Skip to main content
SpringerLink
Log in

New Developments in Latent Variable Models: Non-linear and Dynamic Models

  • Conference paper
COMPSTAT 2008

  • 1247 Accesses

Abstract

The paper reviews recent work on latent variable models for ordinal longitudinal variables and factor models with non-linear terms. The model for longitudinal data has been recently proposed by Cagnone, Moustaki and Vasdekis (2008). The model allows for time-dependent latent variables to explain the associations among ordinal variables within time where the associations among the same items across time are modelled with item-specific random effects. Rizopoulos and Moustaki (2007) extended the generalized latent variable model framework to allow for non-linear terms (interactions and higher order terms). Both models are estimated with full information maximum likelihood. Computational aspects, goodness-of-fit statistics and an application are presented.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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

  • BARNES, S. and KAASE, M.E. (1979): Political action: Mass participation in five western democracies. Beverley Hills and London: Sage Publications.

    Google Scholar 

  • BARTHOLOMEW, D.J. and KNOTT, M. (1999): Latent Variable Models and Factor Analysis (2nd ed.). London: Arnold.

    MATH  Google Scholar 

  • BARTLETT, M.S. (1953): Factor analysis in psychology as a statistician sees it. In Uppsala Symposium of Psychology and Factor Analysis, pp. 23–34. Uppsala: Almqvist & Wicksell.

    Google Scholar 

  • BOLLEN, K.A. and CURRAN, P.J. (2006): Latent Curve Models: a Structural Equation Perspective. New York: John Wiley.

    MATH  Google Scholar 

  • CAGNONE, S., MOUSTAKI, I. and VASDEKIS, V.: Latent variable models for multivariate longitudinal ordinal responses. British Journal of Mathematical and Statistical Psychology. (To appear).

    Google Scholar 

  • EID, M. (1996): Longitudinal confirmatory factor analysis for polytomous item responses: Model definition and model selection on the basis of stochastic measurement theory. Methods of Psychoilogical Research 1(4), 65–85.

    Google Scholar 

  • GIBSON, W.A. (1960): Nonlinear factors in two dimensions. Psychometrika 25, 381–392.

    Article  MATH  MathSciNet  Google Scholar 

  • JÖRESKOG, K.G. (2002): Structural equation modeling with ordinal variables using LISREL. Available at http://www.ssicentral.com/lisrel/ordinal.htm. 164 Moustaki, I.

  • JÖRESKOG, K.G. and MOUSTAKI, I. (2001): Factor analysis of ordinal variables: a comparison of three approaches. Multivariate Behavioral Research 36, 347–387.

    Article  Google Scholar 

  • JÖRESKOG, K.G. and SÖRBOM, D. (1999): LISREL 8 User’s Reference Guide. Chicago: Scientific Software International.

    Google Scholar 

  • KENNY, D.A. and JUDD, C.M. (1984): Estimating the non-linear and interactive effects of latent variables. Psychological Bulletin 96, 201–210.

    Article  Google Scholar 

  • LEE, S.Y. and SONG, X.Y. (2004): Maximum likelihood analysis of a generalized latent variable model with hierarchically mixed data. Biometrics 60, 624–636.

    Article  MathSciNet  Google Scholar 

  • LEE, S.Y. and ZHU, H. (2002): Maximum likelihood estimation of nonlinear structural equation models. Psychometrika 67, 189–210.

    Article  MathSciNet  Google Scholar 

  • MARSH, H. and GRAYSON, D. (1994): Longitudinal confirmatory factor analysis: Common, time-specific, item-specific, and residual-error components of variance. Structural Equation Modeling 2, 116–145.

    Article  Google Scholar 

  • McDONALD, R.P. (1962): A note on the derivation of the general latent class model. Psychometrika 27(2), 203–206.

    Article  MATH  MathSciNet  Google Scholar 

  • RAFFALOVICH, L. and BOHRNSTEDT, G. (1987): Common, specific, and error variance components of factor models. Sociological Methods and Research 15(4), 385–405.

    Article  Google Scholar 

  • RIZOPOULOS, D. and MOUSTAKI, I. (2007): Generalized latent variable models with non-linear effects. British Journal of Mathematical and Statistical Psychology. in press.

    Google Scholar 

  • SCHUMACKER, R. and MARCOULIDES, G.E. (1998): Interaction and Nonlinear Effects in Structural Equation Models. New Jersey: Lawrence Erlbaum Associates.

    Google Scholar 

  • SONG, X.Y. and LEE, S.Y. (2004): Bayesian analysis of two-level nonlinear structural equation models with continuous and polytomous data. British Journal of Mathematical and Statistical Psychology 57, 29–52.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. London School of Economics and Political Science Department of Statistics, Houghton Street, London, WC2A 2AE, U.K.

    Irini Moustaki

  2. Athens University of Economics and Business Department of Statistics, 76 Patission street, Athens, 104 34, Greece

    Irini Moustaki

Authors
  1. Irini Moustaki
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Irini Moustaki .

Editor information

Editors and Affiliations

  1. Faculdade de Economia, Rua Dr. Roberto Frias, 4200-464, Porto, Portugal

    Paula Brito

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Physica-Verlag Heidelberg

About this paper

Cite this paper

Moustaki, I. (2008). New Developments in Latent Variable Models: Non-linear and Dynamic Models. In: Brito, P. (eds) COMPSTAT 2008. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2084-3_13

Download citation

Publish with us

Policies and ethics

Search

Navigation