Cited by 308Psychometric Methodologies and TestingStatistical Methods and Bayesian InferenceMeta-analysis and systematic reviews

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semPower: General power analysis for structural equation models

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Moshagen, Morten, Bader, Martina·2023·Behavior Research Methods

DOI 10.3758/s13428-023-02254-7PMC PMC11522193

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Abstract

Structural equation modeling (SEM) is a widespread and commonly used approach to test substantive hypotheses in the social and behavioral sciences. When performing hypothesis tests, it is vital to rely on a sufficiently large sample size to achieve an adequate degree of statistical power to detect the hypothesized effect. However, applications of SEM rarely consider statistical power in informing sample size considerations or determine the statistical power for the focal hypothesis tests performed. One reason is the difficulty in translating substantive hypotheses into specific effect size values required to perform power analyses, as well as the lack of user-friendly software to automate this process. The present paper presents the second version of the R package semPower which includes comprehensive functionality for various types of power analyses in SEM. Specifically, semPower 2 allows one to perform both analytical and simulated a priori, post hoc, and compromise power analysis for structural equation models with or without latent variables, and also supports multigroup settings and provides user-friendly convenience functions for many common model types (e.g., standard confirmatory factor analysis [CFA] models, regression models, autoregressive moving average [ARMA] models, cross-lagged panel models) to simplify power analyses when a model-based definition of the effect in terms of model parameters is desired.

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Fig. 1 Central and noncentral χ2 distributions, critical χ2 value, and associated decision errors. Note. Central χ2(df) distribution (solid line) and noncentral χ2(df, λ) distributions (dashed lines) with df = 50 and (from top to bottom) non-centrality parameters of λ = 30.25, λ = 46.75, and λ = 62.375. The dotted vertical line indicates a critical value for χc² of 67.50, which corresponds to alpha = .05. The beta-errors are β = .20, β = .03, and β = .003, respectivelyCC BY · PubMed Central

Fig. 2 Statistical power as a function of sample size to detect RMSEA = .05 on 50 df (F0 = 0.125)CC BY · PubMed Central

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G*Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences
Faul, F., Erdfelder, E., Lang, A.-G., & Buchner, A. (2007) · Behavior Research Methods · doi:10.3758/bf03193146 · Cited by 65,971 · cited 2×
“In a power analysis, one of these quantities is computed as a function of the other quantities, giving rise to different types of power analyses (Faul et al., 2007).”
BackgroundMethod
lavaan : An R Package for Structural Equation Modeling
Rosseel, Y. (2012) · Journal of Statistical Software · doi:10.18637/jss.v048.i02 · Cited by 27,955 · cited 1×
“…the model implementing the null hypothesis of interest is then fitted to the population variance–covariance matrix using the lavaan package (Rosseel, 2012), so that the population minimum F 0 along with the resulting model-implied variance covariance matrix ( ̂ 𝚺 ) and mean vector ( ̂ 𝛍…”
Method
Evaluating Goodness-of-Fit Indexes for Testing Measurement Invariance
Cheung, G. W., & Rensvold, R. B. (2002) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0902_5 · Cited by 16,280 · cited 1×
“For example, it has been suggested that a decline of ≥ .02 in the Mc associated with a metric in comparison to a configural invariance model may be considered a meaningful departure from measurement invariance (Cheung & Rensvold, 2002).”
Background
Power analysis and determination of sample size for covariance structure modeling.
MacCallum, R. C., Browne, M. W., & Sugawara, H. M. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.2.130 · Cited by 10,418 · cited 2×
“…of a measure that shows a direct relation to the non-centrality parameter, which is afforded by all non-centrality-based measures of fit such as the minimum of the employed fitting function itself or derived indices such as the RMSEA (because F 0 = df ∙ RMSEA 2 ; e.g., MacCallum et al., 1996).”
Method
The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis.
Curran, P. J., West, S. G., & Finch, J. F. (1996) · Psychological Methods · doi:10.1037/1082-989x.1.1.16 · Cited by 5,512 · cited 1×
“When the comparison is performed against the saturated model, however, simulated power is often higher as a consequence of the well-documented positive bias of the model test when the assumptions are violated (e.g., Curran et al., 1996; Moshagen, 2012).”
Method
How to Use a Monte Carlo Study to Decide on Sample Size and Determine Power
Muthén, L. K., & Muthén, B. O. (2002) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1207/s15328007sem0904_8 · Cited by 2,362
Reporting practices in confirmatory factor analysis: an overview and some recommendations
Jackson, D. L., Gillaspy, J. A., & Purc-Stephenson, R. (2009) · Psychological Methods · doi:10.1037/a0014694 · Cited by 2,242 · cited 8×
“Existing tools providing analytical power analyses specifically for SEM (e.g., MacCallum et al., 1996, 2006; Preacher & Coffman, 2006) require provision of a non-centrality-based measure of effect such as the RMSEA and are thus limited to a model-free approach.”
BackgroundInfluential
Asymptotically distribution-free methods for the analysis of covariance structures.
Browne, M. (1984) · British Journal of Mathematical & Statistical Psychology · doi:10.1111/j.2044-8317.1984.tb00789.x · Cited by 1,890 · cited 2×
“If the H0 model is correct, assuming multivariate normality, a sufficiently large sample size, and several mild regularity conditions (Browne, 1984; Yuan & Bentler, 2007), (1)”
Method
5. Three Likelihood-Based Methods for Mean and Covariance Structure Analysis with Nonnormal Missing Data
Yuan, K.-H., & Bentler, P. (2000) · Sociological Methodology · doi:10.1111/0081-1750.00078 · Cited by 1,847 · cited 1×
“…= list(estimator = ' mlr ' ) leads to a simulated power estimate relying on a corrected test statistic that is asymptotically equivalent to the Yuan & Bentler (2000) statistic, whereas the analytic power estimate is still based on the asymptotically expected distributions based on ML.…”
Determining power and sample size for simple and complex mediation models
Schoemann, A. M., Boulton, A. J., & Short, S. D. (2017) · Social Psychological and Personality Science · doi:10.1177/1948550617715068 · Cited by 1,837 · cited 1×
“…approaches to statistical power necessarily allow for a model-based definition of the effect of interest, most existing tools implement post hoc power analyses only and are typically limited to particular model types (Kievit et al., 2018; Mulder, 2022; Schoemann et al., 2017; Zhang & Liu, 2018).”
Method

