A Zero-Inflated Negative Binomial Factor Model for Microbiome Data Analysis

High-throughput sequencing technology enables a quantitative examination of microbial communities, enhancing the ability to explore connections between the human microbiome and various diseases. Due to the complex nature of microbiome data, which is characterized by high dimensionality, zero inflation, and overdispersion, we propose a zero-inflated negative binomial factor analysis (ZINBFA) model to address these challenges. This model assumes that the sequencing read counts follow a zero-inflated negative binomial (ZINB) distribution, and constructs link functions to analyze the potential low-rank structure of the mean parameter and zero-inflation parameter. To determine the number of latent factors, an information criterion is employed, while the alternating maximum likelihood algorithm is utilized to estimate the unknown parameters within the ZINBFA model. The proposed ZINBFA model is demonstrated to exhibit superior performance and advantages through comprehensive simulation studies and real data applications.