": "https://www.edgepedia.org/serial-mediation-analysis", "markdown_url": "https://www.edgepedia.org/serial-mediation-analysis.md", "license": { "name": "Edgepedia Community License 1.0", "url": "https://www.edgepedia.org/edgepedia/license", "summary": "Free with credit, commercial use included. AI training is open to everyone. For other uses, organizations over USD 100M in revenue or 100M monthly users license separately.", "spdx": "LicenseRef-Edgepedia-Community-1.0" }, "credit": "\"Serial mediation analysis\", Edgepedia (EdgeChat), https://www.edgepedia.org/serial-mediation-analysis. Edgepedia Community License 1.0.", "credit_md": "\"[Serial mediation analysis](https://www.edgepedia.org/serial-mediation-analysis)\", Edgepedia (EdgeChat), [https://www.edgepedia.org/serial-mediation-analysis](https://www.edgepedia.org/serial-mediation-analysis). [Edgepedia Community License 1.0](https://www.edgepedia.org/edgepedia/license).", "credit_html": "\"Serial mediation analysis\", Edgepedia (EdgeChat), https://www.edgepedia.org/serial-mediation-analysis. Edgepedia Community License 1.0.", "speakable": "Serial mediation analysis is a statistical method testing whether an effect passes through two or more mediators in a specified causal order, such as X → M1 → M2 → Y." }