Probing interactions in fixed and multilevel regression: Inferential and graphical techniques
Open accessAbstract
Many important research hypotheses concern conditional relations in which the effect of one predictor varies with the value of another. Such relations are commonly evaluated as multiplicative interactions and can be tested in both fixed- and random-effects regression. Often, these interactive effects must be further probed to fully explicate the nature of the conditional relation. The most common method for probing interactions is to test simple slopes at specific levels of the predictors. A more general method is the Johnson-Neyman (J-N) technique. This technique is not widely used, however, because it is currently limited to categorical by continuous interactions in fixed-effects regression and has yet to be extended to the broader class of random-effects regression models. The goal of our article is to generalize the J-N technique to allow for tests of a variety of interactions that arise in both fixed- and random-effects regression. We review existing methods for probing interactions, explicate the analytic expressions needed to expand these tests to a wider set of conditions, and demonstrate the advantages of the J-N technique relative to simple slopes with three empirical examples.
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Because only a subsample of MIDUS participants provided data for the DNAm project, the sample size of the study was severely limited, which may affect the power of the analyses.
“Finally, because only a subsample of MIDUS participants provided data for the DNAm project, the sample size of the study was also severely limited, which may affect the power of the analyses (Bauer & Curran, 2005).”
From Grandparent Caregiving and Epigenetic Aging among Midlife and Older Adults in the United States (2026) · cites this paper as Bauer & Curran, 2005
In “Evaluating Interactions in Multilevel Models” (page not available), Bauer and Curran caution that small samples can make tests of conditional effects less accurate or stable. That supports a general concern about sample-size limitations, but the paper does not address the MIDUS DNAm subsample or specifically say that a smaller sample reduces statistical power. (LLM, conf=0.72)
Experimental — accuracy not yet measuredSignificant simple effects can occur even when interaction terms are nonsignificant.
“since significant simple effects can occur even when interaction terms are nonsignificant (Bauer & Curran, 2005).”
From Grandparent Caregiving and Epigenetic Aging among Midlife and Older Adults in the United States (2026) · cites this paper as Bauer & Curran, 2005
The significant DunedinPACE simple effect for grandmothers may be a result of low statistical power.
“the significant effect may be a result of low statistical power (Bauer & Curran, 2005).”
From Grandparent Caregiving and Epigenetic Aging among Midlife and Older Adults in the United States (2026) · cites this paper as Bauer & Curran, 2005
The sections on tests of simple slopes and multiple testing discuss how significance is assessed and how Type I error can accumulate across tests. The Figure 1 discussion mentions a trade-off between simultaneous inference and power, but our copy does not say that low statistical power can explain a significant simple effect; it does not address the DunedinPACE result in grandmothers. (LLM, conf=0.76)
Experimental — accuracy not yet measuredGiven the limited sample size, the power to detect interactions may be insufficient.
“Given the limited sample size, the power to detect interactions may be insufficient (Bauer & Curran, 2005).”
From Grandparent Caregiving and Epigenetic Aging among Midlife and Older Adults in the United States (2026) · cites this paper as Bauer & Curran, 2005
The ‘Evaluating Interactions in Multilevel Models’ section says that small upper-level samples can make cross-level interaction results sensitive to the choice of test distribution and that small-sample conditional-effect tests need further study. It does not say that a limited sample reduces power to detect interactions. Searches for sample size, interaction power, and underpowered tests did not establish that claim. (LLM, conf=0.70)
Experimental — accuracy not yet measured
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“Given the limited sample size, the power to detect interactions may be insufficient (Bauer & Curran, 2005).”
Influential
- Authors
- Bauer, D. J., & Curran, P. J.
- Affiliations
- University of North Carolina at Chapel Hill (US)
- Venue
- Multivariate Behavioral Research
- Publisher
- Informa UK Limited
- Published
- 2005-07
- Volume
- 40
- Issue
- 3
- Pages
- 373-400
- ISSN
- 0027-3171 (ISSN-L)
- 1532-7906
- OpenAlex
- W2003258289
- Cited by
- 1,506
- References
- 6
- Citations by year
- 2026: 95 · 2025: 103 · 2024: 121 · 2023: 109 · 2022: 107 · 2021: 120 · 2020: 120 · 2019: 103 · 2018: 81 · 2017: 105 · 2016: 89 · 2015: 71 · 2014: 59 · 2013: 56 · 2012: 44
- FWCI
- 11.07
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Multivariate Behavioral Research (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Applications
- Social Sciences › Economics, Econometrics and Finance › Economics and Econometrics › Spatial and Panel Data Analysis
- Keywords
- interaction effects, random effects regression, fixed effects regression, multilevel regression, conditional relations, graphic techniques
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