دورية أكاديمية

The impact of ordinal scales on Gaussian mixture recovery.

التفاصيل البيبلوغرافية
العنوان: The impact of ordinal scales on Gaussian mixture recovery.
المؤلفون: Haslbeck JMB; Psychological Methods Group, University of Amsterdam, Amsterdam, Netherlands. jonashaslbeck@gmail.com., Vermunt JK; Department of Methodology and Statistics, Tilburg University, Tilburg, Netherlands., Waldorp LJ; Psychological Methods Group, University of Amsterdam, Amsterdam, Netherlands.
المصدر: Behavior research methods [Behav Res Methods] 2023 Jun; Vol. 55 (4), pp. 2143-2156. Date of Electronic Publication: 2022 Jul 13.
نوع المنشور: Journal Article
اللغة: English
بيانات الدورية: Publisher: Springer Country of Publication: United States NLM ID: 101244316 Publication Model: Print-Electronic Cited Medium: Internet ISSN: 1554-3528 (Electronic) Linking ISSN: 1554351X NLM ISO Abbreviation: Behav Res Methods Subsets: MEDLINE
أسماء مطبوعة: Publication: 2010- : New York : Springer
Original Publication: Austin, Tex. : Psychonomic Society, c2005-
مواضيع طبية MeSH: Algorithms*, Humans ; Bayes Theorem ; Normal Distribution
مستخلص: Gaussian mixture models (GMMs) are a popular and versatile tool for exploring heterogeneity in multivariate continuous data. Arguably the most popular way to estimate GMMs is via the expectation-maximization (EM) algorithm combined with model selection using the Bayesian information criterion (BIC). If the GMM is correctly specified, this estimation procedure has been demonstrated to have high recovery performance. However, in many situations, the data are not continuous but ordinal, for example when assessing symptom severity in medical data or modeling the responses in a survey. For such situations, it is unknown how well the EM algorithm and the BIC perform in GMM recovery. In the present paper, we investigate this question by simulating data from various GMMs, thresholding them in ordinal categories and evaluating recovery performance. We show that the number of components can be estimated reliably if the number of ordinal categories and the number of variables is high enough. However, the estimates of the parameters of the component models are biased independent of sample size. Finally, we discuss alternative modeling approaches which might be adopted for the situations in which estimating a GMM is not acceptable.
(© 2022. The Author(s).)
References: Agresti, A. (2018). An introduction to categorical data analysis. Wiley.
Borsboom, D. (2017). A network theory of mental disorders. World Psychiatry, 16(1), 5–13. (PMID: 10.1002/wps.20375281279065269502)
Brusco, M. J., Steinley, D., Hoffman, M., Davis-Stober, C., & Wasserman, S. (2019). On Ising models and algorithms for the construction of symptom networks in psychopathological research. Psychological Methods, 24(6), 735. (PMID: 10.1037/met000020731589062)
Cameron, I. M., Crawford, J. R., Lawton, K., & Reid, I. C. (2008). Psychometric comparison of PHQ-9 and HADS for measuring depression severity in primary care. British Journal of General Practice, 58 (546), 32–36. (PMID: 10.3399/bjgp08X263794)
Clinton, J., Jackman, S., & Rivers, D. (2004). The statistical analysis of roll call data. American Political Science Review, 98(2), 355–370. (PMID: 10.1017/S0003055404001194)
De Ron, J., Fried, E. I., & Epskamp, S. (2021). Psychological networks in clinical populations: Investigating the consequences of Berkson’s bias. Psychological Medicine, 51(1), 168–176. (PMID: 10.1017/S003329171900320931796131)
Feng, H., & Ning, Y. (2019). High-dimensional mixed graphical model with ordinal data: Parameter estimation and statistical inference. In The 22nd international conference on artificial intelligence and statistics (pp. 654–663): PMLR.
Fraley, C., Raftery, A. E., Murphy, T. B., & Scrucca, L. (2012). Mclust version 4 for R: normal mixture modeling for model-based clustering, classification, and density estimation. Technical report.
Frühwirth-Schnatter, S. (2006). Finite mixture and Markov switching models. Springer.
Guo, J., Levina, E., Michailidis, G., & Zhu, J. (2015). Graphical models for ordinal data. Journal of Computational and Graphical Statistics, 24(1), 183–204. (PMID: 10.1080/10618600.2014.88902326120267)
Hartigan, J. A., & Wong, M. A. (1979). Algorithm AS 136: A k-means clustering algorithm. Journal of the Royal Statistical Society. Series C (Applied Statistics), 28(1), 100–108.
