Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood?

Lubke, Gitta H.; Neale, Michael C.

doi:10.1207/s15327906mbr4104_4

Cited by 324 publications

(288 citation statements)

References 33 publications

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“…It would be interesting, however, to evaluate how useful CHull is for picking the correct model out of a wider range of models-including EFA, MFA, and regular mixture models-for instance, using the simulation design of Lubke and Neale (2006).…”

Section: Resultsmentioning

confidence: 99%

CHull as an alternative to AIC and BIC in the context of mixtures of factor analyzers

et al. 2013

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Mixture analysis is commonly used for clustering objects on the basis of multivariate data. When the data contain a large number of variables, regular mixture analysis may become problematic, because a large number of parameters need to be estimated for each cluster. To tackle this problem, the mixtures-of-factor-analyzers (MFA) model was proposed, which combines clustering with exploratory factor analysis. MFA model selection is rather intricate, as both the number of clusters and the number of underlying factors have to be determined. To this end, the Akaike (AIC) and Bayesian (BIC) information criteria are often used. AIC and BIC try to identify a model that optimally balances model fit and model complexity. In this article, the CHull (Ceulemans & Kiers, 2006) method, which also balances model fit and complexity, is presented as an interesting alternative model selection strategy for MFA. In an extensive simulation study, the performances of AIC, BIC, and CHull were compared. AIC performs poorly and systematically selects overly complex models, whereas BIC performs slightly better than CHull when considering the best model only. However, when taking model selection uncertainty into account by looking at the first three models retained, CHull outperforms BIC. This especially holds in more complex, and thus more realistic, situations (e.g., more clusters, factors, noise in the data, and overlap among clusters).Keywords Mixture analysis . Model selection . AIC . BIC . CHullIn the behavioral sciences, researchers often cluster multivariate (i.e., object-by-variable) data in order to capture the heterogeneity that is present in the population. The resulting clusters can differ with regard to their level and/ or covariance structure. A first example pertains to the case in which a number of children are scored on certain psychopathological symptoms. The aim then is to discern different groups and to describe the differences between the groups in terms of the strength of the symptoms and/ or of their linear covariation. A second example is a consumer psychologist who wants to identify different groups of consumers on the basis of their appraisals of a wide range of food products.A commonly used clustering method is mixture analysis (McLachlan & Peel, 2000). In this method, each cluster is described by a different multivariate distribution, and every object belongs to each cluster with a particular probability. As a result, the full data follow a mixture of multivariate distributions. In practice, because of their computational simplicity, multivariate normal distributions are often assumed (McLachlan, Peel, & Bean, 2003), implying that each cluster is characterized by a mean vector and a covariance matrix.When the number of variables increases, such a mixture of multivariate normals may become problematic, in that a large number of variance and covariance parameters need to be estimated for each cluster [i.e., for J variables, J(J + 1)/2 variances and covariances need to be determined]. This problem is aggr...

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Section: Resultsmentioning

confidence: 99%

CHull as an alternative to AIC and BIC in the context of mixtures of factor analyzers

et al. 2013

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“…In addition, other conditions may exist that affect power estimates. For example, power for factor mixture models, in which the structure among variables is specified to hold within each of the derived latent classes, is more complex and is influenced by a number of factors, including the mixing proportion and the separation among clusters (Lubke & Neal, 2006) and model size, covariates, and class-specific parameters in factor mixture models (Lubke & Muthén, 2007). to the eigenvalues of Σ. The following three components determine the geometric features of the observed data: λ parameterizes the volume of the observation, D indicates the orientation, and A represents the shape of the observation.…”

Section: Appendix Amentioning

confidence: 99%

Finding groups using model-based cluster analysis: Heterogeneous emotional self-regulatory processes and heavy alcohol use risk.

