Model-based clustering for social networks

Summary.  Network models are widely used to represent relations between interacting units or actors. Network data often exhibit transitivity, meaning that two actors that have ties to a third actor are more likely to be tied than actors that do not, homophily by attributes of the actors or dyads, and clustering. Interest often focuses on finding clusters of actors or ties, and the number of groups in the data is typically unknown. We propose a new model, the latent position cluster model , under which the probability of a tie between two actors depends on the distance between them in an unobserved Euclidean 'social space', and the actors' locations in the latent social space arise from a mixture of distributions, each corresponding to a cluster. We propose two estimation methods: a two-stage maximum likelihood method and a fully Bayesian method that uses Markov chain Monte Carlo sampling. The former is quicker and simpler, but the latter performs better. We also propose a Bayesian way of determining the number of clusters that are present by using approximate conditional Bayes factors. Our model represents transitivity, homophily by attributes and clustering simultaneously and does not require the number of clusters to be known. The model makes it easy to simulate realistic networks with clustering, which are potentially useful as inputs to models of more complex systems of which the network is part, such as epidemic models of infectious disease. We apply the model to two networks of social relations. A free software package in the R statistical language, latentnet, is available to analyse data by using the model.     

Identity for the NPMLE in Censored Data Models

We derive an identity for nonparametric maximum likelihood estimators (NPMLE) and regularized MLEs in censored data models which expresses the standardized maximum likelihood estimator in terms of the standardized empirical process. This identity provides an effective starting point in proving both consistency and efficiency of NPMLE and regularized MLE. The identity and corresponding method for proving efficiency is illustrated for the NPMLE in the univariate right-censored data model, the regularized MLE in the current status data model and for an implicit NPMLE based on a mixture of right-censored and current status data. Furthermore, a general algorithm for estimation of the limiting variance of the NPMLE is provided. This revised version was published online in July 2006 with corrections to the Cover Date.     

A model for collaboration networks giving rise to a power-law distribution with an exponential cutoff

Recently several authors have proposed stochastic evolutionary models for the growth of complex networks that give rise to power-law distributions. These models are based on the notion of preferential attachment leading to the “rich get richer” phenomenon. Despite the generality of the proposed stochastic models, there are still some unexplained phenomena, which may arise due to the limited size of networks such as protein, e-mail, actor and collaboration networks. Such networks may in fact exhibit an exponential cutoff in the power-law scaling, although this cutoff may only be observable in the tail of the distribution for extremely large networks. We propose a modification of the basic stochastic evolutionary model, so that after a node is chosen preferentially, say according to the number of its inlinks, there is a small probability that this node will become inactive. We show that as a result of this modification, by viewing the stochastic process in terms of an urn transfer model, we obtain a power-law distribution with an exponential cutoff. Unlike many other models, the current model can capture instances where the exponent of the distribution is less than or equal to two. As a proof of concept, we demonstrate the consistency of our model empirically by analysing the Mathematical Research collaboration network, the distribution of which has been shown to be compatible with a power law with an exponential cutoff.     

The acquisition of tacts,mands, and intraverbals by individuals with traumatic brain injury

Two individuals who sustained traumatic brain injuries from motorcycle accidents were taught several verbal responses by using tact, mand, and intraverbal training procedures. The rate of acquisition for each operant and the transfer to untrained verbal operants involving the same response topography were measured. The results showed that tacts and intraverbals were acquired quickest, and training on the tact produced the greatest amount of transfer to the untrained verbal operants. Intraverbal training also resulted in transfer for both subjects, but to varying degrees. Direct mand training proved to be the least efficient way to generate a mand repertoire, and when acquired showed least amount of transfer to the untrained operants. These results seem to be in contrast with the findings of similar research with developmentally disabled individuals, and may have implications for methods of language instruction for the brain injured population.

     

Can a Family Therapist do Statutory Work?

Despite a clear interest in problems such as child abuse it appears that family therapists could work more extensively and constructively with statutory presentations. This paper proposes three reasons as partial explanation for the difficulty many therapists have in working with statutory cases. These reasons are: (i) a belief that social control is not the business of therapy, (ii) a belief in a particular and restrictive notion of neutrality, and (iii) a practice habit of talking less than directly to clients. The existence and persistence of these constraints to the effective provision of statutory services is related to the historical tradition which largely structures professional/client relationships. It is argued that this pattern is highly implicit in our work and can therefore act to restrict our practice and our ability to envisage alternatives.     

The Role of Second-Order Belief-Understanding and Social Context in Children's Self-Attribution of Social Emotions

Children's self-attribution of social emotions was hypothesised (i) to be related to their second-order belief-understanding and (ii) to be more strongly related to social- conventional than moral rule violations. Thirty children aged between 4 and 7 years were presented with Sullivan, Zaitchik & Tager-Flusberg's (1994) second-order false belief task and with four hypothetical scenarios in which they were required to imagine that they had violated particular moral and social conventional rules. As predicted, the self-attribution of social emotions was significantly related to second-order belief understanding, primarily in social-conventional rather than moral contexts.     

Managing urban wetlands for multiple use: research,restoration, and recreation

Conservation of urban wetland habitat is challenging, because multiple uses must coexist. We use examples from California and Wisconsin to describe potential synergies among recreation, restoration and research activities (the 3 R's). Allowing passive recreation is often essential to garner public support for habitat protection, restoration, and research. In turn, restoration activities can improve the appearance of degraded sites, and designing the work as a research experiment can serve the scientific community. Two projects at Tijuana Estuary support the 3 R's. (1) Oneonta Tidal Linkage is a 0.7-ha tidal channel and salt marsh that was excavated from disturbed upland to bring wetland habitat closer to the Visitor Center (thereby reducing visitor intrusion into natural marsh habitat, where endangered species would be disturbed). It supports an ambitious field experiment that is testing the importance of species diversity in restoration; it also includes a bridge that serves the interpretive program, and it adds 0.7 ha of wetland habitat that helps restore regional biodiversity. (2) A larger excavation (8 ha) of former tidal wetland will soon add wetland habitat, while testing the importance of tidal creek networks in ecosystem functioning and offering views and interpretive opportunities. A third situation, at the 485-ha University of Wisconsin–Madison Arboretum, concerns restored wet prairies, which provide habitat for native species and serve many hikers. Urban stormwater flows into and degrades the Henry Greene Prairie, allowing aggressive plants to invade. Research and restoration efforts are planned to sustain the habitat and recreation functions. These three models suggest that recreation, restoration, and research are compatible uses of urban wetland habitats.