<div>Networks and point processes provide flexible tools for representing and modeling complex dependencies in data arising from various social and physical domains. Graphs, or networks, encode relational dependencies between entities, while point processes characterize temporal or spatial interactions among events.</div><div><br></div><div>In the first part of this dissertation, we consider dynamic network data (such as communication networks) in which links connecting pairs of nodes appear continuously over time. We propose latent space point process models to capture two different aspects of the data: (i) communication occurs at a higher rate between individuals with similar latent attributes (i.e., homophily); and (ii) individuals tend to reciprocate communications from others, but in a varied manner. Our framework marries ideas from point process models, including Poisson and Hawkes processes, with ideas from latent space models of static networks. We evaluate our models on several real-world datasets and show that a dual latent space model, which accounts for heterogeneity in both homophily and reciprocity, significantly improves performance in various link prediction and network embedding tasks.</div><div><br></div><div>In the second part of this dissertation, we develop nonparametric goodness-of-fit tests for discrete distributions and point processes that contain intractable normalization constants, providing the first generally applicable and computationally feasible approaches under those circumstances. Specifically, we propose and characterize Stein operators for discrete distributions, and construct a general Stein operator for point processes using the Papangelou conditional intensity function. Based on the proposed Stein operators, we establish kernelized Stein discrepancy measures for discrete distributions and point processes, which enable us to develop nonparametric goodness-of-fit tests for un-normalized density/intensity functions. We apply the kernelized Stein discrepancy tests to discrete distributions (including network models) as well as temporal and spatial point processes. Our experiments demonstrate that the proposed tests typically outperform two-sample tests based on the maximum mean discrepancy, which, unlike our goodness-of-fit tests, assume the availability of exact samples from the null model.</div><div><br></div>

abstract: Although models for describing longitudinal data have become increasingly sophisticated, the criticism of even foundational growth curve models remains challenging. The challenge arises from the need to disentangle data-model misfit at multiple and interrelated levels of analysis. Using posterior predictive model checking (PPMC)—a popular Bayesian framework for model criticism—the performance of several discrepancy functions was investigated in a Monte Carlo simulation study. The discrepancy functions of interest included two types of conditional concordance correlation (CCC) functions, two types of R2 functions, two types of standardized generalized dimensionality discrepancy (SGDDM) functions, the likelihood ratio (LR), and the likelihood ratio difference test (LRT). Key outcomes included effect sizes of the design factors on the realized values of discrepancy functions, distributions of posterior predictive p-values (PPP-values), and the proportion of extreme PPP-values. In terms of the realized values, the behavior of the CCC and R2 functions were generally consistent with prior research. However, as diagnostics, these functions were extremely conservative even when some aspect of the data was unaccounted for. In contrast, the conditional SGDDM (SGDDMC), LR, and LRT were generally sensitive to the underspecifications investigated in this work on all outcomes considered. Although the proportions of extreme PPP-values for these functions tended to increase in null situations for non-normal data, this behavior may have reflected the true misfit that resulted from the specification of normal prior distributions. Importantly, the LR and the SGDDMC to a greater extent exhibited some potential for untangling the sources of data-model misfit. Owing to connections of growth curve models to the more fundamental frameworks of multilevel modeling, structural equation models with a mean structure, and Bayesian hierarchical models, the results of the current work may have broader implications that warrant further research. / Dissertation/Thesis / Doctoral Dissertation Educational Psychology 2015