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Stochastic blockmodels and variants thereof are among the most widely used approaches to community detection for social networks and relational data. A stochastic blockmodel partitions the nodes of a network into disjoint sets, called communities. The approach is inherently related to clustering with mixture models; and raises a similar model selection problem for the number of communities. The Bayesian information criterion (BIC) is a popular solution, however, for stochastic blockmodels, the conditional independence assumption given the communities of the endpoints among different edges is usually violated in practice. In this regard, we propose composite likelihood BIC (CL-BIC) to select the number of communities, and we show it is robust against possible misspecifications in the underlying stochastic blockmodel assumptions. We derive the requisite methodology and illustrate the approach using both simulated and real data. Supplementary materials containing the relevant computer code are available online. [ABSTRACT FROM PUBLISHER]

In this article, for Lasso penalized linear regression models in high-dimensional settings, we propose a modified cross-validation (CV) method for selecting the penalty parameter. The methodology is extended to other penalties, such as Elastic Net. We conduct extensive simulation studies and real data analysis to compare the performance of the modified CV method with other methods. It is shown that the popularK-fold CV method includes many noise variables in the selected model, while the modified CV works well in a wide range of coefficient and correlation settings. Supplementary materials containing the computer code are available online. [ABSTRACT FROM PUBLISHER]