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There is an increasing interest in using longitudinal measures of student achievement to estimate individual teacher effects. Current multivariate models assume each teacher has a single effect on student outcomes that persists undiminished to all future test administrations (complete persistence [CP]) or can diminish with time but remains perfectly correlated (variable persistence [VP]). However, when state assessments do not use a vertical scale or the evolution of the mix of topics present across a sequence of vertically aligned assessments changes as students advance in school, these assumptions of persistence may not be consistent with the achievement data. We develop the “generalized persistence” (GP) model, a Bayesian multivariate model for estimating teacher effects that accommodates longitudinal data that are not vertically scaled by allowing less than perfect correlation of a teacher’s effects across test administrations. We illustrate the model using mathematics assessment data.

When constructed response test items are scored by more than one rater, the repeated ratings allow for the consideration of individual rater bias and variability in estimating student proficiency. Several hierarchical models based on item response theory have been introduced to model such effects. In this article, the authors demonstrate how these models may be extended to include covariates of the rating process. For example, how do features of an essay grader’s training affect his or her performance? The authors show how to include covariates by embedding a linear model at appropriate levels of the model hierarchy. Depending on the level, such covariates may be thought of as determining fixed effects or random effects on the rating process. The authors also discuss the appropriate design matrix for such covariates, discuss how to incorporate needed identifiability constraints, and illustrate the methods using data from a rating study of a student assessment.

There is increased interest in value-added models relying on longitudinal student-level test score data to isolate teachers’ contributions to student achievement. The complex linkage of students to...