Structural equation models of latent interactions: Evaluation of alternative estimation strategies and indicator construction
Abstract
Interactions between (multiple indicator) latent variables are rarely used because of implementation complexity and competing strategies. Based on 4 simulation studies, the traditional constrained approach performed more poorly than did 3 new approaches--unconstrained, generalized appended product indicator, and quasi-maximum-likelihood (QML). The authors' new unconstrained approach was easiest to apply. All 4 approaches were relatively unbiased for normally distributed indicators, but the constrained and QML approaches were more biased for nonnormal data; the size and direction of the bias varied with the distribution but not with the sample size. QML had more power, but this advantage was qualified by consistently higher Type I error rates. The authors also compared general strategies for defining product indicators to represent the latent interaction factor.
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An RMSEA value below .08 is considered acceptable.
“An RMSEA value below .08 is considered acceptable (Marsh et al., 2004)”
From Measuring undergraduate students’ reliance on generative AI during problem-solving: Scale development and validation. (2025) · cites this paper as Marsh et al., 2004
An SRMR value below .08 is considered evidence of a good fit.
“An SRMR value below .08 is considered evidence of a good fit (Marsh et al., 2004)”
From Measuring undergraduate students’ reliance on generative AI during problem-solving: Scale development and validation. (2025) · cites this paper as Marsh et al., 2004
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- Authors
- Marsh, H. W., Wen, Z., & Hau, K.-T.
- Affiliations
- Western Sydney University (AU)
- South China Normal University (CN)
- Chinese University of Hong Kong (HK)
- Venue
- Psychological Methods
- Published
- 2004
- Volume
- 9
- Issue
- 3
- Pages
- 275-300
- ISSN
- 1082-989X (ISSN-L)
- 1939-1463
- OpenAlex
- W2010420668
- Cited by
- 1,205
- References
- 0
- Citations by year
- 2026: 141 · 2025: 118 · 2024: 80 · 2023: 81 · 2022: 71 · 2021: 50 · 2020: 55 · 2019: 64 · 2018: 71 · 2017: 48 · 2016: 60 · 2015: 51 · 2014: 55 · 2013: 49 · 2012: 48
- FWCI
- 19.88
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Psychological Methods (publishedVersion)
- PubMed (publishedVersion)
- Research Bank (Australian Catholic University) (submittedVersion)
- 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 › Psychology › Experimental and Cognitive Psychology › Mental Health Research Topics
- Keywords
- latent interactions, latent variable interactions, constrained estimation, quasi-maximum likelihood estimation, estimation bias, type I error, non-normal data, simulation study
- MeSH terms
- Analysis of Variance, Humans, Mathematical Computing, Psychology, Experimental, Software, Models, Statistical, Likelihood Functions, Nonlinear Dynamics
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