Show all 42 references

Research works printed but not linked: 3

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Addressing Vaccine Hesitancy: Validating the PACV Survey for Croatian Parents
Ćurković, A., & Matana, A. (2025) · Infectious Disease Reports · doi:10.3390/idr17010003 · Cited by 5
Model-implied simulation-based power estimation for correctly specified and distributionally misspecified models: Applications to nonlinear and linear structural equation models
Irmer, J. P., Klein, A., & Schermelleh-Engel, K. (2024) · Behavior Research Methods · doi:10.3758/s13428-024-02507-z · Cited by 7
“The pwr package (Champely, 2020) and WebPower (Zhang & Yuan, 2018) offer implementations for power analysis of many basic statistical tests in R (R Core Team, 2023), with extensions also available for linear structural equation models (SEM, see also Moshagen & Bader, 2024, for an implementation).”
Method
Understanding internal dynamics of state anxiety during COVID‐19 pandemic: Seven‐wave longitudinal findings via panel network analysis
Zhang, Y., & Ma, Z. (2024) · Applied Psychology Health and Well-Being · doi:10.1111/aphw.12599 · Cited by 5
Contracting for circularity: How circular economy clauses shape market and financial performance
Castro-López, A., Iglesias, V., & Santos-Vijande, M. L. (2026) · Journal of Purchasing and Supply Management · doi:10.1016/j.pursup.2026.101153 · Cited by 4
Circular citizenship behaviours to promote systemic change: Influences of values, beliefs, norms, and personal agency
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Towards studying students’ autonomy-regulation strategies as a specific part of their motivation regulation
Zenger, L., Flunger, B., & van Gog, T. (2025) · Learning and Individual Differences · doi:10.1016/j.lindif.2025.102755 · Cited by 6
Ageism and Career Motivation Toward Gerontological Nursing in the Post-Pandemic Era: A Sequential-Parallel Mediation Analysis Among Early-Stage Nursing Students
Chen, S., & Wan, Z. (2025) · Psychology Research and Behavior Management · doi:10.2147/prbm.s539792 · Cited by 4
Modeling health literacy intentions: a structural equation analysis of community residents’ willingness to acquire infectious disease specific health literacy
Chen, J.-F., Liu, K., Cheng, Q., & Wang, L. (2025) · BMC Public Health · doi:10.1186/s12889-025-23842-6 · Cited by 4
Mind the (Social and Emotional Competence) Gap to Support Higher Education Students’ Well-Being: Psychometric Properties of the SECAB-A(S)
Oliveira, S., Maçarico, T., Pacheco, R., Janeiro, I. N., & Pinto, A. M. (2025) · European Journal of Investigation in Health Psychology and Education · doi:10.3390/ejihpe15080162 · Cited by 4
Do spatial navigation and episodic memory rely on the same systems? Evidence from a naturalistic experience with children and adults.
Nguyen, K. V., Olson, I. R., & Newcombe, N. S. (2025) · Journal of Experimental Psychology General · doi:10.1037/xge0001805 · Cited by 5
“A power analysis using semPower in R (Moshagen & Bader, 2024) with a moderate effect size of .15, α of .05, assumed regression slope between latent variables of .20, and the smallest degrees of freedom for planned factor analysis models ( df = 12) revealed a sample size of at least 66 was adequate…”
Dynamic interplay among emotional support, social interaction, COVID-19 news exposure and anxiety symptoms in emerging adults during the early COVID-19 pandemic
Zhang, Y., & Ma, Z. (2025) · Anxiety Stress & Coping · doi:10.1080/10615806.2025.2512922 · Cited by 3
“To ensure our sample size was adequate, we conducted a post hoc power analysis using the semPower package (Moshagen & Bader, 2023).”
In-Home Assistive Technology May Help Protect Dementia Caregivers from Declining Sleep Efficiency: A Randomized Control Trial
