In the Oneway platform, the Robust option provides two methods to reduce the influence of outliers or extreme data points in your data set: Robust Fit and Cauchy Fit. Each method adds a line to the Oneway plot at the robust mean.
• The Robust Fit option reduces the influence of outliers in the response variable. The Huber M-estimation method is used. Huber M-estimation finds parameter estimates that minimize the Huber loss function. The Huber loss function penalizes outliers and increases as a quadratic for small errors and linearly for large errors. For more information about robust fitting, see Huber (1973) and Huber and Ronchetti (2009). See Example of the Robust Fit Option. For more information about the Huber loss function, see Statistical Details for the Robust Fit.
• The Cauchy Fit option assumes that the errors have a Cauchy distribution. A Cauchy distribution has fatter tails than the normal distribution, resulting in a reduced emphasis on outliers. This option can be useful if you have a large proportion of outliers in your data. However, if your data are close to normal with only a few outliers, this option can lead to incorrect inferences. The Cauchy option estimates parameters using maximum likelihood and a Cauchy link function.
Note: The Robust options are not available when a Block variable is specified in the launch window.
There are two tables in the reports that are created for the Robust options. The tables contain the following columns:
Sigma
The sigma value, which is equivalent to the root mean square error (RMSE).
ChiSquare
The test statistic for the hypothesis that the model fits better than the mean of the response.
PValue
The p-value for the chi-square test that the slope is equal to zero.
Logworth
he logworth is a transformation of the p-value defined as -log10(p-value).
Level
The levels of the X variable.
Robust Mean
The robust mean estimated based on either the Huber or the Cauchy method.
Std Error
The estimates of the standard errors of the parameter estimates.