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. 相似文献
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. 相似文献
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.
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. 相似文献