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.

Coho salmon (Oncorhynchus kisutch), Chinook salmon (Oncorhynchus tshawytscha) and steelhead (Oncorhynchus mykiss) in Puget Sound and the Strait of Georgia have exhibited declines in marine survival over the last 40 years. While the cause of these declines is unknown, multiple factors, acting cumulatively or synergistically, have likely contributed. To evaluate the potential contribution of a broad suite of drivers on salmon survival, we used qualitative network modelling (QNM). QNM is a conceptually based tool that uses networks with specified relationships between the variables. In a simulation framework, linkages are weighted and then the models are subjected to user-specified perturbations. Our network had 33 variables, including: environmental and oceanographic drivers (e.g., temperature and precipitation), primary production variables, food web components from zooplankton to predators and anthropogenic impacts (e.g., habitat loss and hatcheries). We included salmon traits (survival, abundance, residence time, fitness and size) as response variables. We invoked perturbations to each node and to suites of drivers and evaluated the responses of these variables. The model showed that anthropogenic impacts resulted in the strongest negative responses in salmon survival and abundance. Additionally, feedbacks through the food web were strong, beginning with primary production, suggesting that several food web variables may be important in mediating effects on salmon survival within the system. With this model, we were able to compare the relative influence of multiple drivers on salmon survival.

We consider a network of interacting individuals, whose actions or transitions are determined by the states (behavior) of their neighbors as well as their own personal decisions. Specifically, we develop a model according to two simple decision-making rules that can describe the growth of the user population of a newly launched product or service. We analyze 22 sets of real-world historical growth data of a variety of products and services, and show that they all follow the growth equation. The numerical procedure for finding the model parameters allows the market size, and the relative effectiveness of customer service and promotional efforts to be estimated from the available historical growth data. We study the growth profiles of products and find that for a product or service to reach a mature stage within a reasonably short time in its user growth profile, the user growth rate corresponding to influenced transitions must exceed a certain threshold. Furthermore, results show that individuals in the group of celebrities having numerous friends become users of a new product or service at a much faster rate than those connected to ordinary individuals having fewer friends.

We present and characterize a multi-host epidemic model of Rift Valley fever (RVF) virusin East Africa with geographic spread on a network, rule-based mitigation measures, andmosquito infection and population dynamics. Susceptible populations are depleted bydisease and vaccination and are replenished with the birth of new animals. We observe thatthe severity of the epidemics is strongly correlated with the duration of the rainy seasonand that even severe epidemics are abruptly terminated when the rain stops. Becausenaturally acquired herd immunity is established, total mortality across 25 years isrelatively insensitive to many mitigation approaches. Strong reductions in cattlemortality are expected, however, with sufficient reduction in population densities ofeither vectors or susceptible (ie. unvaccinated) hosts. A better understanding of RVFepidemiology would result from serology surveys to quantify the importance of herdimmunity in epidemic control, and sequencing of virus from representative animals toquantify the realative importance of transportation and local reservoirs in nucleatingyearly epidemics. Our results suggest that an effective multi-layered mitigation strategywould include vector control, movement control, and vaccination of young animals yearly,even in the absence of expected rainfall.