Scheffer, J. A., Levan, D. T., Wells, J. L., Gallagher-Thompson, D. E., Grimm, K. J., Chen, K., Brown, C. K., Bullard, B. M., Yee, C., Newton, S. L., et al. (2025) · Clinical Gerontologist · doi:10.1080/07317115.2025.2499812 · Cited by 7
“Using the semPower package in R (Moshagen & Bader, 2023), an a priori power analysis indicated that for a condition effect on a linear slope in the model of .05 (small) with 80% power and alpha of .05 with 145 degrees of freedom in the model, we would require 133 participants.”
Feeling Good About Doing Good: How the Perceived Authenticity of Organizational Social Responsibility Impacts Affective Organizational Commitment of Local Government Employees
Meyfroodt, K., Desmidt, S., & Crucke, S. (2025) · Public Performance & Management Review · doi:10.1080/15309576.2025.2491420 · Cited by 4
A new framework to assess the impact of new IT-based technologies on the success of quality management system
Cao, Y., & Alyousuf, F. Q. A. (2025) · Journal of Big Data · doi:10.1186/s40537-025-01061-5 · Cited by 4
“This index is one of the model fit indices that show the power of predicting the dependent variable (criterion) based on the independent variables (predictor) [95].”
Socioeconomic status self‐deception as a way to perpetuate classist societies
Melita, D., Alcañiz‐Colomer, J., Matamoros‐Lima, J., Ríos, S. A., & Moya, M. (2024) · Political Psychology · doi:10.1111/pops.13051 · Cited by 4
“With a sample size as large as this, we estimated to be able to detect an effect size ꞵ ≥ .099 with 95% power and alpha = .05 (estimation with package semPower ; Moshagen & Bader, 2024; constant unidirectional causal effects, and constant autoregressive effects set to ꞵ = .070).”
Past body shaming experiences and food and alcohol disturbance in young adults: indirect effects via psychological distress
Tata, D. D., Bianchi, D., Rossi, F., Fatta, L. M., Sette, S., & Laghi, F. (2024) · Eating and Weight Disorders - Studies on Anorexia Bulimia and Obesity · doi:10.1007/s40519-024-01687-z · Cited by 5
The Psychometric Properties of the Perceived Available Support in Sport Questionnaire: Validity and Reliability of the Turkish Version
Şenel, E., & Sakallı, D. (2024) · Pamukkale spor bilimleri dergisi · doi:10.54141/psbd.1437210 · Cited by 4
Developing to sustain: how informal learning shapes university students’ future careers
Gemmano, C. G., & Manuti, A. (2026) · Education + Training · doi:10.1108/et-05-2025-0370 · Cited by 3
Environmental passion and AI literacy shape the impact of green rewards on pro-environmental behaviors
Xu, L., Li, Y.-Y., Chan, T.-H., & Saleem, F. (2026) · Frontiers in Psychology · doi:10.3389/fpsyg.2026.1699919 · Cited by 3
“Furthermore, a G*Power analysis was conducted to justify the adequacy of the sample size (Moshagen and Bader, 2024).”
Testing a Hierarchical Structural Model of Youth Psychopathology Symptoms Over Time and Across Informants, Gender, and Pubertal Status
Hankin, B. L., Brandes, C. M., & Young, J. F. (2026) · Journal of the American Academy of Child & Adolescent Psychiatry · doi:10.1016/j.jaac.2026.01.017 · Cited by 3
“All analyses were conducted using R packages dplyr, 39 fungible, 40 psych, 41 semPower, 42 and sjmisc.”
Motivational Pathways Diverge Between Frequent and Problematic Pornography Use
Csányi, E., Veszprémi, M. D., Zsido, A. N., & Meskó, N. (2025) · International Journal of Sexual Health · doi:10.1080/19317611.2025.2605517 · Cited by 3
Cross-lagged analyses between peer bullying, teacher-student relationships, and non-suicidal self-injury among high school students
Liu, Y.-L., Li, X., Fang, Y., Yu, L., Li, Y.-Y., Teng, Z.-W., & Zeng, Y. (2025) · BMC Public Health · doi:10.1186/s12889-025-25467-1 · Cited by 3
Exploring the mediating role of motivational regulations in the relationship between body image and physical activity by sex: a structural equation modelling approach
