Matthew James Denny

Stochastic Weighted Graphs: Flexible Model Specification and Simulation

In most domains of network analysis researchers consider networks that arise in nature with weighted edges. Such networks are routinely dichotomized in the interest of using available methods for statistical inference with networks. The generalized exponential random graph model (GERGM) is a recently proposed method used to simulate and model the edges of a weighted graph. The GERGM specifies a joint distribution for an exponential family of graphs with continuous-valued edge weights. However, current estimation algorithms for the GERGM only allow inference on a restricted family of model specifications. To address this issue, we develop a Metropolis -- Hastings method that can be used to estimate any GERGM specification, thereby significantly extending the family of weighted graphs that can be modeled with the GERGM. We show that new flexible model specifications are capable of avoiding likelihood degeneracy and efficiently capturing network structure in applications where such models were not previously available. We demonstrate the utility of this new class of GERGMs through application to two real network data sets, and we further assess the effectiveness of our proposed methodology by simulating non-degenerate model specifications from the well-studied two-stars model. A working R version of the GERGM code is available in the supplement and will be incorporated in the gergm CRAN package.

Statistical Modeling of the Default Mode Brain Network Reveals a Segregated Highway Structure

We investigate the functional organization of the Default Mode Network (DMN) – an important subnetwork within the brain associated with a wide range of higher-order cognitive functions. While past work has shown the whole-brain network of functional connectivity follows small-world organizational principles, subnetwork structure is less well understood. Current statistical tools, however, are not suited to quantifying the operating characteristics of functional networks as they often require threshold censoring of information and do not allow for inferential testing of the role that local processes play in determining network structure. Here, we develop the correlation Generalized Exponential Random Graph Model (cGERGM) – a statistical network model that uses local processes to capture the emergent structural properties of correlation networks without loss of information. Examining the DMN with the cGERGM, we show that, rather than demonstrating small-world properties, the DMN appears to be organized according to principles of a segregated highway – suggesting it is optimized for function-specific coordination between brain regions as opposed to information integration across the DMN. We further validate our findings through assessing the power and accuracy of the cGERGM on a testbed of simulated networks representing various commonly observed brain architectures.

Bag of What? Simple Noun Phrase Extraction for Text Analysis.

Social scientists who do not have specialized natural language processing training often use a unigram bag-of-words (BOW) representation when analyzing text corpora. We offer a new phrase-based method, NPFST, for enriching a unigram BOW. NPFST uses a partof-speech tagger and a finite state transducer to extract multiword phrases to be added to a unigram BOW. We compare NPFST to both ngram and parsing methods in terms of yield, recall, and efficiency. We then demonstrate how to use NPFST for exploratory analyses; it performs well, without configuration, on many different kinds of English text. Finally, we present a case study using NPFST to analyze a new corpus of U.S. congressional bills.

Instrumenting Beliefs in Threshold Public Goods.

Understanding the causal impact of beliefs on contributions in Threshold Public Goods (TPGs) is particularly important since the social optimum can be supported as a Nash Equilibrium and best-response contributions are a function of beliefs. Unfortunately, investigations of the impact of beliefs on behavior are plagued with endogeneity concerns. We create a set of instruments by cleanly and exogenously manipulating beliefs without deception. Tests indicate that the instruments are valid and relevant. Perhaps surprisingly, we fail to find evidence that beliefs are endogenous in either the one-shot or repeated-decision settings. TPG allocations are determined by a base contribution and beliefs in a one shot-setting. In the repeated-decision environment, once we instrument for first-round allocations, we find that second-round allocations are driven equally by beliefs and history. Moreover, we find that failing to instrument prior decisions overstates their importance.

The Importance of Generative Models for Assessing Network Structure

One persistent challenge for scholars who wish to study political networks lies in correctly assessing the structures of the networks under study, and relating their assessments to their substantive theories. In this article, I illustrate the importance of assessing network structure using a generative modelling approach, and of specifying and testing theories about the structure of political networks at multiple levels. Failure to correctly model the generative process can have significant consequences, from missing important alternative explanations for an observed network structure, to specifying a model which does not test the hypotheses that derive from the researchers theory. I introduce a general framework for assessing the structural properties of political networks, and apply it to re-specify an existing political science study that seeks to engage with network concepts. I find that correctly applying generative models can dramatically affect inferences about the structure of a political system.

Inference on the Effects of Observed Features in Latent Space Models for Networks

The latent space model (LSM) for network data is a generative probabilistic model that combines a generalized linear model with a latent spatial embedding of the network. It has been used to decrease error in the estimation of and inference regarding the effects of observed covariates. In applications of the LSM, it is assumed that the latent spatial embedding can control for unmeasured confounding structure that is related to the values of edges in the network. As far as we know, there has been no research that considers the LSM’s performance in adjusting for unmeasured structure to reduce estimation and inferential errors. We investigate the LSM’s performance via a Monte Carlo study. In the presence of an unmeasured covariate that can be appropriately modeled using a latent space, estimation and inferential error remain high under even moderate confounding. However, the prediction error of the LSM when unmeasured network structure is present is substantially lower in most cases. We conclude that the LSM is most appropriately used for exploratory or predictive tasks.