A comparison of scalable estimation methods for large-scale logistic regression models with crossed random effects

Parameter estimation of generalized linear models with crossed random effects for large-scale settings is hampered by challenging numerical hindrances. This contribution focuses on logistic regression with crossed-random intercepts and it investigates the properties of two estimation methods for which a scalable software implementation exists, namely the all-row-column and penalized quasi- likelihood methods. The results of a simulation study for sparse settings inspired by e-commerce data, with sample sizes up to 10^6, suggest that the all-row-column method is preferable over penalized quasi-likelihood.