  The human microbiome plays an important role in human health and disease
status. Next generating sequencing technologies allow for quantifying the
composition of the human microbiome. Clustering these microbiome data can
provide valuable information by identifying underlying patterns across samples.
Recently, Fang and Subedi (2020) proposed a logistic normal multinomial mixture
model (LNM-MM) for clustering microbiome data. As microbiome data tends to be
high dimensional, here, we develop a family of logistic normal multinomial
factor analyzers (LNM-FA) by incorporating a factor analyzer structure in the
LNM-MM. This family of models is more suitable for high-dimensional data as the
number of parameters in LNM-FA can be greatly reduced by assuming that the
number of latent factors is small. Parameter estimation is done using a
computationally efficient variant of the alternating expectation conditional
maximization algorithm that utilizes variational Gaussian approximations. The
proposed method is illustrated using simulated and real datasets.