Haslbeck, J., Ryan, O., & Dablander, F. (2021). The sum of all fears: Comparing networks based on symptom sum-scores. Psychological Methods.
Haslbeck, J., Ryan, O., Robinaugh, D.J., Waldorp, L.J., & Borsboom, D. (2021). Modeling psychopathology: From data models to formal theories. Psychological Methods.
Joshi, A., Kale, S., Chandel, S., & Pal, D. K. (2015). Likert scale: Explored and explained. British Journal of Applied Science & Technology, 7(4), 396. (PMID: 10.9734/BJAST/2015/14975)
Keribin, C. (2000). Consistent estimation of the order of mixture models. Sankhyā: The Indian Journal of Statistics, Series A, 49–66.
Lee, K. H., Chen, Q., DeSarbo, W. S., & Xue, L. (2021). Estimating finite mixtures of ordinal graphical models. Psychometrika, 1–24.
Leroux, B. G. (1992). Consistent estimation of a mixing distribution. The Annals of Statistics, 1350–1360.
Linzer, D. A., & Lewis, J. B. (2011). poLCA: An R package for polytomous variable latent class analysis. Journal of Statistical Software, 42, 1–29. (PMID: 10.18637/jss.v042.i10)
Manisera, M., & Zuccolotto, P. (2021). A mixture model for ordinal variables measured on semantic differential scales. Econometrics and Statistics.
McLachlan, G. J., Lee, S. X., & Rathnayake, S. I. (2019). Finite mixture models. Annual review of statistics and its application, 6, 355–378. (PMID: 10.1146/annurev-statistics-031017-100325)
Morren, M., Gelissen, J. P., & Vermunt, J. K. (2011). Dealing with extreme response style in cross-cultural research: A restricted latent class factor analysis approach. Sociological Methodology, 41(1), 13–47. (PMID: 10.1111/j.1467-9531.2011.01238.x)
Murphy, K. P. (2022). Probabilistic machine learning: An introduction. MIT Press. Retrieved from probml.ai.
Muthén, B., & Muthén, L. (2017). Mplus. In Handbook of item response theory (pp. 507–518).
Paulhus, D. L. (1991). Measurement and control of response bias.
Ranalli, M., & Rocci, R. (2016). Mixture models for ordinal data: a pairwise likelihood approach. Statistics and Computing, 26, 529–547. (PMID: 10.1007/s11222-014-9543-4)
Ryan, O., Bringmann, L., & Schuurman, N. K. (2019). The challenge of generating causal hypotheses using network models.
Scrucca, L., Fop, M., Murphy, T. B., & Raftery, A. E. (2016). mclust 5: clustering, classification and density estimation using Gaussian finite mixture models. The R Journal, 8(1), 289–317. Retrieved from https://doi.org/10.32614/RJ-2016-021 . (PMID: 10.32614/RJ-2016-021278187915096736)
Steele, R. J., & Raftery, A. E. (2010). Performance of Bayesian model selection criteria for Gaussian mixture models. Frontiers of statistical decision making and Bayesian analysis, 2, 113–130.
Suggala, A. S., Yang, E., & Ravikumar, P. (2017). Ordinal graphical models: A tale of two approaches. In International conference on machine learning (pp. 3260–3269): PMLR.
Tijmstra, J., Bolsinova, M., & Jeon, M. (2018). General mixture item response models with different item response structures: Exposition with an application to Likert scales. Behavior research methods, 50(6), 2325–2344. (PMID: 10.3758/s13428-017-0997-0293224006267524)
Van Rosmalen, J., Van Herk, H., & Groenen, P. J. (2010). Identifying response styles: A latent-class bilinear multinomial logit model. Journal of Marketing Research, 47(1), 157–172. (PMID: 10.1509/jmkr.47.1.157)
Vermunt, J. K., & Magidson, J. (2013) Technical guide for Latent GOLD 5.0: Basic, advanced, and syntax. Belmont: Statistical Innovations Inc.
Williams, G. A., & Kibowski, F. (2016). Latent class analysis and latent profile analysis. Handbook of methodological approaches to community-based research: Qualitative, quantitative, and mixed methods, 143–151.
فهرسة مساهمة: Keywords: Gaussian Mixture Modeling; Misspecification; Mixture modeling; Model selection; Ordinal scales
تواريخ الأحداث: Date Created: 20220713 Date Completed: 20230612 Latest Revision: 20240430
رمز التحديث: 20240501
مُعرف محوري في PubMed: PMC10250525
DOI: 10.3758/s13428-022-01883-8
PMID: 35831565
قاعدة البيانات: MEDLINE
الوصف
تدمد:1554-3528
DOI:10.3758/s13428-022-01883-8