A regression model of predictor trade-offs is described. Each regression parameter equals the expected change in Y obtained by trading 1 point from one predictor to a second predictor. The model applies to predictor variables that sum to a constant T for all observations; for example, proportions summing to T=1.0 or percentages summing to T=100…

We consider two-level models where a continuous response R and continuous covariates C are assumed missing at random. Inferences based on maximum likelihood or Bayes are routinely made by estimating their joint normal distribution from observed data R[subscript obs] and C[subscript obs]. However, if the model for R given C includes random…

Student models for adaptive systems may not model collaborative learning optimally. Past research has either focused on modeling individual learning or for collaboration, has focused on group dynamics or group processes without predicting learning. In the current paper, we adjust the Additive Factors Model (AFM), a standard logistic regression…

The purpose of this study was to assess the relative contribution of teacher and tutor ratings of inattentive behavior in two different instructional settings in predicting students' performance on fraction concepts and whole-number calculations. Classroom teachers rated each student's attentive behavior in a whole-class setting and tutors rated…