I would like to report that the recently released mcrPioda-1.3.3 package has refurbished versions of the M-Deming and MM-Deming regression. The new functions are written in C and are much faster that the previous ones. The new release is on the devel branch because on the master branch the legacy version of 2021 is still available.

In detail:

• M-Deming gives exact identical results as the previous one and is approximately 10 times faster. The converging algorithm has a new gradient descending mechanism that reduces resonance phenomena and leads to lower cycles count with the very same numeric result as the 2021 version.

• MM-Deming regression with bisquare redescending weights is available in two new versions. Both have a new feature in the algorithm compared to the legacy MM-Deming published in 2021 (still available in the new package). In the new methods the mad() parameter for scaling the euclidean residuals gets estimated at every cycle instead as only once at the beginning of the iterative process. This leads to a much more stable algorithm. The previous iterative method was rather strongly dependent on the provided starting values, indicating that a plethora of local minima could be present. With the new algorithm the minimum is coherently found with almost no influence given by the starting values (slope and intercept) of the iterative process. For this reason two different versions have been proposed, both of them not anymore using the covSest() functions:

  • NgMMDeming has an initial step for the determination of the starting values. In this step the M-Deming is used twice. The first time just like in the M-Deming regression and in the second part only an adjustable fraction the points (‘bdPoint = 0.5’ as parameter default), those with highest M-weight, are used so as to obtain a robust estimate with an high breakdown point. These starting values are subsequently used to start the bisquare MM-Deming regression.

  • PiMMDeming has no starting values determination step. The starting slope and intercept are “user provided” in a Bayesian style. The default is slope = 1 and intercept = 0. The convergence of the bisquare weighted method is so strong that these values are in most cases a reasonable choice.

All these new methods are under scrutiny for power and power symmetry.