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Biostatistics Advance Access originally published online on August 3, 2005
Biostatistics 2006 7(1):145-163; doi:10.1093/biostatistics/kxi046
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© The Author 2005. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oupjournals.org.

Latent class regression on latent factors

Jia Guo and Melanie Wall*

Division of Biostatistics, School of Public Health, University of Minnesota, A460 Mayo Building, MMC 303, Minneapolis, MN 55455-0378, USA melanie{at}biostat.umn.edu

Yasuo Amemiya

IBM Thomas J. Watson Research Center, 1101 Kitchawan Road, Route 134, Yorktown Heights, NY 10598, USA

* To whom correspondence should be addressed.

In the research of public health, psychology, and social sciences, many research questions investigate the relationship between a categorical outcome variable and continuous predictor variables. The focus of this paper is to develop a model to build this relationship when both the categorical outcome and the predictor variables are latent (i.e. not observable directly). This model extends the latent class regression model so that it can include regression on latent predictors. Maximum likelihood estimation is used and two numerical methods for performing it are described: the Monte Carlo expectation and maximization algorithm and Gaussian quadrature followed by quasi-Newton algorithm. A simulation study is carried out to examine the behavior of the model under different scenarios. A data example involving adolescent health is used for demonstration where the latent classes of eating disorders risk are predicted by the latent factor body satisfaction.

Keywords: Factor analysis; Latent class models; Monte Carlo EM


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