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While generalized linear mixed models are useful, optimal design questions for such models are challenging due to complexity of the information matrices. For longitudinal data, after comparing three approximations for the information matrices, we propose an approximation based on the penalized quasi-likelihood method.We evaluate this approximation for logistic mixed models with time as the single predictor variable. Assuming that the experimenter controls at which time observations are to be made, the approximation is used to identify locally optimal designs based on the commonly used A- and D-optimality criteria. The method can also be used for models with random block effects. Locally optimal designs found by a Particle Swarm Optimization algorithm are presented and discussed. As an illustration, optimal designs are derived for a study on self-reported disability in olderwomen. Finally,we also study the robustness of the locally optimal designs to mis-specification of the covariance matrix for the random effects. 

Previous research has established that peer relationships are important for student success, yet they can be hard to form at regional universities with large commuter populations. In these settings, connections in the classroom become critical. In an effort to gauge the degree to which students have the opportunity to form peer relationships in the classroom, this project utilized social network analysis to investigate to what degree students take repeated courses with the same peers. We report here on the number and nature of connections for a cohort of students who began STEM majors in Fall 2015. Two key findings include that White students have more peer connections than students of color, and the degree of connectivity correlates with graduation rates. Implications for these findings regarding curriculum design will be discussed. 

Previous research has established that peer relationships are important for student success, yet little research has examined connections made in the classroom, as opposed to residence life or extracurricular activities. This project utilized social network analysis in two cohorts of science and mathematics majors to investigate the degree to which students take multiple courses with the same peers. Results showed (1) wide variability in student networks, (2) course selection by students included more repeated connections than random course selection, (3) networks did not vary much by demographic variables (gender, race, first-generation status, and income), and (4) student networks significantly predicted graduation and grades. This correlational research provides a foundation for future experimental research testing the causal impact of classroom-based student networks. This research also serves as a model for how other institutions may analyze institutional data to understand patterns of peer connections and course enrollment at their institution.