Quantile models and estimators for data analysis |
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Authors: | Gilbert W Bassett Jr Mo-Yin S Tam Keith Knight |
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Institution: | (1) University of Illinois at Chicago, 601 South Morgan Chicago, IL 60607, USA, US;(2) University of Toronto, Department of Statistics, 100 St. George St., Toronto, Ont. M5S3G3, Canada, CA |
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Abstract: | Quantile regression is used to estimate the cross sectional relationship between high school characteristics and student
achievement as measured by ACT scores. The importance of school characteristics on student achievement has been traditionally
framed in terms of the effect on the expected value. With quantile regression the impact of school characteristics is allowed
to be different at the mean and quantiles of the conditional distribution. Like robust estimation, the quantile approach detects
relationships missed by traditional data analysis. Robust estimates detect the influence of the bulk of the data, whereas
quantile estimates detect the influence of co-variates on alternate parts of the conditional distribution. Since our design
consists of multiple responses (individual student ACT scores) at fixed explanatory variables (school characteristics) the
quantile model can be estimated by the usual regression quantiles, but additionally by a regression on the empirical quantile
at each school. This is similar to least squares where the estimate based on the entire data is identical to weighted least
squares on the school averages. Unlike least squares however, the regression through the quantiles produces a different estimate
than the regression quantiles. |
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Keywords: | : Quantile Models Regression Quantiles Robustness Student Achievement |
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