A Review of Generalized Linear Latent Variable Models and Related Computational Approaches

Generalized linear latent variable models (GLLVMs) have become mainstream models in this analysis of correlated, m‐dimensional data. GLLVMs can be seen as a reduced‐rank version of generalized linear mixed models (GLMMs) as the latent variables which are of dimension p≪m$$ p\ll m $$ induce a reduced‐rank covariance structure for the model. Models are flexible and can be used for various purposes, including exploratory analysis, that is, ordination analysis, estimating patterns of residual correlation, multivariate inference about measured predictors, and prediction. Recent advances in computational tools allow the development of efficient, scalable algorithms for fitting GLLMVs for any response distribution. In this article, we discuss the basics of GLLVMs and review some options for model fitting. We focus on methods that are based on likelihood inference. The implementations available in R are compared via simulation studies and an example illustrates how GLLVMs can be applied as an exploratory tool in the analysis of data from community ecology.