  Unmeasured or latent variables are often the cause of correlations between
multivariate measurements, which are studied in a variety of fields such as
psychology, ecology, and medicine. For Gaussian measurements, there are
classical tools such as factor analysis or principal component analysis with a
well-established theory and fast algorithms. Generalized Linear Latent Variable
models (GLLVMs) generalize such factor models to non-Gaussian responses.
However, current algorithms for estimating model parameters in GLLVMs require
intensive computation and do not scale to large datasets with thousands of
observational units or responses.
  In this article, we propose a new approach for fitting GLLVMs to
high-dimensional datasets, based on approximating the model using penalized
quasi-likelihood and then using a Newton method and Fisher scoring to learn the
model parameters. Computationally, our method is noticeably faster and more
stable, enabling GLLVM fits to much larger matrices than previously possible.
We apply our method on a dataset of 48,000 observational units with over 2,000
observed species in each unit and find that most of the variability can be
explained with a handful of factors. We publish an easy-to-use implementation
of our proposed fitting algorithm.
