LCA Bibliography

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Introductions and Overviews

Lazarsfeld & Henry (1968) is still the best introduction, but doesn't cover modern estimation methods; Goodman (1974) supplements it nicely. McCutcheon (1987) is handy and inexpensive. Clogg (1995) and Rost (1997; chapter 1) are good chapter-length overviews.
    Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (Ch. 6; pp. 311-359). New York: Plenum.

    Collins, Linda M; Lanza, Stephanie T. Latent class and latent transition analysis: With applications in the social, behavioral, and health sciences. John Wiley & Sons, 2010.

    Goodman, L. A. (1974), "Exploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models," Biometrika, 61, 215-231.

    Haberman, S. J., Qualitative Data Analysis (Vols. 1 & 2), New York, Academic Press, 1979.

    Hagenaars, J. A. (1993). Loglinear models with latent variables. Sage Publications.

    Hagenaars, Jacques A.; McCutcheon, Allan L. Applied Latent Class Analysis. Cambridge University Press, 2002.

    Lazarsfeld, P. F., and Henry, N. W. (1968), Latent Structure Analysis, Boston: Houghton Mifflin.

    Langeheine, R. & Rost, J. (Eds.) (1988). Latent trait and latent class models. New York: Plenum. Mainly contributed chapters detailing methodological extensions of the latent class model; probably not the best choice as an introduction.

    McCutcheon, A. C. (1987). Latent Class Analysis. Beverly Hills: Sage Publications.

A general book on categorical data with an introduction to LCA is: Andersen, E. B. The statistical analysis of categorical data. Second edition, revised. Berlin: Springer-Verlag, 1991

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Software

See LCA Software page.

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Conditional Dependence with LCA

These papers discuss LCA methods that relax conditional independence assumptions. Hagenaars (1988), Qu, Tan & Kutner (1996), and Uebersax (in press) provide a general discussion of the subject. Espeland & Handelman (1989) is a useful source. The remaining papers do not discuss conditional dependence LCA methods explicitly, but the models they present are can be adapted to the problem.
    Espeland, M. A., & Handelman, S. L. (1989). Using latent class models to characterize and assess relative error in discrete measurements. Biometrics, 45, 587-99.

    Hagenaars, J. A. (1988). Latent structure models with direct effects between indicators: Local dependence models. Sociological Methods and Research, 16, 379-405.

    Mislevy, R. J. (1984). Estimating latent distributions. Psychometrika 49, 359-381.

    Qu Y., Tan M., & Kutner M. H. (1996). Random effects models in latent class analysis for evaluating accuracy of diagnostic tests. Biometrics, 52, 797-810.

    Rost, J. (1990). Rasch models in latent classes: An integration of two approaches to item analysis. Applied Psychological Measurement, 14, 271-282.

    Rost, J. (1991). A logistic mixture distribution model for polychotomous item responses. British Journal of Mathematical and Statistical Psychology, 44, 75-92.

    Uebersax, J. S. (1988). Validity inferences from interobserver agreement. Psychological Bulletin, 104, 405-416.

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

    Uebersax, J. S., & Grove, W. M. (1993). A latent trait finite mixture model for the analysis of rating agreement. Biometrics, 49, 823-835.

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Scaling/Discrete Latent Trait Models

Dayton (1999), Heinen (1996), and Lindsay, Clogg & Grego (1991) are places to start.
    Clogg, C. C. (1988), "Latent Class Models for Measuring," in Latent Trait and Latent Class Models, eds. R. Langeheine and J. Rost, New York: Plenum, pp. 173-205.

    Dayton CM. Latent Class Scaling Analysis. Quantitative Applications in the Social Sciences, Vol. 126. Sage Publications, May 1999.

    Dayton, C. M., and Macready, G. B. (1980), "A Scaling Model With Response Errors and Intrinsically Unscalable Respondents," Psychometrika, 45, 343-356.

    Goodman, L. A. (1975), "A New Model for Scaling Response Patterns: An Application of the Quasi-Independence Concept," Journal of the American Statistical Association, 70, 755-768.

    Heinen, T. (1996). Latent class and discrete latent trait models: Similarities and differences. Thousand Oaks, California: Sage.

    Lindsay, B., Clogg, C. C., & Grego, J. (1991). Semiparametric estimation in the Rasch model and related exponential response models, including a simple latent class model for item analysis. Journal of the American Statistical Association, 86, 96-107.

