Skip to main content
SpringerLink
Log in

Loglinear Latent Variable Models for Longitudinal Categorical Data

  • Chapter
  • First Online:
Longitudinal Research with Latent Variables

Abstract

Errors and unreliability in categorical data in the form of independent or systematic misclassifications may have serious consequences for the substantive conclusions. This is especially true in the analysis of longitudinal data where very misleading conclusions about the underlying processes of change may be drawn that are completely the result of even very small amounts of misclassifications. Latent class models offer unique possibilities to correct for all kinds of misclassifications. In this chapter, latent class analysis will be used to show the possible distorting influences of misclassifications in longitudinal research and how to correct for them. Both simple and more complicated analyses will be dealt with, discussing both systematic and independent misclassifications.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Agresti, A. (1990). Categorical data analysis. New York: Wiley.

    MATH  Google Scholar 

  • Allen, M. J., & Yen, W. M. (1979). Introduction to measurement theory. Monterey, CA: Brooks/Cole.

    Google Scholar 

  • Allison, P. D. (2009). Fixed effects regression models. QUASS 160. Newbury Park: Sage.

    Google Scholar 

  • Bassi, F., Hagenaars, J. A., Croon, M. A., & Vermunt, J. K. (2000). Estimating true changes when categorical panel data are affected by uncorrelated and correlated errors. Sociological Methods and Research, 29, 230-268.

    Article  Google Scholar 

  • Bergsma, W. P., Croon M., & Hagenaars, J. A. (2009). Marginal models for dependent, clustered, and longitudinal categorical data. Berlin: Springer.

    MATH  Google Scholar 

  • Bishop, Y. M. M., Fienberg, S. E., & Holland, P. W. (1975). Discrete multivariate analysis: Theory and practice. Cambridge, Mass: MIT Press.

    MATH  Google Scholar 

  • Carlsson, G. (1972). Lagged structures and cross-sectional methods. Acta Sociologica, 15, 323-341.

    Article  Google Scholar 

  • 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 (pp. 311-360). New York: Plenum.

    Google Scholar 

  • Coleman, J. S. (1964). Introduction to mathematical sociology. London: Collier.

    Google Scholar 

  • Converse, Ph. E. (1964). The nature of belief systems in mass publics. In D. Apter (Ed.), Ideology and discontent (pp. 206-261). New York: Free Press.

    Google Scholar 

  • Converse, Ph. E. (1980). Rejoinder to Judd and Milburn. American Sociological Review, 45, 644-646

    Article  Google Scholar 

  • Cox, D. R., & Wermuth, N. (1996). Multivariate dependencies: Models, analysis and interpretation. London: Chapman & Hall.

    MATH  Google Scholar 

  • Dayton, C. M., & Macready, G. B. (1988). Concomitant-variable latent class models. Journal of the American Statistical Association, 83, 173-178.

    Article  MathSciNet  Google Scholar 

  • Dayton, C. M., & Macready, G. B. (2002). Use of categorical and continuous covariates in latent class analysis. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 213-233). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Fay, R. E. (1986). Causal models for patterns of nonresponse. Journal of the American Statistical Association, 81, 354-365.

    Article  Google Scholar 

  • Firebaugh, G. (2008). Seven rules for social research. Princeton: Princeton University Press.

    Google Scholar 

  • Goodman, L. A. (1968). The analysis of cross-classified data: Independence, quasi-independence, and interactions in contingency tables with or without missing entries. Journal of the American Statistical Association, 63, 1091-1131.

    Article  MATH  Google Scholar 

  • Goodman, L. A. (1970). The multivariate analysis of qualitative data: Interactions among multiple classifications. Journal of the American Statistical Association, 65, 225-256.

    Google Scholar 

  • Goodman, L. A. (1973a). The analysis of multidimensional contingency tables when some variables are posterior to others: A modified path analysis approach. Biometrika, 60, 179-192.

    Article  MATH  MathSciNet  Google Scholar 

  • Goodman, L. A. (1973b). Causal analysis of data from panel studies and other kinds of surveys. American Journal of Sociology, 78, 1135-1191.

    Article  Google Scholar 

  • Goodman, L. A. (1974a). The analysis of systems of qualitative variables when some of the variables are unobservable. Part I - a modified latent structure approach. American Journal of Sociology, 79, 1179-1259.

    Article  Google Scholar 

  • Goodman, L. A. (1974b). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215-231.

