EM-Based Bayesian Multinomial Logistic Regression for Unordered Multiple Categories with High-Dimensional Genomic Data

Recently, high-dimensional genomic data consisting of the genotypes of a huge number of SNPs or the expression levels of tens of thousands of genes have been effectively collected for some organisms. Such detailed genomic information is valuable for the analysis of genetic characters and indeed, numerous researches on genome-wide association study (GWAS) and genomic selection (GS) have been performed for ordered traits including continuous and discrete ones. Although some unordered categorical traits such as coat color in animals and fruit shape in plants have been important in breeding and genetics, suitable methods for analyzing such traits based on high-dimensional genomic data remain to be developed, in contrast with the many analytical methods devised for ordered traits. In this study, we developed a method of Bayesian multinomial logistic regression using an EM algorithm suitable for the analysis of unordered multi-categorical characters with high-dimensional genomic data, which can be applied to GWAS and GS with massive SNPs as well as tumor classification with the expression levels of an enormous genes in a unified fashion. We evaluated the performance of the developed method with simulated and actual data and confirmed that the method could as well or better perform in identifying relevant genes and predicting the categorical phenotypes than the existing methods.