    Uebersax, J. S. (1993). Statistical modeling of expert ratings on medical treatment appropriateness. Journal of the American Statistical Association, 88, 421-427.

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Constrained LCA Models

    Clogg, C. C. (1979). Some latent structure models for the analysis of Likert-type data. Social Science Research, 8, 287-301.

    Croon, M. Latent class analysis with ordered latent classes. The British Journal of Mathematical and Statistical Psychology, 1990, 43, 171-192

    Croon, M. A. Investigating Mokken scalability of dichotomous items by means of ordinal latent class analysis.British Journal of Mathematical & Statistical Psychology, 1991, 44, 315-331

    Dayton, C. M., and Macready, G. B. (1988), "Concomitant-Variable Latent Class Models," Journal of the American Statistical Association, 83, 173-178.

    Dayton CM, Macready GB. Use of Categorical and Continuous Covariates in Latent Class Analysis. In: Advances in Latent Class Modeling, McCutcheon A, Hagenaars J (eds.), Cambridge University Press, in press.

    Formann, A. K. (1978). The latent class analysis of polychotomous data. Biometrical Journal, 20, 755-771.

    Formann, A. K. (1985), "Constrained Latent Class Models: Theory and Applications," British Journal of Mathematical and Statistical Psychology, 38, 87-111.

    Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. Journal of the American Statistical Association, 87, 476-486.

    Formann, A. K. (1992). Linear logistic latent class analysis for polytomous data. J. Amer. Statist. Assoc., 87, 476-486.

    Rost, J., "A Latent Class Model for Rating Data," Psychometrika, Vol. 50, No. 1, 37-49, 1985.

    Rost, J. (1988). Rating scale analysis with latent class models. Psychometrika, 53, 327-348.

    Uebersax, J. S. (1993). Statistical modeling of expert ratings on medical treatment appropriateness. Journal of the American Statistical Association, 88, 421-427.

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History of LCA

The papers below describe cumbersome and obsolete LCA estimation methods used before the development of the EM algorithm. Of possibly more interest are several papers by Paul Lazarsfeld (cited in Lazarsfeld & Henry, 1968) that discuss the assumptions, rationale, and "philosophy" of LCA.
    Anderson, T. W. (1959). Some scaling methods and estimation procedures in the latent class model. In Probability and Statistics, U. Grenander, ed. New York: Wiley, pp. 9-38.

    Gibson, W. A. (1959). Three multivariate models: Factor analysis, latent structure analysis, and latent profile analysis. Psychometrika, 24, 229-252.

See also the online paper Latent Structure Analysis at 50 Years by N. W. Henry.

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LCA Applications: Diagnosis, Rater Agreement

One use of LCA is to estimate the accuracy of raters, observers, or diagnostic tests, in the absence of a criterion measure or "gold standard." Agresti (1992) and Uebersax (1992) review this subject; Walter and Irwig (1988) and Uebersax and Grove (1990) give extensive citations. Clogg (1995) includes a brief introduction to this subject.
    Agresti, A. (1992). "Modelling patterns of agreement and disagreement," Statistical Methods in Medical Research, vol. 1(3); pp?.

    Agresti, A., & Lang, J. B. (1993). Quasi-symmetric latent class models, with application to rater agreement. Biometrics 49, 131-139.

    Albert PS, McShane LM, Shih JH. Latent class modeling approaches for assessing diagnostic error without a gold standard: with applications to p53 immunohistochemical assays in bladder tumors. Biometrics 2001 Jun;57(2):610-9.

    Alvord, W. G., Drummond, J. E., Arthur, L. O., Biggar, R. J., Goedert, Vanzanten S.J.O.; Tytgat K.M.A.J.; DeGara C.J.; Goldie J.; Rashid F.A.; Bowen B.M.; Cook R.J.; Riddell R.H.; Switzer I.; Underdown B.; Hunt R.H. A prospective comparison of symptoms and 5 diagnostic tests in patients with helocobacter-pylori positive and negative dyspepsia European Journal of Gastroenterology & Hepatology, 1991, 3, 463-468

    Christensen AH, Gjorup T, Hilden J, Fenger C, Henriksen B, Vyberg M, Ostergaard K, Hansen BF. Observer homogeneity in the histologic diagnosis of Helicobacter pylori. Latent class analysis, kappa coefficient, and repeat frequency. Scand J Gastroenterol 1992;27(11):933-9.

