Exponential Random Graph Models (ERGMs) have been developed for fitting social network data on both static and dynamic levels. However, the lack of large sample asymptotic properties makes it inadequate in assessing the goodness-of-fit of these ERGMs. Simulation-based goodness-of-fit plots were proposed by Hunter et al (2006), comparing the structured statistics of observed network with those of corresponding simulated networks. In this research, we propose an improved approach to assess the goodness of fit of ERGMs. Our method is shown to improve the existing graphical techniques. We also propose a simulation based test statistic with which the model comparison can be easily achieved. / Biostatistics

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This research seeks an answer to the following question: what is the relationship between the structure of researchers' communication network and the structure of their collaborative output networks (e.g. co-authored publications, joint grant proposals, and joint patent applications), and the impact of these structures on their citation performance and the volume of collaborative research outputs? Three complementary studies are performed to answer this main question as discussed below. 1. Study I: A frequently used output to measure scientific (or research) collaboration is co-authorship in scholarly publications. Less frequently used are joint grant proposals and patents. Many scholars believe that co-authorship as the sole measure of research collaboration is insufficient because collaboration between researchers might not result in co-authorship. Collaborations involve informal communication (i.e., conversational exchange) between researchers. Using self-reports from 100 tenured/tenure-track faculty in the College of Engineering at the University of South Florida, researchers' networks are constructed from their communication relations and collaborations in three areas: joint publications, joint grant proposals, and joint patents. The data collection: 1) provides a rich data set of both researchers' in-progress and completed collaborative outputs, 2) yields a rating from the researchers on the importance of a tie to them 3) obtains multiple types of ties between researchers allowing for the comparison of their multiple networks. Exponential Random Graph Model (ERGM) results show that the more communication researchers have the more likely they produce collaborative outputs. Furthermore, the impact of four demographic attributes: gender, race, department affiliation, and spatial proximity on collaborative output relations is tested. The results indicate that grant proposals are submitted with mixed gender teams in the college of engineering. Besides, the same race researchers are more likely to publish together. The demographics do not have an additional leverage on joint patents. 2. Study II: Previous research shows that researchers' social network metrics obtained from a collaborative output network (e.g., joint publications or co-authorship network) impact their performance determined by g-index. This study uses a richer dataset to show that a scholar's performance should be considered with respect to position in multiple networks. Previous research using only the network of researchers' joint publications shows that a researcher's distinct connections to other researchers (i.e., degree centrality), a researcher's number of repeated collaborative outputs (i.e., average tie strength), and a researchers' redundant connections to a group of researchers who are themselves well-connected (i.e., efficiency coefficient) has a positive impact on the researchers' performance, while a researcher's tendency to connect with other researchers who are themselves well-connected (i.e., eigenvector centrality) had a negative impact on the researchers' performance. The findings of this study are similar except that eigenvector centrality has a positive impact on the performance of scholars. Moreover, the results demonstrate that a researcher's tendency towards dense local neighborhoods (as measured by the local clustering coefficient) and the researchers' demographic attributes such as gender should also be considered when investigating the impact of the social network metrics on the performance of researchers. 3. Study III: This study investigates to what extent researchers' interactions in the early stage of their collaborative network activities impact the number of collaborative outputs produced (e.g., joint publications, joint grant proposals, and joint patents). Path models using the Partial Least Squares (PLS) method are run to test the extent to which researchers' individual innovativeness, as determined by the specific indicators obtained from their interactions in the early stage of their collaborative network activities, impacts the number of collaborative outputs they produced taking into account the tie strength of a researcher to other conversational partners (TS). Within a college of engineering, it is found that researchers' individual innovativeness positively impacts the volume of their collaborative outputs. It is observed that TS positively impacts researchers' individual innovativeness, whereas TS negatively impacts researchers' volume of collaborative outputs. Furthermore, TS negatively impacts the relationship between researchers' individual innovativeness and the volume of their collaborative outputs, which is consistent with `Strength of Weak Ties' Theory. The results of this study contribute to the literature regarding the transformation of tacit knowledge into explicit knowledge in a university context.

