On the Question of Effective Sample Size in Network Modeling: An Asymptotic Inquiry

The modeling and analysis of networks and network data has seen an explosion of interest in recent years and represents an exciting direction for potential growth in statistics. Despite the already substantial amount of work done in this area to date by researchers from various disciplines, however, there remain many questions of a decidedly foundational nature - natural analogues of standard questions already posed and addressed in more classical areas of statistics - that have yet to even be posed, much less addressed. Here we raise and consider one such question in connection with network modeling. Specifically, we ask, "Given an observed network, what is the sample size?" Using simple, illustrative examples from the class of exponential random graph models, we show that the answer to this question can very much depend on basic properties of the networks expected under the model, as the number of vertices $n_V$ in the network grows. In particular, adopting the (asymptotic) scaling of the variance of the maximum likelihood parameter estimates as a notion of effective sample size ($n_{\mathrm{eff}}$), we show that when modeling the overall propensity to have ties and the propensity to reciprocate ties, whether the networks are sparse or not under the model (i.e., having a constant or an increasing number of ties per vertex, respectively) is sufficient to yield an order of magnitude difference in $n_{\mathrm{eff}}$, from $O(n_V)$ to $O(n^2_V)$. In addition, we report simulation study results that suggest similar properties for models for triadic (friend-of-a-friend) effects. We then explore some practical implications of this result, using both simulation and data on food-sharing from Lamalera, Indonesia.Comment: Published at http://dx.doi.org/10.1214/14-STS502 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Fitting Latent Cluster Models for Networks with latentnet

latentnet is a package to fit and evaluate statistical latent position and cluster models for networks. Hoff, Raftery, and Handcock (2002) suggested an approach to modeling networks based on positing the existence of an latent space of characteristics of the actors. Relationships form as a function of distances between these characteristics as well as functions of observed dyadic level covariates. In latentnet social distances are represented in a Euclidean space. It also includes a variant of the extension of the latent position model to allow for clustering of the positions developed in Handcock, Raftery, and Tantrum (2007). The package implements Bayesian inference for the models based on an Markov chain Monte Carlo algorithm. It can also compute maximum likelihood estimates for the latent position model and a two-stage maximum likelihood method for the latent position cluster model. For latent position cluster models, the package provides a Bayesian way of assessing how many groups there are, and thus whether or not there is any clustering (since if the preferred number of groups is 1, there is little evidence for clustering). It also estimates which cluster each actor belongs to. These estimates are probabilistic, and provide the probability of each actor belonging to each cluster. It computes four types of point estimates for the coefficients and positions: maximum likelihood estimate, posterior mean, posterior mode and the estimator which minimizes Kullback-Leibler divergence from the posterior. You can assess the goodness-of-fit of the model via posterior predictive checks. It has a function to simulate networks from a latent position or latent position cluster model.

Learning wellness in a new language : exploring views of ESL teachers about refugee mental health

The purpose this research is to explore the potential role that English as a Second Language (ESL) teachers of refugees can play in promoting and supporting their students’ mental health by incorporating a mental health component into their existing curricula. Ten educators were interviewed to discover how ESL teachers of refugees experience and understand refugee mental health and their potential role in it. Data was analyzed using interpretive phenomenological analysis. The analysis yielded the following major themes: Implicit and Explicit Aspects of Teaching Refugees, Relationship with Students, Witnessing and Addressing Mental Health Concerns, Role of ESL in Mental Health, and Pathways to Healing. Results indicated that educators generally see themselves as willing and well-positioned to promote and support refugees’ mental health, but that current structures and systems in ESL education may have a limiting effect on their abilities to do so formally.Educational Psycholog