U.S. school districts differ dramatically in their socioeconomic and demographic characteristics (Reardon, Yun, & Eitle, 1999; Stroub & Richards, 2013), and districts have considerable influence over instructional and organizational practices that may affect academic achievement (Whitehurst, Chingos, & Gallaher, 2013). This paper evaluates a linking method applied to a unique national district-level dataset that may achieve the goal of national district-level comparability for research purposes. The authors fit a heteroskedastic probit model to categorical test score data from the EDFacts Initiative (U.S. Department of Education, 2015), which includes frequencies of students in coarse "achievement levels" from every school district in the U.S. from 2008 to 2012. Data from 2013 are forthcoming. Using a population of all U.S. public school students in grades 3-8 from 2008 to 2013, the authors demonstrate that reparameterization of conventional model parameters recover, with remarkable accuracy, means and standard deviations of district test scores from fine-grained data. One table and one figure are appended. [SREE documents are structured abstracts of SREE conference symposium, panel, and paper or poster submissions.]