Welcome back to the 2015/2016 Workshop on Quantitative Methods in Education, Health and the Social Sciences (QMeHSS). Our first workshop for this year will be on Friday, October 30th, from 10:00-11:30pm. The workshop will be led by Dr. Sean Reardon from Stanford University and will be held in NORC conference room 344. NORC is located at 1155 E. 60th Street. We look forward to seeing you for another year of exciting and stimulating discussion.
Using Heteroskedastic Ordered Probit Models to Recover Moments of Coarsened Test Score Distributions
Sean F. Reardon (Stanford University)
Benjamin R. Shear (Stanford University)
Katherine E. Castellano (Educational Testing Service)
Andrew D. Ho (Harvard Graduate School of Education)
Abstract: Test score distributions of schools or demographic groups are often summarized by frequencies of students scoring in a small number of ordered proficiency categories. We show that heteroskedastic ordered probit (HETOP) models can be used to estimate means and standard deviations of multiple groups' test score distributions from such data. Because the scale of HETOP estimates is indeterminate up to a linear transformation, we develop formulas for converting the HETOP parameter estimates and their standard errors to a scale in which the population distribution of scores is standardized. We demonstrate and evaluate this novel application of the HETOP model with a simulation study and using real test score data from two sources. We find that the HETOP model produces unbiased estimates of group means and standard deviations, except when group sample sizes are small. In such cases, we demonstrate that a "partially heteroskesdastic" ordered probit (PHOP) model can produce estimates with a smaller root mean squared error than the fully heteroskedastic HETOP model.
Bio: Sean Reardon’s research investigates the causes, patterns, trends, and consequences of social and educational inequality. In particular, he studies issues of residential and school segregation and of racial/ethnic and socioeconomic disparities in academic achievement and educational success. In addition, his work develops methods of measuring social and educational inequality (including the measurement of segregation and achievement gaps) and methods of causal inference in educational and social science research.
This event is jointly sponsored by the Workshop on Quantitative Methods in Education, Health and the Social Science, and the Workshop on Education