The New England Journal of Statistics in Data Science

Social networks primarily focus on the phenomenon of the contagion effect when examining behavior patterns within specific social groups. However, the impact of peer effects is characterized by the tendency to imitate the behaviors of friends and the selection process, where individuals tend to affiliate with others sharing similar traits, significantly contributing to shaping social behaviors that are frequently interconnecting. This article presents a Bayesian approach that uses latent-space estimation methods to detect and examine contagion effects, considering the impact of social selection. The research provides a methodological explanation, followed by a sequence of simulation trials designed to explore operational functionalities and possible real-world applications. To illustrate the potential correlation between changes in alcohol use and the influence of social networks, this study concludes by presenting an example of adolescent drinking behavior.

The purpose of this paper is to develop a practical framework for the analysis of the linear mixed-effects models for censored or missing data with serial correlation errors, using the multivariate Student’s t-distribution, being a flexible alternative to the use of the corresponding normal distribution. We propose an efficient ECM algorithm for computing the maximum likelihood estimates for these models with standard errors of the fixed effects and likelihood function as a by-product. This algorithm uses closed-form expressions at the E-step, which relies on formulas for the mean and variance of a truncated multivariate Student’s t-distribution. In order to illustrate the usefulness of the proposed new methodology, artificial and a real dataset are analyzed. The proposed algorithm and methods are implemented in the R package ARpLMEC.