Statistics and Its Interface

Volume 3 (2010)

Number 2

Local linear logistic Peters–Belson regression and its application in employment discrimination cases

Pages: 125 – 144



Efstathia Bura (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)

Joseph L. Gastwirth (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)

Hiro Hikawa (Department of Statistics, George Washington University, Washington, D.C., U.S.A.)


In cases involving possible discrimination in hiring or promotion plaintiffs allege that they were treated differently than similarly qualified majority individuals. The data are typically analyzed using logistic regression with a minority indicator variable. Alternatively, the Peters–Belson (PB) regression method, which fits a regression model to the majority data and compares the status of each minority member to its prediction obtained from the majority equation, has also been accepted by courts. The average difference estimates the disparity in treatment accounting for job-related covariates. The appropriateness of these parametric models depends on whether they reflect the process generating the data. To lessen the dependence of the ultimate inference on the assumed parametric model, the majority equation is fit by local linear logistic regression and the response of each minority is predicted from it. Large sample properties of this PB-type procedure are obtained and a simulation study shows that the method loses little power relative to parametric methods even when the assumed parametric method is correct. Moreover, it yields more reliable estimates of the disparity when the data do not follow the assumed model. Data from the $Berger v. Iron Workers Local 201$ case are used to illustrate the method.


covariate adjustment, disparity studies, employment discrimination, legal statistics, local likelihood estimation, local logistic regression

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