Estimates chemometrics

AJ Berger, MS Feld. Analytical method of estimating chemometric prediction error. Appl Spectrosc 51 725-732, 1997. 

In the context of chemometrics, optimization refers to the use of estimated parameters to control and optimize the outcome of experiments. Given a model that relates input variables to the output of a system, it is possible to find the set of inputs that optimizes the output. The system to be optimized may pertain to any type of analytical process, such as increasing resolution in hplc separations, increasing sensitivity in atomic emission spectrometry by controlling fuel and oxidant flow rates (14), or even in industrial processes, to optimize yield of a reaction as a function of input variables, temperature, pressure, and reactant concentration. The outputs ate the dependent variables, usually quantities such as instmment response, yield of a reaction, and resolution, and the input, or independent, variables are typically quantities like instmment settings, reaction conditions, or experimental media. 

We will explore the two major families of chemometric quantitative calibration techniques that are most commonly employed the Multiple Linear Regression (MLR) techniques, and the Factor-Based Techniques. Within each family, we will review the various methods commonly employed, learn how to develop and test calibrations, and how to use the calibrations to estimate, or predict, the properties of unknown samples. We will consider the advantages and limitations of each method as well as some of the tricks and pitfalls associated with their use. While our emphasis will be on quantitative analysis, we will also touch on how these techniques are used for qualitative analysis, classification, and discriminative analysis. 

Baroni M, Costantino G, Cruciani G, Riganelli D, Valigi R, Clementi S. Generating optimal linear PLS estimations (GOLPE) an advanced chemometric tool for handling 3D-QSAR problems. Quant Struct-Act Relat 1993 12 9-20. 

Chudzinska, M. and Baralkiewicz, D. (2010). Estimation of honey authenticity by multielements characteristics using inductively coupled plasma-mass spectrometry (ICP-MS) combined with chemometrics. Food Chem. Toxicol. 48, 284-290. 

Lorber A, Kowalski BR (1988) Estimation of prediction error for multivariate calibration. J Chemometrics 2 93... 

Furthermore, the development of these cross-products in the case of the Chemometric development of a solution to a data-fitting problem came out of the application of the Least Squares principle. In the case of the Statistical development, neither the Least Square principle nor any other such principles was, or needed to be, applied. The cross-products were arrived at purely from a calculation of a sum of squares, without regard to what those sums of squares represented they were certainly not designed to be a Least Square estimator of anything. 

All regression methods aim at the minimization of residuals, for instance minimization of the sum of the squared residuals. It is essential to focus on minimal prediction errors for new cases—the test set—but not (only) for the calibration set from which the model has been created. It is relatively easy to create a model— especially with many variables and eventually nonlinear features—that very well fits the calibration data however, it may be useless for new cases. This effect of overfitting is a crucial topic in model creation. Definition of appropriate criteria for the performance of regression models is not trivial. About a dozen different criteria— sometimes under different names—are used in chemometrics, and some others are waiting in the statistical literature for being detected by chemometricians a basic treatment of the criteria and the methods how to estimate them is given in Section 4.2. 

Determination of the optimum complexity of a model is an important but not always an easy task, because the minimum of measures for the prediction error for test sets is often not well marked. In chemometrics, the complexity is typically controlled by the number of PLS or PCA components, and the optimum complexity is estimated by CV (Section 4.2.5). Several strategies are applied to determine a reasonable optimum complexity from the prediction errors which may have been obtained by CV (Figure 4.4). CV or bootstrap allows an estimation of the prediction error for each object of the calibration set at each considered model complexity. 

Not just by accident PLS regression is the most used method for multivariate calibration in chemometrics. So, we recommend to start with PLS for single y-variables, using all x-variables, applying CV (leave-one-out for a small number of objects, say for n < 30, 3-7 segments otherwise). The SEPCV (standard deviation of prediction errors obtained from CV) gives a first idea about the relationship between the used x-variables and the modeled y, and hints how to proceed. Great effort should be applied for a reasonable estimation of the prediction performance of calibration models. 

Multidimensional Data Intercomparisons. Estimation of reliable uncertainty intervals becomes quite complex for non-linear operations and for some of the more sophisticated multidimensional models. For this reason, "chemometric" validation, using common, carefully-constructed test data sets, is of increasing importance. Data evaluation intercomparison exercises are thus analogous to Standard Reference Material (SRM) laboratory intercomparisons, except that the final, data evaluation step of the chemical measurement process is being tested. 

Chemometric quality assurance via laboratory and method intercomparisons of standardized test data sets, finally, is becoming recognized as essential for establishing the validity of detection decisions and estimated detection limits, especially when treating multidimensional data with sophisticated algorithms including several chemical components. 

K.H. Esbensen, H.H. Eriis-Petersen, L. Petersen, J.B. Hohn-Nielsen and P.P. Mortensen, Representative process sampling - in practice variographic analysis and estimation of Total Sampling Errors (TSE). Proceedings 5 th Winter Symposium of Chemometrics (WSC-5), Samara 2006. Chemom. Intell. Lab. Syst, Special Issue, 88(1), 41—19 (2007). 

The first results from the use of PLS were reported by Dunn fit al (6) who estimated the composition of PCB contaminated waste oil in terms of Aroclor mixtures. Stalling gt al (13), who reported on the characterization of PCB mixtures and the use of three-dimensional plots derived from principal components, demonstrated that the fractional composition of TCDD and other PCDD residues were related to their geographical origins. These two reports (6,13) described the application of an advanced chemometric tool in residue studies and illustrated the... 

Baroni, M., Constantino, G., Cruciani, G., Riganelli, D., Valigli, R. and Clementi, S. (1993) Generating optimal linear pis estimations (GOLPE) An advanced chemometric tool for handling 3D-QSAR problems. Quantitative Stmcture-Activity Relationships, 12, 9-20. 

Of course, I can only speak for myself with regard to the amount of time that is required to develop, test, deploy, and maintain chemometric models for on-line analytical applications. However, it should be apparent that there are several tasks involved in this process, and many of them have nothing to do with building models. I am tempted to provide my estimate of the fraction of time that is typically spent on each of these steps, but I feel obligated to retreat, so that I do not report too biased an assessment (even though I have received feedback from several colleagues on this matter). Instead, I will simply list the tasks and supply a general indicator of the relative level of time spent on each one. 

Kutz, D.A. (Ed.) Chemometric Estimators of Sampling, Amount and Error, ACS Symposium Series No. 284, American Chemical Society, Washington, D.C., 1985... 

---