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Does nature have joints worth carving? A discussion of taxometrics, model-based clustering and latent variable mixture modeling

Published online by Cambridge University Press:  19 August 2014

G. H. Lubke*
Affiliation:
Department of Psychology, University of Notre Dame, IN, USA Department of Biological Psychology, VU University Amsterdam, The Netherlands
P. J. Miller
Affiliation:
Department of Psychology, University of Notre Dame, IN, USA
*
*Address for correspondence: G. H. Lubke, Ph.D., Department of Psychology, University of Notre Dame, 111 Haggar Hall, Notre Dame, IN 46556, USA. (Email: [email protected])

Abstract

Taxometric procedures, model-based clustering and latent variable mixture modeling (LVMM) are statistical methods that use the inter-relationships of observed symptoms or questionnaire items to investigate empirically whether the underlying psychiatric or psychological construct is dimensional or categorical. In this review we show why the results of such an investigation depend on the characteristics of the observed symptoms (e.g. symptom prevalence in the sample) and of the sample (e.g. clinical, population sample). Furthermore, the three methods differ with respect to their assumptions and therefore require different types of a priori knowledge about the observed symptoms and their inter-relationships. We argue that the choice of method should optimally match and make use of the existing knowledge about the data that are analyzed.

Type
Review Articles
Copyright
Copyright © Cambridge University Press 2014 

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References

Asparouhov, T, Muthén, BO (2013). Auxiliary Variables in Mixture Modeling: 3-Step Approaches Using Mplus. Mplus Web Notes, No. 15 (http://statmodel2.com/examples/webnotes/webnote15.pdf). Accessed 23 January 2014.Google Scholar
Banfield, JD, Raftery, AE (1993). Model-based Gaussian and non-Gaussian clustering. Biometrics 49, 803821.Google Scholar
Beauchaine, TP, Waters, E (2003). Pseudotaxonicity in MAMBAC and MAXCOV analyses of rating-scale data: turning continua into classes by manipulating observer's expectations. Psychological Methods 8, 315.Google Scholar
Bernstein, A, Stickle, TR, Zvolensky, MJ, Taylor, S, Abramowitz, J, Stewart, S (2010). Dimensional, categorical, or dimensional-categories: testing the latent structure of anxiety sensitivity among adults using factor-mixture modeling. Behavior Therapy 41, 515529.Google Scholar
Cleland, C, Haslam, N (1996). Robustness of taxometric analysis with skewed indicators: I. A Monte Carlo study of the MAMBAC procedure. Psychological Reports 79, 243248.Google Scholar
Cleland, CM, Rothschild, L, Haslam, N (2000). Detecting latent taxa: Monte Carlo comparison of taxometric, mixture model, and clustering procedures. Psychological Reports 87, 3747.Google Scholar
Dolan, CV, van der Maas, HLJ (1998). Fitting multivariate normal finite mixtures subject to structural equation modeling. Psychometrika 63, 227253.Google Scholar
Falconer, DS (1981). Introduction to Quantitative Genetics, 2nd edn. Longman: London.Google Scholar
Fraley, C, Raftery, AE (2002). Model-based clustering, discriminant analysis, and density estimation. Journal of the American Statistical Association 97, 611631.Google Scholar
Fraley, C, Raftery, AE, Murphy, TB, Scrucca, L (2012). mclust Version 4 for R: Normal Mixture Modeling for Model-Based Clustering, Classification, and Density Estimation. Technical Report No. 597. Department of Statistics, University of Washington: Seattle, WA (www.stat.washington.edu/research/reports/2012/tr597.pdf). Accessed 23 January 2014.Google Scholar
Frühwirth-Schnatter, S (2006). Finite Mixture and Markov Switching Models. Springer: New York.Google Scholar
