From the Chang et. al. paper: "The scale factor C affects the shape of the GMM [German-McClure M-estimator] weighting function and represents the expected spread of the residuals (i.e., the SD of the residuals) due to Gaussian distributed noise. The scale factor C can be estimated by many robust scale estimators. We used the median absolute deviation (MAD) estimator because it is very robust to outliers having a 50% breakdown point (6, 7). The explicit formula for C using the MAD estimator is C = 1.4826 × MAD = 1.4826 × median{|r1 − r̂|, |r2 − r̂|, … , |rn − r̂|}, where r̂ = median {r1, r2,… , rn} and n is the number of data points. The multiplicative constant 1.4826 makes this an approximately unbiased estimate of scale when the error model is Gaussian."