Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses
Political Analysis (2004) 12 (4): 338-353.
01 November 2004
Many situations exist in which a latent construct has both ordinal and continuous indicators. This presents a problem for the applied researcher because standard measurement models are not designed to accommodate mixed ordinal and continuous data. I address this problem by formulating a measurement model that is appropriate for such mixed multivariate responses. This model unifies standard normal theory factor analysis and item response theory models for ordinal data. I detail a Markov chain Monte Carlo algorithm for model fitting. I apply the model to cross-national data on political-economic risk and find that the model works well. Software for fitting this model is publicly available in the MCMCpack (Martin and Quinn 2004, “MCMCpack 0.4–8”) R package.
Author's note: This work was supported under National Science Foundation Grant SES-0350613. In addition, this project benefitted from related collaborative work with Michael Hechter and Erik Wibbels. Wongi Choe provided valuable research assistance. Dan Ho provided helpful comments on an earlier draft. Any errors are mine alone.