ALAAMEE: Open-source software for fitting autologistic actor attribute models

TL;DR

This work introduces ALAAMEE, open-source Python software for estimation, simulation, and goodness-of-fit testing for ALAAM models, and uses a simulation study to assess the accuracy of the EE algorithm for ALAAM parameter estimation and statistical inference.

Abstract

The autologistic actor attribute model (ALAAM) is a model for social influence, derived from the more widely known exponential-family random graph model (ERGM). ALAAMs can be used to estimate parameters corresponding to multiple forms of social contagion associated with network structure and actor covariates. This work introduces ALAAMEE, open-source Python software for estimation, simulation, and goodness-of-fit testing for ALAAM models. ALAAMEE implements both the stochastic approximation and equilibrium expectation (EE) algorithms for ALAAM parameter estimation, including estimation from snowball sampled network data. It implements data structures and statistics for undirected, directed, and bipartite networks. We use a simulation study to assess the accuracy of the EE algorithm for ALAAM parameter estimation and statistical inference, and demonstrate the use of ALAAMEE with empirical examples using both small (fewer than 100 nodes) and large (more than 10 000 nodes) networks.

Figures (8)

• Figure 1: Configurations used in ALAAMs for undirected networks.
• Figure 2: Example change statistic implementations. Some change statistics for directed networks.
• Figure 3: Configurations used in ALAAMs for directed networks.
• Figure 4: Parameter estimates and estimated standard errors from the EE algorithm. The algorithm was used to estimate the known ALAAM parameters for the Project 90 network with simulated attributes. The error bars show the nominal $95\%$ confidence interval. The horizontal line shows the true value of the parameter, and each plot is annotated with the mean bias, root mean square error (RMSE), the percentage of samples for which the true value is inside the confidence interval (coverage rate), and the Type II error rate (False Negative Rate, FNR). $\mathrm{N_C}$ is the number of samples (of the total 100) for which a converged estimate was found.
• Figure 5: Type II error rate as the number of runs used for each sample is varied.