Multivariate analysis (chemometrics) - quality of multivariate calibration

Transcription

1 Multivariate analysis (chemometrics) - quality of multivariate calibration Wolfhard Wegscheider with contributions by Alessandra Rachetti 15 May 2018

2 Outline Historical reminescence: how it all started Univariate multivariate calibration Selectivity specificity solvability Current applications (analytes, signals, matrices, purpose) Bias vs. variance in calibration Predictive, parsimonious, explanatory models Uncertainty, control charts and traceability Conclusions

3 There is no such thing like a specific analytical method

4 Denver Denver Pratt Joplin

5 Why multivariate? Non-selective signals Many signals (quasi) simultaneously Image compression/comprehension/analysis More analytes/measurands at the same time Faster than classical procedures New analytical problems become accessible

6 Univariate Calibration Y = X B inverse sensitivity B X, signals Y, conc.

7 Univariate Calibration Y = X B B X, signals Y, conc. X, signals Y, conc.

8 Univariate Calibration two signals, one measurand Y = X B B X, signals Y, conc. X, signals Y, conc.

9 Multivariate Calibration two signals, two measurands Y = X B B X, signals Y, conc. Y2, conc. Y1, conc.

10 Multivariate Calibration two signals, two measurands Y = X B B X, signals Y, conc. Y2, conc. Y1, conc.

11 C 3 C 1 C 2

12 Classical Regression signals Y = X B analytes X, signals Y, conc. B samples

13 Classical Regression signals Y = X B analytes B X, signals Y, conc. # of samples > # of sensors samples

14 Classical Regression signals Y = X B analytes samples X, signals B Y, conc. # of samples < # of sensors

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17 Classical Regression vs. PLS (partial least squares) Y = T B Q X, spectra T U Y, conc. P W B Q adapted from Geladi and Kowalski, 1986

18 Purpose Principle Measurand (SI?????) Adulteration/authenifi FT-IR & FT-NIR Glucose, starch, chichory, barley, cation of coffee Composition of coffee FT-NIR caffeine, theobromine, theophylline, moisture, ash, lipid Degree of roasting of coffee Waste water characterization FT-NIR UV-vis Effect of roasting, prediction of roasting degree Total suspended solids, chemical oxygen demand (COD) Honey 1 H-NMR, HPLC-UV Origin and phenolic compounds Olive oil/ adulteration PTR-MS Botanical origin Olive oil SESI-MS Geographical origin Cheese HS-PTR-MS Geographical origin Apples, plums, tomato, mushrooms Banana Tablets, capsules, liquids, suspensions Backscattering images Backscattering images Raman Firmness and elastic modulus Ripeness and chilling injury Active pharmaceutical ingredient (API) content

19 Outline Historical reminescence: how it all started Univariate multivariate calibration Selectivity specificity solvability Current applications (analytes, signals, matrices, purpose) Bias vs. variance in calibration Predictive, parsimonious, explanatory models Uncertainty, control charts and traceability Conclusions

20 Example: P in various steels by OES Trace element 699 standard samples Multielement procedure Signal generation process very complex Expansion to non-linear effects Linear model from 140 variables Variance/bias trade-off gives (only) 13 of those 140 variables

21 Explain variability of concentrations in terms of signal and matrix c A = f (I j, c i ) Concentration of an analyte is function of (potentially) all sensor signals and (potentially) all constituents in the sample Left side: predicted concentration Right side: variables

22 Consequences in complex samples univariate calibration One sensor per sample o.k. multivariate calibration Multiple sensors per sample o.k. Sufficient selectivity? o.k. Not reliable o.k. Effect acceptable? o.k.

23 Validation as a sampling problem signals Y = X B analytes calibrate monitor B calibrate monitor predict predict samples

24 Effect of four selection procedures Westad & Marini, 2015

25 Variance/bias trade-off: optimum from cross-validation Select some of the standards and predict others 13 variables from a total of 140 are left prediction residuals optimum

26 Consequence of bias/variance trade-off: In calibration, we cannot distinguish between systematic and random errors Tragedy for quality assessment? No, we work with a combined effect for measurement uncertainty

27 Measurement of P in steels

28 General problems with complex samples Require complex calibration (or superb selectivity/separation) Little insight Lack of intuitivity Highly variable results of calibration (but not necessarily on predictions): Size of coefficients Variables selected

29 Outline Historical reminescence: how it all started Univariate multivariate calibration Selectivity specificity solvability Current applications (analytes, signals, matrices, purpose) Bias vs. variance in calibration Predictive, parsimonious, explanatory models Uncertainty, control charts and traceability Conclusions

30 Calibration is only one step. we must seek understanding Predictive Parsimonious Explanatory Beware of lurking variables and spurious correlations Consider influential observations

