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Classic item response models assume that all items with the same difficulty have the same response probability among all respondents with the same ability. These assumptions, however, may very well be violated in practice, and it is not straightforward to assess whether these assumptions are violated, because neither the abilities of respondents nor the difficulties of items are observed. An example is an educational assessment where unobserved heterogeneity is present, arising from unobserved variables such as cultural background and upbringing of students, the quality of mentorship and other forms of emotional and professional support received by students, and other unobserved variables that may affect response probabilities. To address such violations of assumptions, we introduce a novel latent space model which assumes that both items and respondents are embedded in an unobserved metric space, with the probability of a correct response decreasing as a function of the distance between the respondent’s and the item’s position in the latent space. The resulting latent space approach provides an interaction map that represents interactions of respondents and items, and helps derive insightful diagnostic information on items as well as respondents. In practice, such interaction maps enable teachers to detect students from underrepresented groups who need more support than other students. We provide empirical evidence to demonstrate the usefulness of the proposed latent space approach, along with simulation results. 

It is a pleasure to congratulate Ni et al. (Stat Methods Appl 490:1–32, 2021) on the recent advances in Bayesian graphical models reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021). The authors have given considerable thought to the construction and estimation of Bayesian graphical models that capture salient features of biological networks. My discussion focuses on computational challenges and opportunities along with priors, pointing out limitations of the Markov random field priors reviewed in Ni et al. (Stat Methods Appl 490:1–32, 2021) and exploring possible generalizations that capture additional features of conditional independence graphs, such as hub structure and clustering. I conclude with a short discussion of the intersection of graphical models and random graph models. 

We consider incomplete observations of stochastic processes governing the spread of infectious diseases through finite populations by way of contact. We propose a flexible semiparametric modeling framework with at least three advantages. First, it enables researchers to study the structure of a population contact network and its impact on the spread of infectious diseases. Second, it can accommodate short- and long-tailed degree distributions and detect potential superspreaders, who represent an important public health concern. Third, it addresses the important issue of incomplete data. Starting from first principles, we show when the incomplete-data generating process is ignorable for the purpose of Bayesian inference for the parameters of the population model. We demonstrate the semiparametric modeling framework by simulations and an application to the partially observed MERS epidemic in South Korea in 2015. We conclude with an extended discussion of open questions and directions for future research. 

A widely used approach to modeling discrete‐time network data assumes that discrete‐time network data are generated by an unobserved continuous‐time Markov process. While such models can capture a wide range of network phenomena and are popular in social network analysis, the models are based on the homogeneity assumption that all nodes share the same parameters. We remove the homogeneity assumption by allowing nodes to belong to unobserved subsets of nodes, called blocks, and assuming that nodes in the same block have the same parameters, whereas nodes in distinct blocks have distinct parameters. The resulting models capture unobserved heterogeneity across nodes and admit model‐based clustering of nodes based on network properties chosen by researchers. We develop Bayesian data‐augmentation methods and apply them to discrete‐time observations of an ownership network of non‐financial companies in Slovenia in its critical transition from a socialist economy to a market economy. We detect a small subset of shadow‐financial companies that outpaces others in terms of the rate of change and the desire to accumulate stocks of other companies.

 

Statistical inference for exponential-family models of random graphs with dependent edges is challenging. We stress the importance of additional structure and show that additional structure facilitates statistical inference. A simple example of a random graph with additional structure is a random graph with neighborhoods and local dependence within neighborhoods. We develop the first concentration and consistency results for maximum likelihood and M-estimators of a wide range of canonical and curved exponentialfamily models of random graphs with local dependence. All results are nonasymptotic and applicable to random graphs with finite populations of nodes, although asymptotic consistency results can be obtained as well. In addition, we show that additional structure can facilitate subgraph-to-graph estimation, and present concentration results for subgraph-to-graph estimators. As an application, we consider popular curved exponential-family models of random graphs, with local dependence induced by transitivity and parameter vectors whose dimensions depend on the number of nodes. 

A random graph is given by a pair (G, P), where G is a set of graphs and P is a probability distribution with support G. Random graphs have been studied since the middle of the twentieth century and have witnessed a surge of interest since the turn of the twenty‐first century, fueled by the rise of the Internet and social networks and the growing realization that today's world is a connected world.