Bayesian Factor Analysis for Binary and Ordinal Phenotypes with Missingness

Binary and ordinal phenotypes are common in clinical screening and self-reported questionnaires, but many factor analysis and matrix factorization methods are only applicable for quantitative phenotypes with real-valued and/or continuous data distributions. To address this, we propose FABOr (Factor Analysis of Binary and Ordinal data), a Bayesian framework for matrix factorization in which the low-rank matrices are latent variables with continuous priors while the phenotypes are observed variables modeled with appropriate binary/ordinal likelihoods. We also develop missing not at random (MNAR) extensions of FABOr for analyzing data with structured missingness. In experiments with simulated phenotypes, we found that FABOr performs similarly to the best-performing benchmark methods on binary data at imputation and exceeds the performance of all tested benchmark methods on ordinal data. We then applied FABOr to analyze real-world binary and ordinal phenotypes from the Simons Foundation SPARK dataset on autism spectrum disorder (ASD) and found that it improved imputation accuracy by up to 5% on binary data and up to 23% on ordinal data relative to the benchmark methods.