Detecting outliers when fitting data with nonlinear regression - a new method based on robust nonlinear regression and the false discovery rate

BMC Bioinformatics
Harvey J Motulsky, Ronald E Brown

Abstract

Nonlinear regression, like linear regression, assumes that the scatter of data around the ideal curve follows a Gaussian or normal distribution. This assumption leads to the familiar goal of regression: to minimize the sum of the squares of the vertical or Y-value distances between the points and the curve. Outliers can dominate the sum-of-the-squares calculation, and lead to misleading results. However, we know of no practical method for routinely identifying outliers when fitting curves with nonlinear regression. We describe a new method for identifying outliers when fitting data with nonlinear regression. We first fit the data using a robust form of nonlinear regression, based on the assumption that scatter follows a Lorentzian distribution. We devised a new adaptive method that gradually becomes more robust as the method proceeds. To define outliers, we adapted the false discovery rate approach to handling multiple comparisons. We then remove the outliers, and analyze the data using ordinary least-squares regression. Because the method combines robust regression and outlier removal, we call it the ROUT method. When analyzing simulated data, where all scatter is Gaussian, our method detects (falsely) one or more outlier in o...Continue Reading

References

Jul 1, 1990·Statistics in Medicine·Y Hochberg, Y Benjamini

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Citations

May 20, 2011·Proceedings. Biological Sciences·Xingli GiamPaul R Ehrlich
Oct 3, 2013·Applied Microbiology and Biotechnology·Rebecca SydenhamReginald Storms
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Software Mentioned

MathType
GraphPad Prism

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