Navas-León, S., Tajadura‐Jiménez, A., Morales, L., Mas, M. D. L. M. B., Navarro, M. L. A., & Sánchez-Martín, M. (2025) · BMC Psychology · doi:10.1186/s40359-025-03476-4 · Cited by 4
An Exploratory Study of Chatbot-Based Mindfulness for Mental Health Support
Wang, Y., & Farb, N. A. S. (2025) · Mindfulness · doi:10.1007/s12671-025-02685-7 · Cited by 6
Exploring grit in online learning systems: a novel approach to linking self-control and conscientiousness with academic success
Daud, M., Siswanti, D. N., & Nugraha, D. Y. (2025) · Cogent Psychology · doi:10.1080/23311908.2025.2520665 · Cited by 3
“…was carried out when applied under different method conditions (hair et al., 2019b). this evaluation includes power assessment parameters (Moshagen & Bader, 2024), robustness check tests using the Ramsey’s ReSet method (Ramsey, 1969; Sarstedt et al., 2020), and sensitivity analysis with…”
The role of emotion regulation strategies in the association between physical abuse and borderline symptoms among deprived youth in Ecuador
Murgueitio, N., Trueba, A. F., & Pluck, G. C. (2025) · Children and Youth Services Review · doi:10.1016/j.childyouth.2025.108430 · Cited by 3
A 2-wave study on the associations between dissociative experiences, maladaptive daydreaming, bodily dissociation, and problematic social media use
Casale, S., Ghinassi, S., & Elhai, J. D. (2025) · Journal of Behavioral Addictions · doi:10.1556/2006.2025.00075 · Cited by 3
From the Heart to the Mental States of Others: Linking Cardiac Autonomic Activity to Theory of Mind Ability in Young Adulthood
Hsu, B., Hsu, Y., & Weng, C. (2025) · Psychophysiology · doi:10.1111/psyp.70132 · Cited by 3
The role of social media in constructing meaning in life: a SEM analysis
Tran, C., Pikó, B., & Nguyen, T. V. (2025) · i-com · doi:10.1515/icom-2024-0060 · Cited by 3
Psychometric properties of the Italian Traumatic Grief Inventory-Self Report Plus (TGI-SR+)
Lenzo, V., Fontana, A., Santoro, G., Cuzzocrea, G., Miniati, V., Quattropani, M., Boelen, P. A., Caretti, V., Schimmenti, A., & Sideli, L. (2025) · Death Studies · doi:10.1080/07481187.2025.2537978 · Cited by 3
“Based on this criterion, our sample of 308 participants provided adequate statistical power (Moshagen & Bader, 2024).”
The different ways students base their self-worth on academics: typologies identified by a factor mixture modeling approach
Lawrence, J. S., & Wang, Y. (2025) · Self and Identity · doi:10.1080/15298868.2025.2522423 · Cited by 4
“In order to explore this concern, we conducted a post hoc power analysis using the semPower software and the analytical model-free power analysis (Moshagen & Bader, 2024).”
Identifying cognitive‐affective mechanisms underlying disability in episodic migraine: Using the fear avoidance model to examine interactions
Fox, J., Gaul, C., Kuhlencord, M., Peperkorn, N., Ohse, J., Krutzki, J., & Shiban, Y. (2025) · Headache · doi:10.1111/head.14988 · Cited by 3
“The analysis was performed using R (version 4.4.2; R Core Team, 2023), and the packages semPower (version 2.1.1) 24 and lavaan (version 0.6–19).”
Influential
Longitudinal Associations Between Perceived Inclusivity Norms and Opinion Polarization in Adolescence
Shani, M., Berns, M., Bergen, L., Richters, S., Krämer, K., de Lede, S., & van Zalk, M. H. W. (2025) · Social Inclusion · doi:10.17645/si.10122 · Cited by 4
“A priori power analysis using the semPower package (Moshagen & Bader, 2023) indicated that 792 participants would provide adequate power (80”
Cross-Cultural Adaptation of the Short Dark Tetrad (SD4) in the Brazilian Context
Guilhermino, C. S., Bonfá-Araujo, B., de Azevedo, T. G., Silva, J. L. P., Hauck, N., Bandeira, P., Tondin, C. F., & Alvarenga, M. A. S. (2025) · Psychological Test Adaptation and Development · doi:10.1027/2698-1866/a000100 · Cited by 3
