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Generalized latent variables models with non-linear effects

By Dimitris Rizopoulos and Irini Moustaki

Abstract

Until recently, item response models such as the factor analysis model for metric responses, the two-parameter logistic model for binary responses and the multinomial model for nominal responses considered only the main effects of latent variables without allowing for interaction or polynomial latent variable effects. However, non-linear relationships among the latent variables might be necessary in real applications. Methods for fitting models with non-linear latent terms have been developed mainly under the structural equation modelling approach. In this paper, we consider a latent variable model framework for mixed responses (metric and categorical) that allows inclusion of both non-linear latent and covariate effects. The model parameters are estimated using full maximum likelihood based on a hybrid integration–maximization algorithm. Finally, a method for obtaining factor scores based on multiple imputation is proposed here for the non-linear model

Topics: QA Mathematics
Publisher: Wiley-Blackwell on behalf of the British Psychological Society
Year: 2008
DOI identifier: 10.1348/000711007X213963
OAI identifier: oai:eprints.lse.ac.uk:5421
Provided by: LSE Research Online
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