Deming, Theil-Sen, and Passing-Bablock Regression

Least squares regression of y on x assumes that the x variate is measured without error, and minimizes the sum of squared vertical distance between the data points y and the fitted regression line. Regression of x on y minimizes the horizontal distances. Adcock [1] in 1878 suggested minimizing the sum of squared horizontal + vertical distances to the predicted values. However the idea of Adcock remained largely unnoticed for more than 50 years, until it was widely propogated in the book by Deming [2]. The latter has become so well known that the common label for the method is “Deming regression” in nearly all fields in which it is used. There are a number of alternate ways to compute this regression line. The Deming line will be the first principle component of the centered data, the first eignevector of the matrix Z whose 2 columns are the centered x and y vectors, or the first component of a singular value decomposition or factor analysis of Z. A partial least squares (PLS) or structural equation modeling (SEM) model fit to x and y will also recover the Deming estimate of slope. There would appear to be little need for yet another program to compute this quantity other than providing a recognizable name to search for in the R libraries. For laboratory work, however, it is the generalized Deming method that is of most interest. Returning to our original