Relational event models for longitudinal network data with an application to interhospital patient transfers

The main objective of this paper is to introduce and illustrate relational event models, a new class of statistical models for the analysis of time-stamped data with complex temporal and relational dependencies. We outline the main differences between recently proposed relational event models and more conventional network models based on the graph-theoretic formalism typically adopted in empirical studies of social networks. Our main contribution involves the definition and implementation of a marked point process extension of currently available models. According to this approach, the sequence of events of interest is decomposed into two components: (a) event time, and (b) event destination. This decomposition transforms the problem of selection of event destination in relational event models into a conditional multinomial logistic regression problem. The main advantages of this formulation are the possibility of controlling for the effect of event-specific data and a significant reduction in the estimation time of currently available relational event models. We demonstrate the empirical value of the model in an analysis of interhospital patient transfer within a regional community of health care organizations. We conclude with a discussion of how the models we presented help to overcome some the limitations of statistical models for networks that are currently available

A copula model for marked point processes

The final publication (Diao, Liqun, Richard J. Cook, and Ker-Ai Lee. (2013) A copula model for marked point processes. Lifetime Data Analysis, 19(4): 463-489) is available at Springer via http://dx.doi.org/10.1007/s10985-013-9259-3Many chronic diseases feature recurring clinically important events. In addition, however, there often exists a random variable which is realized upon the occurrence of each event reflecting the severity of the event, a cost associated with it, or possibly a short term response indicating the effect of a therapeutic intervention. We describe a novel model for a marked point process which incorporates a dependence between continuous marks and the event process through the use of a copula function. The copula formulation ensures that event times can be modeled by any intensity function for point processes, and any multivariate model can be specified for the continuous marks. The relative efficiency of joint versus separate analyses of the event times and the marks is examined through simulation under random censoring. An application to data from a recent trial in transfusion medicine is given for illustration.Natural Sciences and Engineering Research Council of Canada (RGPIN 155849); Canadian Institutes for Health Research (FRN 13887); Canada Research Chair (Tier 1) – CIHR funded (950-226626

Point-process models of social network interactions: Parameter estimation and missing data recovery

Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time. We adopt a self-exciting Hawkes process model for this behaviour. First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made. Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks. Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a non-vanishing derivative. Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy. The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed. The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy

Simulation and estimation of probabilities of phases of the Pacific Decadal Oscillation

The Pacific Decadal Oscillation (PDO) index defines the leading mode of monthly sea surface temperature (SST) anomalies in the North Pacific Ocean. Time series analysis in both the frequency and time domains is applied to 107 years of monthly PDO index values. Simulations of a model fitted to the data are used to estimate p-values associated with particular events observed in the raw data. The simulations are further used to estimate the distribution of various quantities, such as the length (in years) of a positive phase, or the absolute difference between the longest positive and negative phase (in years). The results show that the probability of occurrence of a negative phase surrounded by two positive phases within a 107-year period is approximately 9.9%. The raw data's mean positive phase length is close to the simulation mean and median, while the absolute difference in maximum positive/negative phase lengths corresponds to a p-value of 14.9%. The methodology developed in this paper can be useful to ecologists in assessing the potential ecological effects due to PDO variation, and for estimating the probabilities associated with future phases or other events. Copyright © 2009 John Wiley and Sons, Ltd