The insightful discussions by Raudenbush, Rubin, Stuart and Zanutto (RSZ) and Reckase identify important challenges for interpreting the output of VAM and for its use with test-based accountability. As these authors note, VAM are statistical models for the correlations among scores from students who share common teachers or schools during the years of schooling when testing occurs. We follow the convention in this literature of using the phrase teacher to describe the source of correlation among scores from students who shared a teacher, but teachers are not the only source of this correlation, and the estimated do not necessarily correspond to any well defined causal effect or attribute of the teacher. Many factors including the causal effects of teachers and schools identified by Raudenbush and RSZ as well as context effects, noneducational inputs, and the characteristics of tests all contribute to these correlations. As Reckase points out careful consideration of testing alone suggests that these statistical models will need to be highly complex to adequately describe the likely correlation structure in longitudinal student test data. In our article, we developed a model for these correlations that is more flexible than those currently used for VAM. Our model can estimate features of the data that other models cannot, and it provides a framework for understanding the similarities and differences of various approaches that have been used or suggested for VAM. Furthermore, our analytic evaluations identified circumstances that cause This research was supported by Grant B7230 from the Carnegie Corporation of New York. The statements made and views expressed are solely the responsibility of the authors.
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