    Clogg, C. C. (1995). Latent class models. In G. Arminger, C. C. Clogg, & M. E. Sobel (Eds.), Handbook of statistical modeling for the social and behavioral sciences (Ch. 6; pp. 311-359). New York: Plenum.

    Dawid, A. P., and Skene, A. M. (1979), "Maximum Likelihood Estimation of Observer Error-Rates Using the EM Algorithm," Applied Statistics, 28, 20-28.

    Dillon, W. R., and Mulani, N. (1984), "A Probabilistic Latent Class Model for Assessing Inter-Judge Reliability," Multivariate Behavioral Research, 19, 438-458.

    Espeland, M. A., and Handelman, S. L. (1989), "Using Latent Class Models to Characterize and Assess Relative Error in Discrete Measurements," Biometrics, 45, 587-599.

    Gelfand, A. E., H. Solomon, "A Study of Poisson's Models for Jury Verdicts in Criminal and Civil Trials," Journal of the American Statistical Association, Vol. 68, 271-278, 1973.

    Gelfand, A. E., H. Solomon, "Modeling Jury Verdicts in the American Legal System, "Journal of the American Statistical Association, Vol. 69, 32-37, 1974.

    Gelfand, A. E., and Solomon, H. (1975), "Analyzing the Decision-Making Process of the American Jury," Journal of the American Statistical Association, 70, 305-310.

    Goetghebeur E, Liinev J, Boelaert M, Van der Stuyft P. Diagnostic test analyses in search of their gold standard: latent class analyses with random effects. Stat Methods Med Res 2000 Jun;9(3):231-48.

    Guggenmoos-Holzmann I, Vonk R. Kappa-like indices of observer agreement viewed from a latent class perspective. Stat Med 1998;17(8):797-812

    Kraemer, H. C. (1979). Ramifications of a population model for kappa as a coefficient of reliability. Psychometrika 44, 461-472.

    Rindskopf, R., and W. Rindskopf, "The Value of Latent Class Analysis in Medical Diagnosis," Statistics in Medicine, 1986, Vol. 5, pp. 21-27.

    Uebersax, J. S. (1988). Validity inferences from interobserver agreement. Psychological Bulletin, 104, 405-416.

    Uebersax, J. S. (1992). A review of modeling approaches for the analysis of observer agreement. Investigative Radiology, 17, 738-743.

    Uebersax, J. S. (1993). Statistical modeling of expert ratings on medical treatment appropriateness. Journal of the American Statistical Association, 88, 421-427.

    Uebersax, J. S., Grove, W. M. (1989). Latent structure agreement analysis. The RAND Corporation, N-3029-RC, Santa Monica, CA, October 1989.

    Uebersax, J. S., Grove, W. M. (1990). Latent class analysis of diagnostic agreement. Statistics in Medicine, 9, 559-572.

    Uebersax, J. S., Grove, W. M. (1993). A latent trait finite mixture model for the analysis of rating agreement. Biometrics, 49, 823-835.

    Walter, S. D. "Measuring the reliability of clinical data: the case for using three observers," Revue d'Epidemiologie et de Sante Publique, 32, 206-211 (1984).

    Walter, S. D., and Irwig, L. M. (1988), "Estimation of Test Error Rates, Disease Prevalence and Relative Risk from Misclassified Data: A Review," Journal of Clinical Epidemiology, 41, 923-937.

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LCA Applications: Psychiatry

This list is by no means complete. For additional references, try searching the National Library of Medicine's PubMed system (free web access--search for "PubMed" with a search engine).
    Eaton, W. W., Dryman, A., Sorenson, A., McCutcheon, A. DSM-III major depressive disorder in the community--A latent class analysis of data from the NIMH epidemiologic catchment-area program British Journal of Psychiatry, 1989, 155, 48-54

    Golden, R. R., P. E. Meehl, "Detection of the Schizoid Taxon with MMPI Indicators," Journal of Abnormal Psychology, Vol. 88, 217-233, 1979.

    Golden, R. R. "A Taxometric Model for the Detection of a Conjectured Latent Taxon," Multivariate Behavioral Research, Vol. 16, 389-416, 1982.

    Goldstein, J. M., Santangelo, S. L., Simpson, J. C., Tsuang, M. T. The role of gender in identifying subtypes of schizophrenia--A latent class analytic approach Schizophrenia Bulletin, 1990, 16, 263-275

    Grove, W. M., Andreasen, N. C., Young, M., Endicott, J., Keller, M. B., Hirschfeld, R. M. A. and Reich, T. "Isolation and characterization of a nuclear depressive syndrome", Psychological Medicine, \fB17, 471-484 , 1987.

