Latent Class Analysis and Psychiatry Research

To the Editor:

The statistical procedure, latent class analysis (LCA), has been increasingly applied to problems of psychiatric typology. In the last two years, nearly two dozen major articles making use of LCA have appeared in the psychiatry literature.[1,2] These articles have been of a very high quality, but certain methodological issues have received insufficient attention. Some major concerns are as follows:

  • Conditional dependence

    An essential assumption of LCA is that of "conditional independence." This requires that all observed variables (e.g., symptoms) be statistically independent (roughly, uncorrelated) within each latent class. Many studies have analyzed symptoms that would appear to violate this assumption a priori. For example, "increased appetite" and "decreased appetite" [2] can scarcely be independent for any group of patients. Such dependent items exert a distorting influence on results. Generally, they promote emergence of extra, spurious latent classes as the estimation algorithm tries to reconcile conditional independence assumptions with the data.

    The problem can be lessened by eliminating clearly dependent items from analysis, or by combining them to form a single item.[1] Simple graphical methods can be used to verify conditional independence.[3] Extensions of LCA exist that accommodate dependent items.[4-5] [for more information, see A Practical Guide to Local Dependence in Latent Class Models.]

  • Local maxima

    LCA is subject to the problem of "local maxima," where the computer program, trying to find best-fitting values for quantities such as the population base rates of the latent classes, instead converges on values that are not best-fitting; the phenomenon is more common when the number of latent classes exceeds two or three. There is no reason to think such nonoptimal values will be even approximately the same as the true optimal values. Extra computation, such as beginning estimation several times with different initial parameter values, is needed for reasonable assurance that the best solution is found. Some LCA programs do this automatically. The recent articles have mostly not addressed this issue, raising concerns about how well reported results reflect best-fitting solutions.

  • Number of latent classes

    The issue of comparing and choosing among LCA solutions with different numbers of latent classes requires more attention. Many articles have made such comparisons via a difference likelihood-ratio chi-squared statistic [6] and associated p-value. However, it is widely accepted that, for technical reasons, this statistical test is inappropriate for comparing models with different numbers of latent classes.[7] Model choice is probably better based on values of some information index, such as the Akaike Information Criterion and related indices.[8] Promising resampling methods also exist for determining the number of latent classes.[9]

  • Continuous vs. discrete traits

    Whether a pschiatric disorder represents extreme levels of traits continuously distributed in the population, or whether it represents a qualitatively distinct entity is an important issue. For example, if diagnosed ADHD or depression are often only stronger-than-average manifestations of ordinary behavioral traits, it lessens arguments for their pharmacological treatment.

    Fit of a latent class model to data does not in itself mean the disorder is qualitiative. Thorough investigation of this would involve comparison of latent class models to latent trait models [Ref. 12; see also Ref. 13].

Again, the recent studies represent considerable progress in the application of statistical methods to psychiatric taxonomy. Nevertheless, we wish to encourage researchers to endeavor to apply still more advanced methods. We believe this will both enhance the interpretability and relevance of results and motivate progress in statistical methods.

John S. Uebersax, PhD
P.O. Box 31361
Flagstaff, AZ 86003
email: jsuebersax@yahoo.com

William Grove, PhD
Department of Psychology
University of Minnesota
Minneapolis, MN 55455
email: william.m.grove-1@tc.umn.edu

References

  1. Kendler KS, Karkowski LM, Walsh D. The structure of psychosis: latent class analysis of probands from the Roscommon Family Study. Arch Gen Psychiatry. 1998;55:492-499.

  2. Sullivan PF, Kessler RC, Kendler KS. Latent class analysis of lifetime depressive symptoms in the national comorbidity survey. Am J Psychiatry. 1998;155:1398-406.

  3. Qu Y, Tan M, Kutner MH. Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics. 1996;52:797-810.

  4. Uebersax JS. Probit latent class analysis: conditional independence and conditional dependence models. Appl Psychol Measurement, in press.

  5. Hagenaars JA. Latent structure models with direct effects between indicators: local dependence models. Sociol Method Res. 1988;16:379-405.

  6. Bishop YMM, Fienberg SE, Holland PW. Discrete multivariate analysis: theory and practice. Cambridge, Mass: The MIT press; 1975.

  7. McLachlan GJ, Basford KE. Mixture models. New York: Dekker; 1988.

  8. Sclove, S. Application of model-selection criteria to some problems in multivariate analysis. Psychometrika. 1987;52:333-343.

  9. van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform statistical tests in a LCA of anti-social behaviour. In: Rost J, Langeheine R, eds. Applications of Latent Trait and Latent Class Models in the Social Sciences. New York, NY: Waxmann; 1997:196-208.

  10. van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform statistical tests in a LCA of anti-social behaviour. In: Rost J, Langeheine R, eds. Applications of Latent Trait and Latent Class Models in the Social Sciences. New York, NY: Waxmann; 1997:196-208.

  11. van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform statistical tests in a LCA of anti-social behaviour. In: Rost J, Langeheine R, eds. Applications of Latent Trait and Latent Class Models in the Social Sciences. New York, NY: Waxmann; 1997:196-208.

  12. Uebersax JS. (1997). Analysis of student problem behaviors with latent trait, latent class, and related probit mixture models. In: Rost J, Langeheine R, eds. Applications of Latent Trait and Latent Class Models in the Social Sciences. New York, NY: Waxmann; 1997:188-195.

  13. Uebersax JS. Statistical modeling of expert ratings on medical treatment appropriateness. Journal of the American Statistical Association, 88, 421-427, 1993.

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