摘要：The current environment of test-based accountability in public education has fostered increased interest in analyzing longitudinal data on student achievement. In particular, “value-added models” (VAM) that use longitudinal student achievement data linked to teachers and schools to make inferences about teacher and school effectiveness have burgeoned. Depending on the available data and desired inferences, the models can range from straightforward hierarchical linear models to more complicated and computationally demanding cross-classified models. The purpose of this article is to demonstrate how R, via the lme function for linear mixed effects models in the nlme package (Pinheiro and Bates, 2000), can be used to estimate all of the most common valueadded models used in educational research. After providing background on the substantive problem, we develop notation for the data and model structures that are considered. We then present a sequence of increasingly complex models and demonstrate how to estimate the models in R. We conclude with a discussion of the strengths and limitations of the R facilities for modeling longitudinal student achievement data.
