Hostname: page-component-7dd5485656-hw7sx Total loading time: 0 Render date: 2025-11-02T21:22:37.572Z Has data issue: false hasContentIssue false
  • English
  • Français

Generalized Latent Trait Models

Published online by Cambridge University Press:  01 January 2025

Irini Moustaki  and
Martin Knott
Irini Moustaki*
Affiliation:
London School of Economics and Political Science
Martin Knott
Affiliation:
London School of Economics and Political Science
*
Requests for reprints should be sent to Irini Moustaki, Department of Statistics, London School of Economics, Houghton Street, London WC2A 2AE, UK. E-mail: i.moustaki @lse.ac.uk
Get access Rights & Permissions [Opens in a new window]

Abstract

In this paper we discuss a general model framework within which manifest variables with different distributions in the exponential family can be analyzed with a latent trait model. A unified maximum likelihood method for estimating the parameters of the generalized latent trait model will be presented. We discuss in addition the scoring of individuals on the latent dimensions. The general framework presented allows, not only the analysis of manifest variables all of one type but also the simultaneous analysis of a collection of variables with different distributions. The approach used analyzes the data as they are by making assumptions about the distribution of the manifest variables directly.

Keywords

generalized linear modelslatent trait modelEM algorithmscoring methods

Information

Type
Original Paper
Information
Psychometrika , Volume 65 , Issue 3 , September 2000 , pp. 391 - 411
Copyright
Copyright © 2000 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