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Thesis (MSc)--Stellenbosch University, 2011 / ENGLISH ABSTRACT: With billions of current internet users interacting through social networks, the need has arisen to analyze the structure of these networks. Many authors have proposed random graph models for social networks in an attempt to understand and reproduce the dynamics that govern social network development. This thesis proposes a random graph model that generates social networks using a community-based approach, in which users’ affiliations to communities are explicitly modeled and then translated into a social network. Our approach explicitly models the tendency of communities to overlap, and also proposes a method for determining the probability of two users being connected based on their levels of commitment to the communities they both belong to. Previous community-based models do not incorporate community overlap, and assume mutual members of any community are automatically connected. We provide a method for fitting our model to real-world social networks and demonstrate the effectiveness of our approach in reproducing real-world social network characteristics by investigating its fit on two data sets of current online social networks. The results verify that our proposed model is promising: it is the first community-based model that can accurately reproduce a variety of important social network characteristics, namely average separation, clustering, degree distribution, transitivity and network densification, simultaneously. / AFRIKAANSE OPSOMMING: Met biljoene huidige internet-gebruikers wat deesdae met behulp van aanlyn sosiale netwerke kommunikeer, het die analise van hierdie netwerke in die navorsingsgemeenskap toegeneem. Navorsers het al verskeie toevalsgrafiekmodelle vir sosiale netwerke voorgestel in ’n poging om die dinamika van die ontwikkeling van dié netwerke beter te verstaan en te dupliseer. In hierdie tesis word ’n nuwe toevalsgrafiekmodel vir sosiale netwerke voorgestel wat ’n gemeenskapsgebaseerde benadering volg, deurdat gebruikers se verbintenisse aan gemeenskappe eksplisiet gemodelleer word, en dié gemeenskapsmodel dan in ’n sosiale netwerk omskep word. Ons metode modelleer uitdruklik die geneigdheid van gemeenskappe om te oorvleuel, en verskaf ’n metode waardeur die waarskynlikheid van vriendskap tussen twee gebruikers bepaal kan word, op grond van hulle toewyding aan hulle wedersydse gemeenskappe. Vorige modelle inkorporeer nie gemeenskapsoorvleueling nie, en aanvaar ook dat alle lede van dieselfde gemeenskap vriende sal wees. Ons verskaf ’n metode om ons model se parameters te pas op sosiale netwerk datastelle en vertoon die vermoë van ons model om eienskappe van sosiale netwerke te dupliseer. Die resultate van ons model lyk belowend: dit is die eerste gemeenskapsgebaseerde model wat gelyktydig ’n belangrike verskeidenheid van sosiale netwerk eienskappe, naamlik gemiddelde skeidingsafstand, samedromming, graadverdeling, transitiwiteit en netwerksverdigting, akkuraat kan weerspieël.

In this dissertation, we have proposed two new algorithms for statistical inference for models with intractable normalizing constants: the Monte Carlo Metropolis-Hastings algorithm and the Bayesian Stochastic Approximation Monte Carlo algorithm. The MCMH algorithm is a Monte Carlo version of the Metropolis-Hastings algorithm. At each iteration, it replaces the unknown normalizing constant ratio by a Monte Carlo estimate. Although the algorithm violates the detailed balance condition, it still converges, as shown in the paper, to the desired target distribution under mild conditions. The BSAMC algorithm works by simulating from a sequence of approximated distributions using the SAMC algorithm. A strong law of large numbers has been established for BSAMC estimators under mild conditions. One significant advantage of our algorithms over the auxiliary variable MCMC methods is that they avoid the requirement for perfect samples, and thus it can be applied to many models for which perfect sampling is not available or very expensive. In addition, although the normalizing constant approximation is also involved in BSAMC, BSAMC can perform very robustly to initial guesses of parameters due to the powerful ability of SAMC in sample space exploration. BSAMC has also provided a general framework for approximated Bayesian inference for the models for which the likelihood function is intractable: sampling from a sequence of approximated distributions with their average converging to the target distribution. With these two illustrated algorithms, we have demonstrated how the SAMCMC method can be applied to estimate the parameters of ERGMs, which is one of the typical examples of statistical models with intractable normalizing constants. We showed that the resulting estimate is consistent, asymptotically normal and asymptotically efficient. Compared to the MCMLE and SSA methods, a significant advantage of SAMCMC is that it overcomes the model degeneracy problem. The strength of SAMCMC comes from its varying truncation mechanism, which enables SAMCMC to avoid the model degeneracy problem through re-initialization. MCMLE and SSA do not possess the re-initialization mechanism, and tend to converge to a solution near the starting point, so they often fail for the models which suffer from the model degeneracy problem.

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