Bayesian Factor Analysis for Mixed Ordinal and Continuous Responses

Kevin M. Quinn

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Psychometric Methodologies and Testing Statistical Methods and Bayesian Inference Bayesian Methods and Mixture Models

Abstract

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 theMCMCpack(Martin and Quinn 2004, “MCMCpack 0.4–8”)Rpackage.

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