Search

The Bradley-Terry model is widely used for pairwise comparison data analysis. In this paper, we analyze the asymptotic behavior of the maximum likelihood estimator of the Bradley-Terry model in its logistic parameterization, under a general class of linear identifiability constraints. We show that the constraint requiring the Bradley-Terry scores for all compared objects to sum to zero minimizes the sum of the variances of the estimated scores, and recommend using this constraint in practice.

We study regularized estimation in high-dimensional longitudinal classification problems, using the lasso and fused lasso regularizers. The constructed coefficient estimates are piecewise constant across the time dimension in the longitudinal problem, with adaptively selected change points (break points). We present an efficient algorithm for computing such estimates, based on proximal gradient descent. We apply our proposed technique to a longitudinal data set on Alzheimer's disease from the Cardiovascular Health Study Cognition Study, and use this data set to motivate and demonstrate several practical considerations such as the selection of tuning parameters, and the assessment of model stability.

In modern psychometric analysis of cognitive assessment, there is a choice between psychometric vs. cognitive science paradigms for modeling the latent scale. The first involves as few as one continuous latent ability parameter, while the second focuses on a set of binary latent skills. When the expert cognitive model is qualitatively specified (eg. paragraphs describing general trends in observable behavior for a set of developmental stages), interpretation of responses and latent variables is flexible, and may even be ambiguous. Models incorporating aspects from both psychometric and cognitive science paradigms can help in exploring response patterns, and refining both the exam design and the cognitive model. Here we present two such analyses of a pilot study of proportional reasoning. The first is a Rasch model using binary response coding with a continuous latent trait, which can approximate a set of developmental stages through careful item design and milestones. The second is a Bayes net model using polytomous response coding linked compensatorily to a set of latent skills, which allows for a factor-analytic approach to skill interpretation. We explore each scheme’s usefulness in inferring a student’s current state of knowledge, directing program planners, and directing assessment developers toward refining either the qualitative cognitive model or exam items.

Online tools, including social networks, are becoming more prevalent in teacher support and professional development. However, little is known about how existing online communities of educators function. If online social networks are to be used as part of ongoing teacher development, training or support, we must better understand successful networks and their participants. We present an analysis of Classroom 2.0, an established, active and growing community dedicated to helping teachers incorporate web 2.0 technologies into their classrooms. Web 2.0 technologies are collaborative tools, such as wikis, blogs, and podcasts that allow users to share content and/or create it together. We drew from the Communities of Practice literature to explore the structure of ties and the content of interactions between members. Latent Dirichlet Allocation was used to analyze the content of network interactions, and ego networks were used to characterize patterns of interaction. We found two separate sub-communities within Classroom 2.0, one dedicated toward substantive discussions of education and technology, the other dedicated toward forming relationships with new colleagues.