Gangestad, S, Snyder, M (1985). ‘To carve nature at its joints’: on the existence of discrete classes in personality. Psychological Review 92, 317349.Google Scholar
Gordon, K, Holm-Denoma, J, Smith, A, Fink, E, Joiner, T (2007). Taxometric analysis: introduction and overview. International Journal of Eating Disorders 40, S35S39.Google Scholar
Grove, WM (2004). The maxslope taxometric procedure: mathematical derivation, parameter estimation, consistency tests. Psychological Reports 95, 517550.Google Scholar
Haslam, N, Cleland, C (1996). Robustness of taxometric analysis with skewed indicators: II. A Monte Carlo study of the MAXCOV procedure. Psychological Reports 79, 10351039.Google Scholar
Haslam, N, Cleland, C (2002). Taxometric analysis of fuzzy categories: a Monte Carlo study. Psychological Reports 90, 401404.Google Scholar
Haslam, N, Holland, E, Kuppens, P (2011). Categories versus dimensions in personality and psychopathology: a quantitative review of taxometric research. Psychological Medicine 42, 903920.Google Scholar
Hay, DA, Bennett, KS, Levy, F, Sergeant, J, Swanson, J (2007). A twin study of attention-deficit/hyperactivity disorder dimensions rated by the strengths and weaknesses of ADHD-symptoms and normal-behavior (SWAN) scale. Biological Psychiatry 61, 700705.Google Scholar
Kihlstrom, JF (2002). To honor Kraepelin…: from symptoms to pathology in the diagnosis of mental illness. In Rethinking the DSM: A Psychological Perspective (ed. Beutler, L. E. and Malik, M. L.), pp. 279303. American Psychological Association: Washington, DC.Google Scholar
Lenzenweger, MF, McLachlan, G, Rubin, DB (2007). Resolving the latent structure of schizophrenia endophenotypes using expectation-maximization-based finite mixture modeling. Journal of Abnormal Psychology 116, 1629.Google Scholar
Lubke, GH, Hudziak, JJ, Derks, EM, van Bijsterveldt, TC, Boomsma, DI (2009). Maternal ratings of attention problems in ADHD: evidence for the existence of a continuum. Journal of the American Academy of Child and Adolescent Psychiatry 48, 10851093.Google Scholar
Lubke, GH, Muthén, BO (2005). Investigating population heterogeneity with factor mixture models. Psychological Methods 10, 2139.Google Scholar
Lubke, GH, Muthen, BO, Moilanen, IK, McGough, JJ, Loo, SK, Swanson, JM, Yang, MH, Taanila, A, Hurtig, T, Järvelin, MR, Smalley, SL (2007). Subtypes versus severity differences in attention-deficit/hyperactivity disorder in the Northern Finnish Birth Cohort. Journal of the American Academy of Child and Adolescent Psychiatry 46, 15841593.Google Scholar
Lubke, GH, Neale, MC (2006). Distinguishing between latent classes and continuous factors: resolution by maximum likelihood? Multivariate Behavioral Research 41, 499532.Google Scholar
Lubke, GH, Neale, MC (2008). Distinguishing between latent classes and continuous factors with categorical outcomes: class invariance of parameters of factor mixture models. Multivariate Behavioral Research 43, 592620.Google Scholar
Lubke, GH, Tueller, S (2010). Latent class detection and class assignment: a comparison of the MAXEIG taxometric procedure and factor mixture modeling approaches. Structural Equation Modeling 17, 605628.Google Scholar
Manchia, M, Cullis, J, Turecki, G, Rouleau, GA, Uher, R, Alda, M (2013). The impact of phenotypic and genetic heterogeneity on results of genome wide association studies of complex diseases. PloS ONE 8, e76295.Google Scholar
Maraun, MD, Slaney, K, Goddyn, L (2003). An analysis of Meehl's MAXCOV-HITMAX procedure for the case of dichotomous indicators. Multivariate Behavioral Research 38, 81112.Google Scholar
McCarthy, MI, Abecasis, GR, Cardon, LR, Goldstein, DB, Little, J, Ioannidis, JPA, Hirschhorn, JN (2008). Genome-wide association studies for complex traits: consensus, uncertainty and challenges. Nature Reviews Genetics 9, 356369.Google Scholar
