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. (Contains 3 tables, 3 figures and 6 notes.)