Detecting mixtures from structural model differences using latent variable mixture modeling: a comparison of relative model fit statistics
Abstract
The accuracy of structural model parameter estimates in latent variable mixture modeling was explored with a 3 (sample size) × 3 (exogenous latent mean difference) × 3 (endogenous latent mean difference) × 3 (correlation between factors) × 3 (mixture proportions) factorial design. In addition, the efficacy of several likelihood-based statistics (Akaike's Information Criterion [AIC], Bayesian Information Ctriterion [BIC], the sample-size adjusted BIC [ssBIC], the consistent AIC [CAIC], the Vuong-Lo-Mendell-Rubin adjusted likelihood ratio test [aVLMR]), classification-based statistics (CLC [classification likelihood information criterion], ICL-BIC [integrated classification likelihood], normalized entropy criterion [NEC], entropy), and distributional statistics (multivariate skew and kurtosis test) were examined to determine which statistics best recover the correct number of components. Results indicate that the structural parameters were recovered, but the model fit statistics were not exceedingly accurate. The ssBIC statistic was the most accurate statistic, and the CLC, ICL-BIC, and aVLMR showed limited utility. However, none of these statistics were accurate for small samples (n = 500).
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BIC tends to overestimate the number of classes.
“BIC tends to overestimate the number of classes (Enders and 227 Tofighi, 2008; Henson et al., 2007; Nylund et al., 2007).”
From Time in treatment: Examining mental illness trajectories across inpatient psychiatric treatment (2020) · cites this paper as Henson et al., 2007
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Trajectories of posttraumatic growth and depreciation after two major earthquakes.
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- Authors
- Henson, J. M., Reise, S. P., & Kim, K. H.
- Affiliations
- Old Dominion University (US)
- University of California, Los Angeles (US)
- University of Pittsburgh (US)
- Venue
- Structural Equation Modeling: A Multidisciplinary Journal
- Publisher
- Informa UK Limited
- Published
- 2007-05
- Volume
- 14
- Issue
- 2
- Pages
- 202-226
- ISSN
- 1070-5511 (ISSN-L)
- 1532-8007
- OpenAlex
- W1985321835
- Cited by
- 429
- References
- 45
- Citations by year
- 2026: 13 · 2025: 23 · 2024: 24 · 2023: 21 · 2022: 29 · 2021: 34 · 2020: 43 · 2019: 26 · 2018: 23 · 2017: 24 · 2016: 30 · 2015: 30 · 2014: 18 · 2013: 28 · 2012: 18
- FWCI
- 15.26
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Structural Equation Modeling A Multidisciplinary Journal (publishedVersion)
- Topics
- Social Sciences › Decision Sciences › Management Science and Operations Research › Psychometric Methodologies and Testing
- Physical Sciences › Computer Science › Artificial Intelligence › Bayesian Methods and Mixture Models
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Methods and Bayesian Inference
- Keywords
- model fit statistics, number of components, sample size, Akaike information criterion, Bayesian information criterion, entropy (information theory)
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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