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In statistics, Deming regression, named after W. Edwards Deming, is an errors-in-variables model that tries to find the line of best fit for a two-dimensional data set. It differs from the simple linear regression in that it accounts for errors in observations on both the x - and the y - axis.
It is a generalization of Deming regression and also of orthogonal regression, and can be applied to both linear and non-linear models. The total least squares approximation of the data is generically equivalent to the best, in the Frobenius norm , low-rank approximation of the data matrix.
In Deming regression, a type of linear curve fitting, if the dependent and independent variables have equal variance this results in orthogonal regression in which the degree of imperfection of the fit is measured for each data point as the perpendicular distance of the point from the regression line.
Procedures for method evaluation and method comparison include ROC curve analysis, [6] Bland–Altman plot, [7] as well as Deming and Passing–Bablok regression. [ 8 ] The software also includes reference interval estimation, [ 9 ] meta-analysis and sample size calculations.
Linear errors-in-variables models were studied first, probably because linear models were so widely used and they are easier than non-linear ones. Unlike standard least squares regression (OLS), extending errors in variables regression (EiV) from the simple to the multivariable case is not straightforward, unless one treats all variables in the same way i.e. assume equal reliability.
The iterative proportional fitting procedure (IPF or IPFP, also known as biproportional fitting or biproportion in statistics or economics (input-output analysis, etc.), RAS algorithm [1] in economics, raking in survey statistics, and matrix scaling in computer science) is the operation of finding the fitted matrix which is the closest to an initial matrix but with the row and column totals of ...
Deming circle, an iterative management method; Deming regression, a 2D regression method that accounts for errors in both variables; Takming (德明), “Deming” in Cantonese pronunciation
Passing and Bablok define a method for calculating a 95% confidence interval (CI) for both and in their original paper, [1] which was later refined, [4] though bootstrapping the parameters is the preferred method for in vitro diagnostics (IVD) when using patient samples. [7]