Evaluation of the Spanish Version of the Machismo Measure with Mexican Men Who Have a History of Domestic Violence
Carrola, P. A., Han, E., Rocha, J., Valles, A. C., Valles, M. N. G., Martínez, J. R. L., & Anguiano, J. (2025) · doi:10.1080/07481756.2024.2401438 · Cited by 3
“In addition, we calculated the prior sample size requirement using lavaan and semPower2 package within R (Moshagen & Bader, 2023), which recommended the number of participants of 190 with desired power of .80, alpha of .05, and factor correlation of .25 with 10 indicators for each factor.”
Psychometric properties of the Chinese version of the quality of nursing care scale among hospital nurses: a bifactor exploratory structural equation modeling analysis
Fang, C., Li, C.-H., Ma, S., Hwang, F., Martins, M. M., & Chou, F. (2025) · BMC Nursing · doi:10.1186/s12912-025-03012-0 · Cited by 2
Positive cardiovascular health: longitudinal investigation of sustained health behavior in a cross-lagged model
Ocsovszky, Z., Ehrenberger, B., Berényi, B., Assabiny, A., Otohal, J., Martos, T., Papp-Zipernovszky, O., Hegedus, F., Merkely, B., Csabai, M., et al. (2024) · Frontiers in Public Health · doi:10.3389/fpubh.2024.1400849 · Cited by 3
“Statistical power complements the beta error and gives the probability of rejecting a null hypothesis if this hypothesis is factually wrong (and thus to accept a true alternative hypothesis) (38).”
BackgroundMethodInfluential
Silent ripples: negative CSR associations' impact in non-crisis situations
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Stay at Home Behavior during COVID-19: The Role of Person-Home Relationships
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The Impact of Relationship Quality on Couples With an Incarcerated Partner With Co-Occurring Mental Health and Substance Use Issues
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Hilbig, B. (2024) · Judgment and Decision Making · doi:10.1017/jdm.2024.33 · Cited by 3
When myths shape verdicts: A theory and intervention for jury biases against victim-survivors in rape trials
Kelleher, S. M., Ciardha, C. Ó., & Ildeniz, G. (2026) · Journal of Criminal Justice · doi:10.1016/j.jcrimjus.2026.102619 · Cited by 3
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Authors: Moshagen, M., & Bader, M.
Affiliations: Universität Ulm (DE)
Corresponding author: Moshagen, Morten
ORCID: Moshagen, Morten
Bader, Martina
Venue: Behavior Research Methods
Publisher: Springer Science and Business Media LLC
Published: 2023-11-10
Volume: 56
Issue: 4
Pages: 2901-2922
ISSN: 1554-351X (ISSN-L)
1554-3528
DOI: 10.3758/s13428-023-02254-7
PMC: PMC11522193
OpenAlex: W4388558341
Cited by: 308
References: 42
Citations by year: 2026: 121 · 2025: 133 · 2024: 50 · 2023: 3
FWCI: 56.57
Type: journal article
Language: en
Open access: hybrid
doi.org
Licence: cc-by
creativecommons.org/licenses/by/4.0 (tdm)
creativecommons.org/licenses/by/4.0 (vor)
Locations: Behavior Research Methods (publishedVersion, cc-by)
PubMed Central (publishedVersion, cc-by)
PubMed (publishedVersion)
OPen Access Repositorium der Universität Ulm (OPARU) (Ulm University) (submittedVersion, cc-by)
Funders: Universität Ulm
Topics: Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
Social Sciences › Decision Sciences › Statistics, Probability and Uncertainty › Meta-analysis and systematic reviews
Keywords: structural equation modeling, statistical power analysis, sample size determination, a priori power analysis, post hoc power analysis, effect size, multigroup analysis, confirmatory factor analysis, cross-lagged panel model, ARMA models, latent variables
MeSH terms: Latent Class Analysis, Data Interpretation, Statistical, Factor Analysis, Statistical, Humans, Software, Models, Statistical, Sample Size

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