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Multivariate data that combine binary, categorical, count and continuousoutcomes are common in the social and health sciences. We propose asemiparametric Bayesian latent variable model for multivariate data ofarbitrary type that does not require specification of conditionaldistributions. Drawing on the extended rank likelihood method by Hoff [Ann.Appl. Stat. 1 (2007) 265-283], we develop a semiparametric approach for latentvariable modeling with mixed outcomes and propose associated Markov chain MonteCarlo estimation methods. Motivated by cognitive testing data, we focus onbifactor models, a special case of factor analysis. We employ oursemiparametric Bayesian latent variable model to investigate the associationbetween cognitive outcomes and MRI-measured regional brain volumes.

A semiparametric approach to mixed outcome latent variable models: Estimating the association between cognition and regional brain volumes