31 Quality of prediction and indicators Quality of prediction: RMSECV. Root mean squared error of cross validation Indicators: which variables are important for prediction VIP: modelling power on x and y X-weight describes covariance of x and y SR selectivity ratio: influence on y OR orthogonal ratio: non-influence on y Reproduced correlation

32 Model data: XRF on sediments Advantage: completely understood on basis of first (physical) principles Remaining problems: inhomogeneity, mineralogical effects, grain size distribution Scientific background is geochemical Are there any accounts of the Nbanomaly? COLTAN research

33 Two model elements: Ti and Pb DataSet: Sediments, Ti.k(fit) vs Ti Ti. k (fit) C Pb vs I Pb L C Ti vs I Ti K Ti Created: 09/17/15 07:57:26 Pb.l(fit) DataSet: Sediments, Pb.l(fit) vs Pb Pb Created: 09/15/15 08:56:40

34 PLS on Ti and Pb Predicted (Ti) C Pb meas vs C Pb pred Measured (Ti) C Ti meas vs C Ti pred Predicted (Pb) Created: 09/14/15 14:53: Measured (Pb) Created: 09/15/15 09:45:01

35 OR Ti indicators: black Ti.k(fit) Comp. 2 (21.6%) Ca.k(fit) K.k(fit) Mn.k(fit) Rb.k(fit) RbSr.k(fit) Pb Sr W.l(fit) Cu K Ge.k(fit) Mo Cu.k(fit) W Pb.l(fit) Ni.k(fit) Fe.k(fit) Mo.k(fit) Ca FeZr.k(fit) Y.k(fit) Y Nb.k(fit) Mn Nb SR reg coeff x rep weight r Comp. 1 (57.9%)

36 OR Mn.k(fit) Pb indicators: black Ti.k(fit) Comp. 2 (21.4%) K Ti Y Zr Nb W Ca.k(fit) K.k(fit) Nb.k(fit) Ni.k(fit) Y.k(fit) Rb.k(fit) Sr.k(fit) Ge.k(fit) Mn Pb.l(fit) Sr Mo.k(fit) Cu.k(fit) Zr.k(fit) W.l(fit) Fe Fe.k(fit) Ca Mo reg coeff x rep weight r SR Cu Comp. 1 (62.8%)

37 Pb vs Cu: spurious correlation Cu 6.00 A Pb Created:

38 Where do spurious correlations come from? Calibration models depend on the physics/chemistry of the measurement process, but also on the internal correlations in the calibration set (here: from geochemistry) We actually have a sampling problem

39 Regression for classification signals Y = X B analytes membership samples X, signals B

40 Origin of Styrian pumpkin seed oil PGI (protected geographical indication) Zettl et al., 2017

41 148 oils, 37 elemental variables, external validation set from Austrian Food Authority Zettl et al., 2017

42 Outline Historical reminescence: how it all started Univariate multivariate calibration Selectivity specificity solvability Current applications (analytes, signals, matrices, purpose) Bias vs. variance in calibration Predictive, parsimonious, explanatory models Uncertainty, control charts and traceability Conclusions

43 NIR spectra of brick cheese Infometrix Applications Overview 1996 best wavelength for moisture

44 Calibration on wavelength 9 useless

45 Multivariate prediction of moisture

46 h leverage

47 h leverage vs. spectra

48 IUPAC Approach to uncertainty Pure Appl. Chem. 78, No. 3, pp , 2006 variance of prediction leverage * var. of conc. of standards leverage * var. of (signals/sensitivity) variance of (signals/sensitivity)

49 Effect as extra-rmsep in % moisture Noise of 2% added to Effect (in %moisture) Spectra of standards Spectra of unknowns Concentration of standards Sum (IUPAC) All three RMSEP root mean squared error of prediction o The IUPAC-proposed summation does not work o Expected reason: no allowance for significant correlations o Full Monte-Carlo procedure is required instead

50 Multivariate control charts Kourti & MacGregor, 1995

51 Automation to achieve traceable calibration models a. Expand variables for (potential) nonlinearities b. Derive latent variables c. Cross-validate for good variance/bias balance d. Crop all superfluous variables e. Highlight influential observations f. Apply calibration model W. Wegscheider & A. Rachetti, Tel Aviv 2015

52 Conclusions Multivariate calibration will be even more prominent in the future So far, too little has been invested in the understanding of the calibration models Traceability (and reproducibility) of calibrations require a fixed and hopefully automated protocol Many univariate QC measures are not useful

53 Acknowledgements Böhler Co, Kapfenberg, for cooperation in metals analysis Department of Applied Geosciences, Leoben, for cooperation on sediment samples O. Kvalheim (Bergen, NOR) for making available the newest version of Sirius

54 Thank you for your interest