Measurement methods comparison with errors-in-variables regressions. From horizontal to vertical OLS regression, review and new perspectives
(2014) Chemometrics and Intelligent Laboratory Systems — Vol. 134, n° 1, p. 123-139 (2014)
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- Authors
Govaerts, Bernadette 
- Abstract
- This paper summarizes and confronts the relationships between six well-known regressions applied in the context of measurement methods comparison with or without replicated data. When two measurement methods are equivalent, it can be expected that there is no analytical bias between them and they must provide the same results on average notwithstanding the measurement errors. Usually, there is no golden-standard (like a calibration problem) and each measurement method is compared to another one and vice-versawith a linear regression analysis. If there is no bias, the results should not be far from the identity line Y=X. Unfortunately, the measurement errors in each axis must be taken into account in the regression analysis (and ideally the switching of axes) by applying a linear errors-in-variables regression. Therefore, the OLS (Ordinary Least Square) regression lines provide biased estimated lines while the errors-in-variables regressions lines lie between the two extreme OLS lines. DR (Deming Regression) and BLS (Bivariate Least Square) regressions are the most general regressions and provide (asymptotically) unbiased estimated lines which are confounded under homoscedasticity. The biases and coverage probabilities of the six regressions are compared with simulations where the results are displayed in charts instead of large data sets. As the precision ratio λ of two measurement methods is a very important parameter in errors-in-variables regressions, it will be a leitmotiv in this paper and all the charts will be linked to it. An unbiased estimator of λ is also given. The approximate CI (Confidence Intervals) provided by BLS are very easy to compute and provide coverage probabilities close to the nominal level. On the other hand, the CI provided by DR are less easy to compute but provide better coverage probabilities whatever λ for large sample sizes (N > 20). Finally, the regression techniques are applied with real data and this paper proposes to plot all the possible values of the estimated parameters and their CI in a chartwith respect to λ. Then, the equivalence hypothesis can sometimes be rejected (or not rejected) whatever λ. This is very usefulwhen λ is unknown and inestimable because of no replicated data.
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Citations
Francq, B. G., & Govaerts, B. (2014). Measurement methods comparison with errors-in-variables regressions. From horizontal to vertical OLS regression, review and new perspectives. Chemometrics and Intelligent Laboratory Systems, 134(1), 123-139. https://doi.org/10.1016/j.chemolab.2014.03.006 (Original work published 2014)