Bayesian analysis of mixtures in structural equation models with non-ignorable missing data

The British Journal of Mathematical and Statistical Psychology
Jing-Heng Cai, Xin-Yuan Song

Abstract

Structural equation models (SEMs) have become widely used to determine the interrelationships between latent and observed variables in social, psychological, and behavioural sciences. As heterogeneous data are very common in practical research in these fields, the analysis of mixture models has received a lot of attention in the literature. An important issue in the analysis of mixture SEMs is the presence of missing data, in particular of data missing with a non-ignorable mechanism. However, only a limited amount of work has been done in analysing mixture SEMs with non-ignorable missing data. The main objective of this paper is to develop a Bayesian approach for analysing mixture SEMs with an unknown number of components and non-ignorable missing data. A simulation study shows that Bayesian estimates obtained by the proposed Markov chain Monte Carlo methods are accurate and the Bayes factor computed via a path sampling procedure is useful for identifying the correct number of components, selecting an appropriate missingness mechanism, and investigating various effects of latent variables in the mixture SEMs. A real data set on a study of job satisfaction is used to demonstrate the methodology.

References

Jun 14, 2003·The British Journal of Mathematical and Statistical Psychology·Sik-Yum Lee, Xin-Yuan Song
Sep 2, 2009·The British Journal of Mathematical and Statistical Psychology·Yong Li, Hai-Zhong Wang
Jun 1, 1984·IEEE Transactions on Pattern Analysis and Machine Intelligence·S Geman, D Geman

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Citations

Jul 1, 2011·Multivariate Behavioral Research·Zhenqiu Laura LuGitta Lubke
Dec 12, 2012·Canadian Journal on Aging = La Revue Canadienne Du Vieillissement·Maximiliane E Szinovacz, Adam Davey
Dec 12, 2017·Statistical Methods in Medical Research·Deng PanXinyuan Song
Oct 3, 2018·Development and Psychopathology·Alan MecaHeather H McClure
Jan 1, 2014·Identity : the Journal of the Society for Research on Identity Formation·Yuko HommaSabrina T Wong

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