The DOI matches its Crossref record; 45 of the 45 references it cites were found in a registry or an index.
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).
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“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
Citations
Cites
A new look at the statistical model identification
Akaike, H. (1974) · IEEE Transactions on Automatic Control · doi:10.1109/tac.1974.1100705 · Cited by 51,879
Estimating the Dimension of a Model
Schwarz, G. (1978) · The Annals of Statistics · doi:10.1214/aos/1176344136 · Cited by 47,033
On Information and Sufficiency
Kullback, S., & Leibler, R. A. (1951) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177729694 · Cited by 20,193
McLachlan, G., & Peel, D. (2000) · Wiley Series in Probability and Statistics · doi:10.1002/0471721182 · Cited by 10,991
Applied Longitudinal Data Analysis: Modeling Change and Event Occurrence
Singer, J. D., & Willett, J. B. (2003) · doi:10.1093/acprof:oso/9780195152968.001.0001 · Cited by 10,647
EQS : structural equations program manual
Bentler, P. M. (1989) · Medical Entomology and Zoology · Cited by 9,669
Modeling by shortest data description
Rissanen, J. (1978) · Automatica · doi:10.1016/0005-1098(78)90005-5 · Cited by 6,011
Likelihood Ratio Tests for Model Selection and Non-Nested Hypotheses
Vuong, Q. H. (1989) · Econometrica · doi:10.2307/1912557 · Cited by 5,929
Measures of Multivariate Skewness and Kurtosis with Applications
Mardia, K. V. (1970) · Biometrika · doi:10.1093/biomet/57.3.519 · Cited by 5,125
Testing the number of components in a normal mixture
Lo, Y. (2001) · Biometrika · doi:10.1093/biomet/88.3.767 · Cited by 4,640
Bozdogan, H. (1987) · Psychometrika · doi:10.1007/bf02294361 · Cited by 4,468
Test Theory: A Unified Treatment
Zwick, R., & McDonald, R. P. (2000) · Journal of the American Statistical Association · doi:10.2307/2669496 · Cited by 3,640
Muthén, B., & Muthén, L. K. (2000) · Alcoholism Clinical and Experimental Research · doi:10.1111/j.1530-0277.2000.tb02070.x · Cited by 3,161
Statistical Analysis of Finite Mixture Distributions.
Lindsay, B. G., Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1987) · Journal of the American Statistical Association · doi:10.2307/2289504 · Cited by 2,906
(1999) · Cited by 2,653
Application of model-selection criteria to some problems in multivariate analysis
Sclove, S. L. (1987) · Psychometrika · doi:10.1007/bf02294360 · Cited by 2,541
An entropy criterion for assessing the number of clusters in a mixture model
Celeux, G., & Soromenho, G. (1996) · Journal of Classification · doi:10.1007/bf01246098 · Cited by 2,448 · cited 7×
“Finally, to evaluate Celeux and Soromenho’s (1996) proposed methodology for comparing the NEC statistics between a k-component model and a one-component model, constrained mixture models were estimated as well.”
BackgroundMethodInfluentialMixture models : inference and applications to clustering
McLachlan, G. J., & Basford, K. E. (1988) · M. Dekker eBooks · Cited by 2,094
Simultaneous Factor Analysis in Several Populations
Jöreskog, K. G. (1971) · Psychometrika · doi:10.1007/bf02291366 · Cited by 2,051
Statistical Analysis of Finite Mixture Distributions.
Newton, J., Titterington, D. M., Smith, A. F. M., & Makov, U. E. (1986) · Biometrics · doi:10.2307/2531224 · Cited by 1,986
Investigating population heterogeneity with factor mixture models.
Lubke, G. H., & Muthén, B. (2005) · Psychological Methods · doi:10.1037/1082-989x.10.1.21 · Cited by 1,189
An Empirical Pooling Approach for Estimating Marketing Mix Elasticities with PIMS Data
Ramaswamy, V., DeSarbo, W. S., Reibstein, D. J., & Robinson, W. T. (1993) · Marketing Science · doi:10.1287/mksc.12.1.103 · Cited by 1,155
Bauer, D. J., & Curran, P. J. (2003) · Psychological Methods · doi:10.1037/1082-989x.8.3.338 · Cited by 1,115
Mixture Models: Inference and Applications to Clustering.
Lindsay, B. G., McLachlan, G. J., Basford, K. E., & Dekker, M. (1989) · Journal of the American Statistical Association · doi:10.2307/2289892 · Cited by 1,062
Latent Variable Modeling in Heterogeneous Populations
Muthén, B. (1989) · Psychometrika · doi:10.1007/bf02296397 · Cited by 1,008
McLachlan, G. J. (1987) · Journal of the Royal Statistical Society Series C (Applied Statistics) · doi:10.2307/2347790 · Cited by 709
A Method for Simulating Non-Normal Distributions
Fleishman, A. I. (1978) · Psychometrika · doi:10.1007/bf02293811 · Cited by 709
Statistical and Substantive Checking in Growth Mixture Modeling: Comment on Bauer and Curran (2003).
