Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T08:56:05.970Z Has data issue: false hasContentIssue false
  • English
  • Français

A Composite Likelihood Inference in Latent Variable Models for Ordinal Longitudinal Responses

Published online by Cambridge University Press:  01 January 2025

Vassilis G. S. Vasdekis,
Silvia Cagnone and
Irini Moustaki
Vassilis G. S. Vasdekis*
Affiliation:
Athens University of Economics and Business
Silvia Cagnone
Affiliation:
University of Bologna
Irini Moustaki
Affiliation:
London School of Economics and Political Science
*
Requests for reprints should be sent to Vassilis G.S. Vasdekis, Department of Statistics, Athens University of Economics and Business, 76 Patission Street, 10434 Athens, Greece. E-mail: vasdekis@aueb.gr
Get accessRights & Permissions [Opens in a new window]

Abstract

The paper proposes a composite likelihood estimation approach that uses bivariate instead of multivariate marginal probabilities for ordinal longitudinal responses using a latent variable model. The model considers time-dependent latent variables and item-specific random effects to be accountable for the interdependencies of the multivariate ordinal items. Time-dependent latent variables are linked with an autoregressive model. Simulation results have shown composite likelihood estimators to have a small amount of bias and mean square error and as such they are feasible alternatives to full maximum likelihood. Model selection criteria developed for composite likelihood estimation are used in the applications. Furthermore, lower-order residuals are used as measures-of-fit for the selected models.

Keywords

composite likelihoodlongitudinalordinal datalatent variablesgoodness-of-fit measures

Information

Type
Original Paper
Information
Psychometrika , Volume 77 , Issue 3 , July 2012, pp. 425 - 441
Copyright
Copyright © 2012 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Arnold, B.C., Strauss, D. (1991). Pseudolikelihood estimation: some examples. Sankya: The Indian Journal of Statistics, 53, 233–243Google Scholar
Azzalini, A. (1983). Maximum likelihood estimation of order m for stationary stochastic processes. Biometrika, 70, 381–387CrossRefGoogle Scholar
Bartholomew, D.J., Leung, S.O. (2002). A goodness-of-fit test for sparse 2p contingency tables. British Journal of Mathematical & Statistical Psychology, 55, 1–15CrossRefGoogle ScholarPubMed
Besag, J.E. (1974). Spatial interaction and the statistical analysis of lattice systems (with discussion). Journal of the Royal Statistical Society, Series B, 36, 192–236CrossRefGoogle Scholar
Cagnone, S., Moustaki, I., Vasdekis, V. (2009). Latent variable models for multivariate longitudinal ordinal responses. British Journal of Mathematical & Statistical Psychology, 62, 401–415CrossRefGoogle ScholarPubMed
Cai, L. (2010). A two-tier full-information item factor analysis model with applications. Psychometrika, 75, 581–612CrossRefGoogle Scholar
Cai, L., Maydeu-Olivares, A., Coffman, D.L., Thissen, D. (2006). Limited information goodness-of-fit testing of item response theory models for sparse 2p tables. British Journal of Mathematical & Statistical Psychology, 59, 173–194CrossRefGoogle ScholarPubMed
Cox, D.R. (1975). Partial likelihood. Biometrika, 62, 269–274CrossRefGoogle Scholar
Cox, D.R., Reid, N. (2004). A note on pseudolikelihood constructed from marginal densities. Biometrika, 91, 729–737CrossRefGoogle Scholar
Dunson, B. (2003). Dynamic latent trait models for multidimensional longitudinal data. Journal of the American Statistical Association, 98, 555–563CrossRefGoogle Scholar
Feddag, M., Bacci, S. (2009). Pairwise likelihood for the longitudinal mixed Rasch model. Computational Statistics & Data Analysis, 53, 1027–1037CrossRefGoogle Scholar
Geys, H., Molenberghs, G., Ryan, L.M. (1999). Pseudolikelihood modeling of multivariate outcomes in developmental toxicology. Journal of the American Statistical Association, 94, 734–745CrossRefGoogle Scholar
Gibbons, R.D., Hedeker, D. (1992). Full-information item bifactor analysis. Psychometrika, 57, 423–436CrossRefGoogle Scholar
Heagerty, P., Lele, S. (1998). A composite likelihood approach to binary spatial data. Journal of the American Statistical Association, 93, 1099–1111CrossRefGoogle Scholar
Huber, P., Ronchetti, E., Victoria-Feser, M.-P. (2004). Estimation of generalized linear latent variable models. Journal of the Royal Statistical Society, Series B, 66, 893–908CrossRefGoogle Scholar
Joe, H., Maydeu-Olivares, A. (2010). A general family of limited information goodness-of-fit statistics for multinomial data. Psychometrika, 75, 393–419CrossRefGoogle Scholar
Jöreskog, K.G., Moustaki, I. (2001). Factor analysis of ordinal variables: a comparison of three approaches. Multivariate Behavioral Research, 36, 347–387CrossRefGoogle ScholarPubMed
Lindsay, B. (1988). Composite likelihood methods. In Prabhu, N.U. Statistical inference from stochastic processes, Providence: Am. Math. Soc. 221239CrossRefGoogle Scholar
Louis, T.A. (1982). Finding the observed information matrix when using the EM algorithm. Journal of the Royal Statistical Society, Series B, 44, 226–233CrossRefGoogle Scholar
Maydeu-Olivares, A., Joe, H. (2005). Limited and full-information estimation and goodness-of-fit testing in 2n contingency tables: a unified framework. Journal of the American Statistical Association, 100, 1009–1020CrossRefGoogle Scholar
Maydeu-Olivares, A., Joe, H. (2006). Limited information goodness-of-fit testing in multidimensional contingency tables. Psychometrika, 71, 713–732CrossRefGoogle Scholar
Rabe-Hesketh, S., Skrondal, A., Pickles, A. (2005). Maximum likelihood estimation of limited and discrete dependent variable models with nested random effects. Journal of Econometrics, 128, 301–323CrossRefGoogle Scholar
Reiser, M. (1996). Analysis of residuals for the multinomial item response model. Psychometrika, 61, 509–528CrossRefGoogle Scholar
Ronchetti, E. (1997). Robustness aspects of model choice. Statistica Sinica, 7, 327–338Google Scholar
Schilling, S., Bock, R. (2005). High-dimensional maximum marginal likelihood item factor analysis by adaptive quadrature. Psychometrika, 70, 533–555CrossRefGoogle Scholar
Stone, M. (1977). An asymptotic equivalence of choice of model by cross-validation and Akaike’s criterion. Journal of the Royal Statistical Society, Series B, 39, 44–47CrossRefGoogle Scholar
Straud, A.H., Sechrest, D. (1966). Gaussian quadrature formulas, Englewood Cliffs: Prentice HallGoogle Scholar
Tsonaka, R., Moustaki, I. (2007). Parameter constraints in generalized linear latent variable models. Computational Statistics & Data Analysis, 51, 4164–4177CrossRefGoogle Scholar
Varin, C. (2008). On composite marginal likelihoods. Advances in Statistical Analysis, 92, 1–28CrossRefGoogle Scholar
Varin, C., Reid, N., Firth, D. (2011). An overview of composite likelihood methods. Statistica Sinica, 21, 5–42Google Scholar
Varin, C., Vidoni, P. (2005). A note on composite likelihood inference and model selection. Biometrika, 92, 519–528CrossRefGoogle Scholar