    Jorgensen, P., Jensen, J. Latent class analysis of deluded patients Psychopathology, 1990, 23, 46-51

    Kendler, K. S., Eaves, L. J., Walters, E. E., Neale, M. C., Heath, A. C., & Kessler, R. C. (1996). The identification and validation of distinct depressive syndromes in a population-based sample of female twins. Archives of General Psychiatry,, 53, 391 399.

    Kendler KS, Eaves LJ, Walters EE, Neale MC, Heath AC, Kessler RC The identification and validation of distinct depressive syndromes in a population-based sample of female twins. Arch Gen Psychiatry 1996;53:391-9

    Kendler KS, Karkowski-Shuman L, O'Neill FA, Straub RE, MacLean CJ, Walsh D Resemblance of psychotic symptoms and syndromes in affected sibling pairs from the Irish Study of High-Density Schizophrenia Families: evidence for possible etiologic heterogeneity. Am J Psychiatry 1997;154:191-8

    Kendler KS, Karkowski LM, Walsh D The structure of psychosis: latent class analysis of probands from the Roscommon Family Study. Arch Gen Psychiatry 1998;55:492-9

    Kessler RC, Stein MB, Berglund P Social phobia subtypes in the National Comorbidity Survey. Latent class analysis of lifetime depressive symptoms in the national Am J Psychiatry 1998 May;155(5):613-9

    Maier, W. and Philipp, M. "Construct validity of the DSM-III and RDC classification of melancholia (endogenous depression)," Journal of Psychiatric Research, 20(4), 289-299 (1986).

    Parker, G., Hadzipavlovic, D., Hickie, I., Boyce, P., Mitchell, P., Wilhelm, K., Brodaty, H. Distinguishing psychotic and nonpsychotic melancholia Journal of Affective Disorders, 1991, 22, 135-148

    Solomon A, Haaga DA, Arnow B. Is clinical depression distinct from subthreshold depressive symptoms? A review of the continuity issue in depression research. J Nerv Ment Dis 2001 Aug;189(8):498-506.

    Sullivan PF, Kessler RC, Kendler KS Latent class analysis of lifetime depressive symptoms in the national comorbidity survey. Am J Psychiatry 1998 Oct;155(10):1398-406

    Uebersax, J. S. (1994). Latent class analysis of substance abuse patterns. In L. Collins & L. Seitz (Eds.), Advances in data analysis for prevention intervention research. NIDA research monograph, No. 142. Rockville, MD: National Institute on Drug A use.

    Ulbricht, Christine M.; Chrysanthopoulou, Stavroula A.; Levin, Len; Lapanea, Kate L. The use of latent class analysis for identifying subtypes of depression: A systematic review. Psychiatry Research 266 (2018): 228-246.

    Young, M. A., "Evaluating Diagnostic Criteria: A Latent Class Paradigm," Journal of Psychiatric Research, Vol. 17, 285-296, 1983.

    Young, M. A., R. Abrams, M. A. Taylor, and H. Y. Meltzer, "Establishing Diagnostic Criteria for Mania," Journal of Nervous and Mental Disease, Vol. 171, 676-682, 1983.

    Young, M. A., W. A. Scheftner, G. K. Klerman, N. C. Andreasen, R. M. Hirschfeld, "The Endogenous Sub-type of Depression: A Study of its Internal Construct Validity," British Journal of Psychiatry, Vol. 148, 257-267, 1986.

    Young, M. A. and Tanner, M. A., "Recent advances in the analysis of qualitative data with applications to diagnostic classification," In Gibbons, R. D. and Dysken, M. (eds.) Statistical and Methodological Advances in Psychiatric Research, Spectrum, New York, 1983.

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LCA Applications: Education

    Aitkin, M., Anderson, D., & Hinde, J. (1981). Statistical modeling of data on teaching styles (with discussion). J. R. Statist. Soc. A, 144, 419-461.

    Bergan, J. R., "Latent-Class Models in Educational Research," in E. W. Gordon (ed.), Review of Research in Education 10, American Educational Research Association, Washington, DC, 1983.

    Dayton, C. M. Educational applications of latent class analysis Measurement and Evaluation in Counseling and Development, 1991, 24, 131-141

    Uebersax, J. S. (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.