Muthén, B. (2003) · Psychological Methods · doi:10.1037/1082-989x.8.3.369 · Cited by 691
A GENERAL METHOD FOR STUDYING DIFFERENCES IN FACTOR MEANS AND FACTOR STRUCTURE BETWEEN GROUPS
Sörbom, D. (1974) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1974.tb00543.x · Cited by 677
Rasch Models in Latent Classes: An Integration of Two Approaches to Item Analysis
Rost, J. (1990) · Applied Psychological Measurement · doi:10.1177/014662169001400305 · Cited by 554
Computing Science and Statistics
(1992) · Springer eBooks · doi:10.1007/978-1-4612-2856-1 · Cited by 458
Simulating Multivariate Nonnormal Distributions
Vale, C. D., & Maurelli, V. A. (1983) · Psychometrika · doi:10.1007/bf02293687 · Cited by 444
Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997) · Marketing Science · doi:10.1287/mksc.16.1.39 · Cited by 441
Mixtures of Conditional Mean- and Covariance-Structure Models
Arminger, G., Stein, P., & Wittenberg, J. (1999) · Psychometrika · doi:10.1007/bf02294568 · Cited by 195
A logistic mixture distribution model for polychotomous item responses
Rost, J. (1991) · British Journal of Mathematical and Statistical Psychology · doi:10.1111/j.2044-8317.1991.tb00951.x · Cited by 194
Identifying trajectories of adolescent smoking: An application of latent growth mixture modeling.
Colder, C. R., Mehta, P. D., Balanda, K. P., Campbell, R. T., Mayhew, K. P., Stanton, W. R., Pentz, M. A., & Flay, B. R. (2001) · Health Psychology · doi:10.1037/0278-6133.20.2.127 · Cited by 182
An improvement of the NEC criterion for assessing the number of clusters in a mixture model
Christophe Biernacki, A., Celeux, G., & Govaert, G. (1999) · Pattern Recognition Letters · doi:10.1016/s0167-8655(98)00144-5 · Cited by 175
Fitting Multivariage Normal Finite Mixtures Subject to Structural Equation Modeling
Dolan, C. V., & van der Maas, H. L. J. (1998) · Psychometrika · doi:10.1007/bf02294853 · Cited by 167
Li, F., Duncan, T. E., & Hops, H. (2001) · Journal of Studies on Alcohol · doi:10.15288/jsa.2001.62.199 · Cited by 143
Lubke, G. (2003) · Intelligence · doi:10.1016/s0160-2896(03)00051-5 · Cited by 122
STEMM: A General Finite Mixture Structural Equation Model
Jedidi, K., Jagpal, H. S., & DeSarbo, W. S. (1997) · Journal of Classification · doi:10.1007/s003579900002 · Cited by 112
Assessing a Mixture Model for Clustering with the Integrated Classification Likelihood
Christophe Biernacki, A., Celeux, G., & Govaert, G. (1998) · OpenGrey (Institut de l'Information Scientifique et Technique) · Cited by 101
Everitt, B. S. (1981) · Multivariate Behavioral Research · doi:10.1207/s15327906mbr1602_3 · Cited by 98
A note on 'Testing the number of components in a normal mixture'
Jeffries, N. O. (2003) · Biometrika · doi:10.1093/biomet/90.4.991 · Cited by 74
Lubke, G. H., Dolan, C. V., Kelderman, H., & Mellenbergh, G. J. (2003) · British Journal of Mathematical and Statistical Psychology · doi:10.1348/000711003770480020 · Cited by 62
Research works printed but not linked: 5
- Cutler A., 1993, Proceedings of the first U. S.-Japan conference on the Frontiers of Statistical Modeling, 149
- Hays W. L., 1994, Statistics.
- Leroux B. G., 1992, AnnalsofStatistics, 20, 1350
- Mardia K. V., 1974, Sankhya, 36, 115
- Muthén L. K., 2001, Mplus user's guide,
Cited by
Sorted by citations
Jiang, K., Lepak, D. P., Hu, J. J., & Baer, J. C. (2012) · Academy of Management Journal · doi:10.5465/amj.2011.0088 · Cited by 2,857
Spurk, D., Hirschi, A., Wang, M., Valero, D., & Kauffeld, S. (2020) · Journal of Vocational Behavior · doi:10.1016/j.jvb.2020.103445 · Cited by 2,119
Vrieze, S. I. (2012) · Psychological Methods · doi:10.1037/a0027127 · Cited by 1,948
Marsh, H. W., Lüdtke, O., Trautwein, U., & Morin, A. J. S. (2009) · Structural Equation Modeling: A Multidisciplinary Journal · doi:10.1080/10705510902751010 · Cited by 1,245
Practitioner’s guide to latent class analysis: Methodological considerations and common pitfalls
Sinha, P., Calfee, C. S., & Delucchi, K. L. (2021) · Critical Care Medicine · doi:10.1097/ccm.0000000000004710 · Cited by 1,204
Metadata
- 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)
About these checks
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.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