Mun¹,

Eye²,

Bates³

et al. 2008

Developmental Psychology

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Model-based cluster analysis is a new clustering procedure to investigate population heterogeneity utilizing finite mixture multivariate normal densities. It is an inferentially based, statistically principled procedure that allows comparison of non-nested models using the Bayesian Information Criterion (BIC) to compare multiple models and identify the optimum number of clusters. The current study clustered 36 young men and women based on their baseline heart rate (HR) and HR variability (HRV), chronic alcohol use, and reasons for drinking. Two cluster groups were identified and labeled High Alcohol Risk and Normative groups. Compared to the Normative group, individuals in the High Alcohol Risk group had higher levels of alcohol use and more strongly endorsed disinhibition and suppression reasons for use. The High Alcohol Risk group showed significant HRV changes in response to positive and negative emotional and appetitive picture cues, compared to neutral cues. In contrast, the Normative group showed a significant HRV change only to negative cues. Findings suggest that the individuals with autonomic selfregulatory difficulties may be more susceptible to heavy alcohol use and use alcohol for emotional regulation. KeywordsModel-based Cluster Analysis; Mixture Model; Emotional Regulation; Heart Rate Variability (HRV); Alcohol Use Finding or classifying groups of individuals who are similar to one another within a group but sufficiently different from those of other groups has been a key interest in the behavioral sciences. Cluster analysis is a widely used approach for this purpose. It is empirically driven and exploratory in the sense that the number of groups and nature of the groups are unknown in advance (Everitt, Landau, & Leese, 2001;Webb, 2002). In the field of developmental psychology, a number of influential studies have found clusters of individuals based on their early temperamental and behavioral styles, and characterized their long-term patterns of behavioral outcomes, including the classic work on three temperamental styles from the New York Longitudinal Study (easy, difficult, slow to warm up;Thomas, Chess & Birch, 1968) and the more contemporary work from the Dunedin Multidisciplinary Health and Development (undercontrolled, inhibited, well-adjusted;Caspi, 2000;Caspi & Silva, 1995 NIH-PA Author ManuscriptNIH-PA Author Manuscript NIH-PA Author ManuscriptFurthermore, recent literature has increasingly postulated that qualitatively heterogeneous subpopulations exist in developmental pathways, and heterogeneous causal processes exist for subpopulations. Evidence of heterogeneity consisting of normative as well as atypical processes can be found in many behaviors, including depressive symptoms, aggressive behaviors, and substance use behaviors (for a brief review, see Mun, Windle, & Schainker, 2008). In addition, identifying heterogeneous subpopulations can be useful for determining individuals who may be at different stages of development. For example, in the domain of cognitive stage develo...

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“…As introduced in the next section, famous information criteria such as Akaike Information Criterion (AIC) (Akaike, 1973) and Bayesian Information Criterion (BIC) (Schwarz, 1978) are classified qw likelihood-based statistics. Even if they differ in their exact definition of a "good model", different information criteria do have the same aim of identifying good models (Acquah, 2010), and then the performance of these criteria for model selection has been compared in the mixture-modeling context (e.g., Bauer & Curran, 2003;Henson et al, 2007;Lubke & Neale, 2006;Nylund et al, 2007;Vrieze, 2012). Vrieze (2012) reviewed the features of AIC and BIC, and compared the performance of the AIC and BIC by a novel simulation study and showed that BIC outperformed the AIC when (i) the true model is among the candidate models considered, (ii) the true model is simple (i.e., the small number of classes), (iii) degree of separation (i.e., mean differences among classes) is large, (iv) sample size is large, (v) mixture proportion is not extreme (i.e., class sizes are not very disparate).…”

Section: Introductionmentioning

confidence: 99%

Performance of Information Criteria for Model Selection in a Latent Growth Curve Mixture Model

Usami

2014

Journal of the Japanese Society of Computational Statistics

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Novel simulation studies are performed to investigate the performance of likelihood-based and entropy-based information criteria for estimating the number of classes in latent growth curve mixture models, considering influences of true model complexity and model misspecification. Simulation results can be summarized as (1) Increased model complexity worsens the performance of all criteria, and this is salient in Bayesian Information Criteria (BIC) and Consistent Akaike Information Criteria (CAIC). (2) The classification likelihood information criterion (CLC) and integrated completed likelihood criterion with BIC approximation (ICL.BIC) frequently underestimate the number of classes. (3) Entropy-based criteria correctly estimate the number of classes more frequently. (4) When a normal mixture is incorrectly fit to non-normal data including outliers, although this seriously worsens the performance of many criteria, BIC, CAIC, and ICL.BIC are relatively robust. Additionally, overextracted classes with trivially small mixture proportions can be detected when the sample size is large. (5) When there is an upper bound of measurement, although this worsens the performance of almost all criteria, entropy-based criteria are robust. (6) Although no single criterion is always best, ICL.BIC shows better performance on average.

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Distinguishing Between Latent Classes and Continuous Factors: Resolution by Maximum Likelihood?

Cited by 324 publications

References 33 publications

CHull as an alternative to AIC and BIC in the context of mixtures of factor analyzers

CHull as an alternative to AIC and BIC in the context of mixtures of factor analyzers

Finding groups using model-based cluster analysis: Heterogeneous emotional self-regulatory processes and heavy alcohol use risk.

Performance of Information Criteria for Model Selection in a Latent Growth Curve Mixture Model

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