Relationships among teachers are known to influence their teaching-related perceptions. We study whether and how teachers' advising relationships (networks) are related to their perceptions of satisfaction, students, and influence over educational policies, recorded as their responses to a questionnaire (item responses). We propose a novel joint model of network and item responses (JNIRM) with correlated latent variables to understand these co-varying ties. This methodology allows the analyst to test and interpret the dependence between a network and item responses. Using JNIRM, we discover that teachers' advising relationships contribute to their perceptions of satisfaction and students more often than their perceptions of influence over educational policies. In addition, we observe that the complementarity principle applies in certain schools, where teachers tend to seek advice from those who are different from them. JNIRM shows superior parameter estimation and model fit over separately modeling the network and item responses with latent variable models.

Item response theory (IRT) models are widely used in psychometrics and educational measurement, being deployed in many high stakes tests such as the GRE aptitude test. IRT has largely focused on estimation of a single latent trait (e.g. ability) that remains static through the collection of item responses. However, in contemporary settings where item responses are being continuously collected, such as Massive Open Online Courses (MOOCs), interest will naturally be on the dynamics of ability, thus complicating usage of traditional IRT models. We propose DynAEsti, an augmentation of the traditional IRT Expectation Maximization algorithm that allows ability to be a continuously varying curve over time. In the process, we develop CurvFiFE, a novel non-parametric continuous-time technique that handles the curve-fitting/regression problem extended to address more general probabilistic emissions (as opposed to simply noisy data points). Furthermore, to accomplish this, we develop a novel technique called grafting, which can successfully approximate distributions represented by graphical models when other popular techniques like Loopy Belief Propogation (LBP) and Variational Inference (VI) fail. The performance of DynAEsti is evaluated through simulation, where we achieve results comparable to the optimal of what is observed in the static ability scenario. Finally, DynAEsti is applied to a longitudinal performance dataset (80-years of competitive golf at the 18-hole Masters Tournament) to demonstrate its ability to recover key properties of human performance and the heterogeneous characteristics of the different holes. Python code for CurvFiFE and DynAEsti is publicly available at github.com/chausies/DynAEstiAndCurvFiFE. This is the full version of our ICDM 2019 paper.