    Article  MATH  MathSciNet  Google Scholar 

  • Haberman, S. J. (1979). Analysis of qualitative data: Vol. 2. New developments. New York: Academic Press.

    Google Scholar 

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

    Article  Google Scholar 

  • Hagenaars, J. A. (1990). Categorical longitudinal data: Log-linear, panel, trend, and cohort analysis. Newbury Park: Sage.

    Google Scholar 

  • Hagenaars, J. A. (1993). Loglinear models with latent variables. Newbury Park: Sage.

    Google Scholar 

  • Hagenaars, J. A. (1998). Categorical causal modeling: Latent class analysis and directed loglinear models with latent variables. Sociological Methods and Research, 26, 436-486.

    Article  Google Scholar 

  • Hagenaars, J. A. (2002). Directed loglinear modeling with latent variables: Causal models for categorical data with nonsystematic and systematic measurement errors. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 234-286). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Hagenaars, J. A. (2005). Misclassification phenomena in categorical data analysis: Regression toward the mean and tendency toward the mode. In L. A. van der Ark, M. A. Croon, & K. Sijtsma (Eds.), New developments in categorical data analysis for the social and behavioral sciences (pp. 15-39). Mahwah, NJ: Lawrence Erlbaum.

    Google Scholar 

  • Hagenaars J. A., Heinen, A. G. J., & Hamers P. A. M. (1980). Causale modellen met diskrete latente variabelen: Een variant op de LISREL-benadering. Methoden en Data Nieuwsbrief, 5, 38-54. VVS-Vereniging voor Statistiek; SWS-Sociaal-Wetenschappelijke Sectie.

    Google Scholar 

  • Hagenaars, J. A., & McCutcheon, A. L. (2002). Applied latent class analysis. Cambridge, UK: Cambridge University Press.

    Book  MATH  Google Scholar 

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

    Google Scholar 

  • Kiiveri, H., & Speed, T. P. (1982). Structural analysis of multivariate data: A review. In S. Leinhardt (Ed.), Sociological methodology 1982 (pp. 209-289). San Francisco, CA: Jossey-Bass.

    Google Scholar 

  • Kendall, P. (1954). Conflict and mood; Factors affecting stability and response. Glencoe, IL: Free Press.

    Google Scholar 

  • Kohfeld, C. W., & Salert, B. (1982). Representation of dynamic models. Political Methodology, 8, 1-32.

    Google Scholar 

  • Koster, J. A. (1997). Gibbs and Markov properties of graphs. Annals of Mathematics and Artificial Intelligence, 21, 13-26.

    Article  MATH  MathSciNet  Google Scholar 

  • Knoke D., & Burke P. J. (1980). Loglinear models. Beverly Hills, CA: Sage.

    Google Scholar 

  • Langeheine, R., & van de Pol, F. (2002). Latent markov chains. In J. A. Hagenaars & A. L. McCutcheon (Eds.), Applied latent class analysis (pp. 304-344). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Lazarsfeld, P. F., & Henry, N. W. (1968). Latent structure analysis. Boston, MA: Houghton Mifflin.

    MATH  Google Scholar 

  • Lazarsfeld P. F. (1972). The problem of measuring turnover. In P. F. Lazarsfeld, A. K. Pasanella, & M. Rosenberg (Eds.), Continuities in the language of social research (pp. 388-398). New York: Free Press.

    Google Scholar 

  • Lauritzen, S. L. (1996). Graphical models. Oxford: Clarendon Press.

    Google Scholar 

  • Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

    MATH  Google Scholar 

  • Molenberghs, G., & Verbeke, G. (2005). Models for discrete longitudinal data. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Mooijaart, A., & van Montfort, K. (2006). Latent Markov models for categorical variables and time-dependent covariates. In K. van Montfort, J. Oud, & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences (pp. 1-18). Mahwah, NJ: Lawrence Erlbaum Associates.

    Google Scholar 

  • Muthén, L. K., & Muthén, B. O. (2006). Mplus: Statistical analysis with latent variables (User’s guide, 4th ed.). Los Angeles, CA: Muthén and Muthén.

    Google Scholar 

  • Pearl, J. (2000). Causality: Models, reasoning, and inference. Cambridge, UK: Cambridge University Press.

    MATH  Google Scholar 

  • Saris, W. E., & Sniderman P. M. (Eds.) (2004). Studies in public opinion: Attitudes, nonattitudes, measurement error, and change. Princeton: Princeton University Press.