McGrath, RE, Walters, GD (2012). Taxometric analysis as a general strategy for distinguishing categorical from dimensional latent structure. Psychological Methods 17, 284293.Google Scholar
McLachlan, G, Peel, D (2004). Finite Mixture Models. Wiley: New York.Google Scholar
Meehl, PE (1965). Detecting Latent Clinical Taxa by Fallible Quantitative Indicators Lacking an Accepted Criterion. Report No. PR-65-2. Research Laboratories of the Department of Psychiatry, University of Minnesota: Minnesota, MN (www.psych.umn.edu/people/meehlp/065TechRep1.pdf). Accessed 23 January 2014.Google Scholar
Meehl, PE (1992). Factors and taxa, traits and types, differences of degree and differences in kind. Journal of Personality 60, 117174.Google Scholar
Meehl, PE (1995). Bootstraps taxometrics: solving the classification problem in psychopathology. American Psychologist 50, 266275.Google Scholar
Meehl, PE (1999). Clarifications about taxometric method. Applied and Preventive Psychology 8, 165174.Google Scholar
Meehl, PE (2004). What's in a taxon? Journal of Abnormal Psychology 113, 3943.Google Scholar
Meehl, PE, Yonce, LJ (1994). Taxometric analysis: I. Detecting taxonicity with two quantitative indicators using means above and below a sliding cut (MAMBAC procedure). Psychological Reports 73(Pt 2), 10591274.Google Scholar
Meehl, PE, Yonce, LJ (1996). Taxometric analysis: II. Detecting taxonicity using covariance of two quantitative indicators in successive intervals of a third indicator (MAXCOV procedure). Psychological Reports 78, 10911227.Google Scholar
Muthén, BO, Shedden, K (1999). Finite mixture modeling with mixture outcomes using the EM algorithm. Biometrics 55, 463469.Google Scholar
Muthén, LK, Muthén, BO (2012). Mplus User's Guide, 7th edn. Muthén & Muthén: Los Angeles, CA.Google Scholar
Nylund, KL, Asparouhov, T, Muthén, BO (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: a Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal 14, 535569.Google Scholar
Ruscio, J (2012). Taxometric Programs for the R Computing Environment: User's Manual (www.tcnj.edu/~ruscio/taxometrics.html). Accessed 23 January 2014.Google Scholar
Ruscio, J, Kaczetow, W (2009). Differentiating categories and dimensions: evaluating the robustness of taxometric analyses. Multivariate Behavioral Research 44, 259280.Google Scholar
Ruscio, J, Ruscio, AM (2002). A structure-based approach to psychological assessment matching measurement models to latent structure. Assessment 9, 416.Google Scholar
Ruscio, J, Ruscio, AM, Meron, M (2007). Applying the bootstrap to taxometric analysis: generating empirical sampling distributions to help interpret results. Multivariate Behavioral Research 42, 349386.Google Scholar
Titterington, DM, Smith, AFM, Makov, UE (1985). Statistical Analysis of Finite Mixture Distributions, vol. 7. Wiley: New York.Google Scholar
Trull, TJ, Durrett, CA (2005). Categorical and dimensional models of personality disorder. Annual Review of Clinical Psychology 1, 355380.Google Scholar
Tueller, S, Lubke, GH (2010). Evaluation of structural equation mixture models: parameter estimates and correct class assignment. Structural Equation Modeling: A Multidisciplinary Journal 17, 165192.Google Scholar
Waller, NG, Meehl, PE (1998). Multivariate Taxometric Procedures: Distinguishing Types from Continua. Sage Publications: Thousand Oaks, CA.Google Scholar
Walters, GD, McGrath, RE, Knight, RA (2010). Taxometrics, polytomous constructs, and the comparison curve fit index: a Monte Carlo analysis. Psychological Assessment 22, 149156.Google Scholar
Walters, GD, Ruscio, J (2010). Where do we draw the line? Assigning cases to subsamples for MAMBAC, MAXCOV, and MAXEIG taxometric analyses. Assessment 17, 321333.Google Scholar
Vermunt, JK (2010). Latent class modeling with covariates: two improved three-step approaches. Political Analysis 18, 450469.Google Scholar
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