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Computing confidence intervals for the slope of the biweight midregression and Winsorized regression lines
Author(s) -
Wilcox Rand R.
Publication year - 1994
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1994.tb01042.x
Subject(s) - ordinary least squares , confidence interval , statistics , outlier , regression , robust regression , regression analysis , least trimmed squares , robust confidence intervals , mathematics , linear regression , econometrics , computer science , total least squares
Robust and resistant regression has taken on new importance in recent years with the realization that psychometric measures often have heavy‐tailed distributions with extreme outliers. While many resistant regression methods are available, little is known about how a researcher might compute a confidence interval for the corresponding parameters. The primary goal in this paper is finding a method of computing reasonably accurate confidence intervals for the slope of two resistant regression methods: the biweight midregression and Winsorized regression. Several ‘obvious’ bootstrap methods for computing confidence intervals were found to be highly unsatisfactory. A relatively unobvious method was found to perform reasonably well when using biweight midregression, and fairly well for the other regression method except for one extreme situation described in the paper. In terms of power, no situation was found where ordinary least squares is to be preferred over Winsorized regression, while Winsorized regression can have a substantial advantage over ordinary least squares. There are situations where the biweight midregression has substantially more power than ordinary least squares, but when the predictor has a highly skewed distribution, there are situations where the reverse is true. The relative merits of the two resistant regression methods are discussed.