Maximum likelihood estimation based on the Laplace approximation for p2 network regression models with crossed random effects

The class of p2 models is suitable for modelling binary relation data in social network analysis. A p2 model is essentially a regression model for multinomial responses, featuring within-dyad dependence and correlated crossed random effects to represent heterogeneity of actors. It has some desirable properties, including simple generation of networks from a given model specication, or the possibility of extension to multilevel data structures. Despite these points, this class of models is used much less frequently in empirical applications than other models for network data. A possible reason for this fact may lie in the computational difficulties existing to estimate such models. The estimation methods proposed in the literature for estimating the parameters of p2 models include joint maximization methods and Bayesian methods based on MCMC, both with some drawbacks. The aim of this paper is to investigate maximum likelihood estimation based on the Laplace approximation approach, that may be equipped with importance sampling. Practical implementation requires some attention, but it can be performed in an efficient manner, and the paper provides details on software implementation using R and ADMB. Numerical examples and simulation studies illustrate the methodology.