Akaike, H. (1987). Factor analysis and AIC. Psychometrika, 52, 317–332CrossRefGoogle Scholar
Arminger, G., Küsters, U. (1988). Latent trait models with indicators of mixed measurement level. In Langeheine, R., Rost, J. (Eds.), Latent trait and latent class models (pp. 51–73). New York: Plenum PressCrossRefGoogle Scholar
Bartholomew, D. J. (1980). Factor analysis for categorical data. Journal of the Royal Statistical Society, Series B, 42, 293–321CrossRefGoogle Scholar
Bartholomew, D. J. (1981). Posterior analysis of the factor model. British Journal of Mathematical and Statistical Psychology, 34, 93–99CrossRefGoogle Scholar
Bartholomew, D. J. (1984). Scaling binary data using a factor model. Journal of the Royal Statistical Society, Series B, 46, 120–123CrossRefGoogle Scholar
Bartholomew, D. J., Knott, M. (1999). Latent variable models and factor analysis 2nd ed., London: ArnoldGoogle Scholar
Bartholomew, D. J., Tzamourani, P. (1999). The goodness-of-fit of latent trait models in attitude measurement. Sociological Methods and Research, 27, 525–546CrossRefGoogle Scholar
Birnbaum, A. (1968). Test scores, sufficient statistics, and the information structures of tests. In Lord, F. M., Novick, M. R. (Eds.), Statistical theories of mental test scores (pp. 425–435). Reading, Mass.: Addison-WesleyGoogle Scholar
Bock, R. D. (1972). Estimating item parameters and latent ability when responses are scored in two or more nominal categories. Psychometrika, 37, 29–51CrossRefGoogle Scholar
Bock, R. D., Aitkin, M. (1981). Marginal maximum likelihood estimation of item parameters: Application of EM algorithm. Psychometrika, 46, 443–459CrossRefGoogle Scholar
Gifi, A. (1990). Nonlinear multivariate analysis. New York: John Wiley & SonsGoogle Scholar
Green, M. (1996). Generalized factor analysis. Proceedings of the 11th International Workshop on Statistical Modelling. Orvieto, Italy.Google Scholar
Jöreskog, K. G. (1990). New developments in LISREL: Analysis of ordinal variables using polychoric correlations and weighted least squares. Quality and Quantity, 24, 387–404CrossRefGoogle Scholar
Jöreskog, K. G. (1994). On the estimation of polychoric correlations and their asymptotic covariance matrix. Psychometrika, 59, 381–389CrossRefGoogle Scholar
Knott, M., Albanese, M. T. (1993). Conditional distributions of a latent variable and scoring for binary data. Revista Brasileira de Probabilidade e Estatística, 6, 171–188Google Scholar
Lawley, D. N., Maxwell, A. E. (1971). Factor analysis as a statistical method. London: ButterworthGoogle Scholar
Lee, S.-Y., Poon, W.-Y., Bentler, P. (1992). Structural equation models with continuous and polytomous variables. Psychometrika, 57, 89–105CrossRefGoogle 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
Masters, G. N. (1982). A Rasch models for partial credit scoring. Psychometrika, 47, 149–174CrossRefGoogle Scholar
McCullagh, P., Nelder, J. (1989). Generalized linear models 2nd ed., London: Chapman & HallCrossRefGoogle Scholar
Mellenbergh, G. (1992). Generalized linear item response theory. Psychological Bulletin, 115, 300–307CrossRefGoogle Scholar
Moustaki, I. (1996). A latent trait and a latent class model for mixed observed variables. British Journal of Mathematical and Statistical Psychology, 49, 313–334CrossRefGoogle Scholar
Moustaki, I. (1999). LATENT: A computer program for fitting a one- or two-factor latent variable model to categorical, metric and mixed observed items with missing values (Technical report). London School of Economics and Political Science, Statistics Department.Google Scholar
Moustaki, I. (in press). A latent variable model for ordinal variables. Applied Psychological Measurement.Google Scholar
Muraki, E., Bock, R. D. (1991). PARSCALE: Parameter scaling of rating data. Chicago: Scientific SoftwareGoogle Scholar
Muthén, B. (1984). A general structural equation model with dichotomous, ordered categorical and continuous latent variables indicators. Psychometrika, 49, 115–132CrossRefGoogle Scholar
Nelder, J., Wedderburn, R. (1972). Generalized linear models. Journal of the Royal Statistical Society, Series A, 135, 370–384CrossRefGoogle Scholar
Olsson, U. (1979). Maximum likelihood estimation of the polychoric correlation coeficient. Psychometrika, 44, 443–460CrossRefGoogle Scholar
Olsson, U., Drasgow, F., Dorans, N. (1982). The polyserial correlation coeficient. Psychometrika, 47, 337–347CrossRefGoogle Scholar
O'Muircheartaigh, C., Moustaki, I. (1999). Symmetric pattern models: a latent variable approach to item non-response in attitude scales. Journal of the Royal Statistical Society, Series A, 162, 177–194CrossRefGoogle Scholar
Reiser, M., VandenBerg, M. (1994). Validity of the chi-square test in dichotomous variable factor analysis when expected frequencies are small. British Journal of Mathematical and Statistical Psychology, 47, 85–107CrossRefGoogle Scholar
Samejima, F. (1969). Estimation of latent ability using a response pattern of graded scores. Psychometrika Monograph Supplement No. 17.CrossRefGoogle Scholar
Sammel, M., Ryan, L., Legler, J. (1997). Latent variable models for mixed discrete and continuous outcomes. Journal of the Royal Statistical Society, Series B, 59, 667–678CrossRefGoogle Scholar
Sclove, S. (1987). Application of model-selection criteria to some problems in multivariate analysis. Psychometrika, 52, 333–343CrossRefGoogle Scholar
Takane, Y., De Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408CrossRefGoogle Scholar
Thissen, D. (1991). MULTILOG: Multiple, categorical items analysis and test scoring using item response theory. Chicago: Scientific SoftwareGoogle Scholar
Thissen, D., Steinberg, L. (1984). A model for multiple choice items. Psychometrika, 49, 501–519CrossRefGoogle Scholar
Verhelst, N. D., Glas, C. A. W. (1993). A dynamic generalization of the rasch model. Psychometrika, 58, 395–415CrossRefGoogle Scholar