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Model Selection, Goodness of Fit, Estimation

    Agresti, A., & Yang, M. (1986). An empirical investigation of some effects of sparseness in contingency tables. Computational Statistics and Data Analysis, 5, 9-21.

    Aitkin, M., Anderson, D., & Hinde, J. (1981). Statistical modeling of data on teaching styles (with discussion). J. R. Statist. Soc. A, 144, 419-461.

    Bozdogan, H. (1987). Model selection and Akaike's information criterion (AIC): The general theory and its analytical extensions. Psychometrika, 52, 345-370.

    Chandler, J. P. (1969). STEPIT--Finds local minima of a smooth function of several parameters. Computer program abstract. Behavioral Science, 14, 81-82.

    Garrett ES, Zeger SL. Latent class model diagnosis. Biometrics 2000 Dec;56(4):1055-67. (PubMed abstract)

    Langeheine R, Pannekoek J, van de Pol, F.  Bootstrapping goodness-of-fit measures in categorical data analysis.  Sociological Methods and Research, 24, 492-516, 1996.

    Lin TH, Dayton CM. Model selection information criteria for non-nested latent class models. Journal of Educational and Behavioral Statistics 1997, 22(3), 249-264.

    Press, W. H., Teukolsky, S. A., Vettering, W. T., & Flannery, B. P. (1989). Numerical recipes in FORTRAN: The art of scientific computing. New York: Cambridge University Press.

    Read, T. R. C., & Cressie, N. A. C. (1988). Goodness-of-fit statistics for discrete multivariate data. New York: Springer-Verlag.

    Schwarz, G. (1978). Estimating the dimension of a model. Annals of Statistics, 6(2), 461-464.

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

    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.

    von Davier M. Bootstrapping goodness-of-fit statistics for sparse categorical data: results of a Monte Carlo study. Methods of Psychological Research 1997, Vol. 2 No. 2. http://www.pabst-publishers.de/mpr/issue3/art5/article.html

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Related Statistical Methods

    Bartholomew, David J. 1987. Latent Variable Models and Factor Analysis. New York: Oxford University Press.

    Day, N. E. Estimating the components of a mixture of normal distributions. Biometrika, 1969, 56, 463-474.

    Collins, L. M. (1992). Latent transition analysis. Presented at NIDA technical review, "Statistical Methods for Substance Abuse Prevention Research," Bethesda, MD, August 1992.

    Everitt, B. S. (1988). A finite mixture model for the clustering of mixed-model data. Statistics and Probability Letters, 6, 305-309.

    Everitt, B. S., & Merette, C. (1990). The clustering of mixed-mode data: A comparison of possible approaches. Journal of Applied Statistics, 17, 283-297.

    Henkelman, R. M., Kay, I., & Bronskill, M. J. (1990). Receiver operator characteristic (ROC) analysis without truth. Medical Decision Making, 10, 24-29.

    Jorgensen, M., & Hunt, L. (1995). Report on mixture model clustering of data sets with categorical and continuous variables. Research Report 36, Series II. Department of Statistics, University of Waikato, Hamilton, New Zealand.

    Langeheine R., F. van de Pol, "A Unifying Framework for Markov Modeling in Discrete Space and Discrete Time," Sociological Methods and Research, Vol. 18, No. 3, 1990.

    Quinn, M. F. (1989), "Relation of Observer Agreement to Accuracy According to a Two-Receiver Signal Detection Model of Diagnosis," Medical Decision Making, 9, 196-206.

    Titterington, D. M., Smith, A. F. M., & Makov, U. E. Statistical analysis of finite mixture distributions. New York: Wiley, 1985.

    Uebersax, J. S. (1996). On the dimensionality of a latent class analysis solution. (Unpublished paper; based on 'Dimension reduction and latent class analysis,' paper presented at the annual meeting of the Classification Society of North America, Pittsburgh, June 1993).

    Wolfe, J. H. Pattern clustering by multivariate mixture analysis. Multivariate Behavioral Research, 1970, 5, 329-350.

    Woodbury, M. A., K. G. Manton (1982). A new procedure for analysis of medical classification. Methods of Information in Medicine, Vol. 21, pp. 210-220.

    Yamamoto, K. (1989). HYBRID model of IRT and latent class model. ETS research report series (RR 89-41). Princeton, NJ: Educational Testing Service.

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