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.[45]
[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 bestfitting values for quantities such as the population base rates of the latent
classes, instead converges on values that are not bestfitting; 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 bestfitting 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 likelihoodratio chisquared statistic [6] and associated pvalue.
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 strongerthanaverage
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.grove1@tc.umn.edu
References

Kendler KS, Karkowski LM, Walsh D. The structure of psychosis: latent class analysis
of probands from the Roscommon Family Study. Arch Gen Psychiatry.
1998;55:492499.

Sullivan PF, Kessler RC, Kendler KS. Latent class analysis of lifetime depressive
symptoms in the national comorbidity survey. Am J Psychiatry. 1998;155:1398406.

Qu Y, Tan M, Kutner MH. Random effects models in latent class analysis for evaluating
accuracy of diagnostic tests. Biometrics. 1996;52:797810.

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

Hagenaars JA. Latent structure models with direct effects between indicators: local
dependence models. Sociol Method Res. 1988;16:379405.

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

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

Sclove, S. Application of modelselection criteria to some problems in multivariate
analysis. Psychometrika. 1987;52:333343.

van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform
statistical tests in a LCA of antisocial behaviour. In: Rost J, Langeheine R, eds.
Applications of Latent Trait and Latent Class Models in the Social Sciences. New York,
NY: Waxmann; 1997:196208.

van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform
statistical tests in a LCA of antisocial behaviour. In: Rost J, Langeheine R, eds.
Applications of Latent Trait and Latent Class Models in the Social Sciences. New York,
NY: Waxmann; 1997:196208.

van der Heijden P, 't Hart H, Dessens J. A parametric bootstrap procedure to perform
statistical tests in a LCA of antisocial behaviour. In: Rost J, Langeheine R, eds.
Applications of Latent Trait and Latent Class Models in the Social Sciences. New York,
NY: Waxmann; 1997:196208.

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; 1997:188195.

Uebersax JS. Statistical modeling of expert ratings on medical
treatment appropriateness. Journal of the American Statistical Association,
88, 421427, 1993.
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