Two algorithms for fitting constrained marginal models

There are two main algorithms which have been considered for fitting constrained marginal models to discrete data; these are studied in detail and their properties clarified. The two procedures are shown to be equivalent, in the sense that the updates they produce are identical, each method being advantageous in different circumstances. An extension is provided to one of the algorithms for modelling the effect of exogenous individual-level covariates, and an application of the method to likelihood-based estimation under $L_1$-penalties is also considered.