    Google Scholar 

  • Schoenberg, R. (1977.) Dynamic models and cross-sectional data: the consequences of dynamic misspecification. Social Science Research, 6, 133-144.

    Article  Google Scholar 

  • Schuman H., & S. Presser (1981). Questions and answers in attitude surveys; experiments on question form, wording, and context. New York: Academic Press.

    Google Scholar 

  • Sutcliffe, J. P. (1965a). A probability model for errors of classification. I. General considerations. Psychometrika, 30, 73-96.

    Article  MATH  MathSciNet  Google Scholar 

  • Sutcliffe, J. P. (1965b). A probability model for errors of classification. II. Particular cases. Psychometrika, 30, 129-155.

    Article  MATH  MathSciNet  Google Scholar 

  • van der Heijden, P. G. M., Dessens, J., & Böckenholt, U. (1996). Estimating the concomitant variable latent class model with the EM algorithm. Journal of Educational and Behavioral Statistics, 21, 215-229.

    Google Scholar 

  • Vermunt, J. K. (1997a). Log-linear models for event histories. Thousand Oaks, CA: Sage.

    Google Scholar 

  • Vermunt, J. K. (1997b). LEM: A general program for the analysis of categorical data: Users manual(Tech. Rep.). Tilburg, The Netherlands: Tilburg University.

    Google Scholar 

  • Vermunt, J. K. (1999). A general class of nonparametric models for ordinal categorical data. Sociological Methodology 1999, 29, 187-223. Washington DC: American Sociological Association.

    Google Scholar 

  • Vermunt, J. K., & Magidson, J. (2002). Latent class cluster analysis. In J. A. Hagenaars & A. McCutcheon (Eds.), Applied latent class analysis. (pp. 89-106). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Vermunt, J. K. (2003). Multilevel latent class analysis. In R. M. Stolzenberg (Ed.), Sociological Methodology 2003. (pp. 213-240). Washington, DC: American Sociological.

    Google Scholar 

  • Vermunt, J. K. (2004). An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models. Statistica Neerlandica, 58, 220-233.

    Article  MATH  MathSciNet  Google Scholar 

  • Vermunt, J. K. (2007). Growth models for categorical response variables: Standard, latent-class, and hybrid approaches. In K. van Montfort, J. Oud & A. Satorra (Eds.), Longitudinal models in the behavioral and related sciences. (pp. 139-158). Mahwah, NJ: Erlbaum.

    Google Scholar 

  • Vermunt, J. K., & Hagenaars, J. A. (2004). Ordinal longitudinal data analysis. In R. C. Hauspie, N. Cameron, & L. Molinari (Eds.), Methods in human growth research. (pp. 374-393). Cambridge, UK: Cambridge University Press.

    Chapter  Google Scholar 

  • Vermunt, J. K., & Magidson, J. (2005) Latent GOLD 4.0 user’s guide. Belmont, Massachusetts: Statistical Innovations Inc.

    Google Scholar 

  • Wiggins, L. M. (1973). Panel analysis. Latent probability models for attitude and behavior processes. Amsterdam, NL: Elsevier.

    Google Scholar 

  • Whittaker, J. W. (1990). Graphical models in applied multivariate statistics. New York: Wiley.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Methodology and Statistics, Tilburg University, Tilburg, The Netherlands

    Jacques A. Hagenaars

Authors
  1. Jacques A. Hagenaars
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jacques A. Hagenaars .

Editor information

Editors and Affiliations

  1. Dept. Econometrics & Operations, Research, Vrije Universiteit Amsterdam, De Boelelaan 1105, Amsterdam, 1081 HV, Netherlands

    Kees van Montfort

  2. Behavioural Science Institute, Radboud University Nijmegen, Montessorilaan 3, Nijmegen, 6525 HR, Netherlands

    Johan H.L. Oud

  3. , Department of Economics and Business, Universitat Pompeu Fabra, Ramon Trias Fargas 25-27, Barcelona, 08005, Spain

    Albert Satorra

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Berlin Heidelberg

About this chapter

Cite this chapter

Hagenaars, J.A. (2010). Loglinear Latent Variable Models for Longitudinal Categorical Data. In: van Montfort, K., Oud, J., Satorra, A. (eds) Longitudinal Research with Latent Variables. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11760-2_1

Download citation

Publish with us

Policies and ethics

Search

Navigation