Terje V. Karstang

Interpretation of latent-variable regression models

Abstract In this work, we show that the projections of the predictors on the normalized regression vectors represent a target rotation with the responses (concentration vectors) as targets. By means of this operation the predictive ability of a latent-variable (LV) regression model and the importance of each predictor for all the responses is obtained. The two features can be portrayed simultaneously and quantitatively in an LV regression BIPLOT display. This graph shows how modelled interferents influence prediction, information as important as the detection of and correction for unmodelled interferents when using a regression model for prediction. For samples characterized by whole digital profiles rather than a collection of peaks, graphs showing the covariances between the responses and the original or the reproduced predictor space appear to provide the most useful information for interpreting an LV regression model.

Chapter 7 SIMCA - Classification by Means of Disjoint Cross Validated Principal Components Models

Publisher Summary The classification method Soft Independent Modelling of Class Analogies (SIMCA) is such a method that each class of samples is described by its own principal component model. Thus, in principle, any degree of data collinearity can be accommodated by the models. The chapter presents with a discussion on the important role played by correlation when assessing similarity, and introduces the properties of principal component modelling of relevance to a classification problem. All basic concepts and steps in the SIMCA approach to supervised modelling are thoroughly explored using chemical data obtained in an environmental study. Definition of distance is central in all classification procedures. Euclidean distance in variable space is the most commonly used for measuring similarity between samples. This measure is presented in two-dimensional space. Principal component modelling plays two different roles in the classification of multivariate data, they are as follows: (1) it is a tool for data reduction to obtain low-dimensional orthogonal representations of the multivariate variable- and object-space in which object and variable relationships can be explored, (2) it is used in the SIMCA method to separate the data into a model and a residual matrix from which a scale can be obtained for later classification of samples. Sometimes SIMCA classification is preceded by an unsupervised principal component modelling of the whole data set. The process of detecting and deleting outliers represents one side of the process termed “polishing of classes.”

Optimized scaling: A novel approach to linear calibration with closed data sets

Abstract Karstang, T.V. and Manne, R., 1992. Optimized scaling. A novel approach to linear calibration with closed data sets. Chemometrics and Intelligent Laboratory Systems , 14: 165–173. Optimized scaling is a new calibration method for closed data sets which corrects for multiplicative effects or errors in the calibration step. The predictive ability is compared to the methods of partial least squares (PLS) regression and principal component regression. On data sets where multiplicative effects are present, optimized scaling gave the lowest prediction errors. On data sets where multiplicative corrections are not needed, optimized scaling gave comparable results to PLS regression.

Maturity of kerogen and asphaltenes determined by partial-least-squares (PLS) calibration and target projection of diffuse reflectance Fourier transformed infrared spectra

Abstract Maturation of sedimentary organic matter expressed as: (1) vitrinite reflectance; (2) depth within the same geological formation; and (3) pyrolysis temperature in hydrous pyrolysis experiments is assessed by diffuse reflectance i.r. spectroscopy either using an index defined from intensities of specific peaks or through a multivariate calibration of the spectral profiles with their respective maturation indicators as dependent variables. The samples were of three kinds: (a) kerogen samples (46) of varying maturity from the North Sea; (b) asphaltene samples (108) prepared from sediments obtained from two different wells and a reservoir from the North Sea; and (c) asphaltene samples prepared from hydrous pyrolysate of a sediment containing type II kerogen. The spectra show that the following chemical processes take place during maturation: (i) elimination of carbonyl groups; (ii) depletion of aliphatic chains; and (iii) increase in aromatic content. The univariate index, although sensitive to changes in organic facies, seems applicable within the oil window with the best results obtained for type III kerogen. Multivariate calibration of kerogen samples reveals the capability of the PLS method for predicting vitrinite reflectance. Target projections of the PLS components provide validated spectral profiles, related to the collective changes taking place during both natural and simulated evolution.

Analysis of Nontransparent Polymers: Mixture Design, Second-Derivative Attenuated Total Internal Reflectance FT-IR, and Multivariate Calibration

The composition of nontransparent polymers has been predicted from the fingerprint region in the mid-IR. The polymers were analyzed by the Horizontal Attenuated Total internal Reflection (HATR) FT-IR technique. The polymers were blends of three different master batches: (1) a polymer of ethylene with carbon black, (2) a co-polymer of ethylene and propylene monomers, and (3) an ethylene-propylene-diene elastomer. A calibration set was defined by use of mixture design. Partial least-squares (PIS) regression was used to calculate models for prediction of the relative concentrations of each master batch (one at a time). Second-derivated IR profiles normalized to 100% were used as predictive variables. Two alternative criteria were compared for optimizing the predictive ability of the calibration models: (1) squared prediction error of all the calibration samples, and (2) prediction error of replicated calibration samples of the centerpoint in the design only. The latter criterion turned out to be the more useful for the purpose of this study. This is because the centerpoint represents the target sample of the blending process. The one-component PLS models, suggested by the latter optimization criterion, gave predictions within 1% of the stated relative concentrations and with standard deviations from 0.5 to 1.3% for all three master batches.

Infrared spectroscopy and multivariate calibration used in quantitative analysis of additives in high-density polyethylene

Abstract Karstang, T.V. and Henriksen, A., 1992. Infrared spectroscopy and multivariate calibration used in quantitative analysis of additives in high-density polyethylene. Chemometrics and Intelligent Laboratory Systems, 14: 331–339. Different techniques for normalization and calibration of additives in one high-density polyethylene product are compared. The infrared spectra are calibrated against the concentration of three additives. The prediction results from optimized scaling of the raw data are similar to the results using partial least squares regression on data normalized using an internal standard. The performance of three background correction techniques on three other qualities of high-density polyethylene is also compared. By applying background correction techniques a calibration model designed for one product of high-density polyethylene can be used on other products with only a small loss in predictive power.

Comparison between three techniques for background correction in quantitative analysis

Abstract Karstang, T.V. and Kvalheim, O.M., 1991. Comparison between three techniques for background correction in quantitative analysis. Chemometrics and Intelligent Laboratory Systems, 12: 147–154. The three background techniques compared in this work all take as their starting point a principal component (PC) model that describes the calibration space. The PC model is then combined with a function that describes the spectrum of the background constituents. Three data sets are analyzed, of which two are normalized to constant sum for the concentrations. The results using (1) curve fitting (CF), (2) iterative target transformation factor analysis, and (3) local curve fitting (LCF), indicate that the curve fitting techniques (LCF and CF) give smallest prediction errors.

Diffuse reflectance Fourier-transformed infrared spectroscopy in petroleum exploration: a multivariate approach to maturity determination

The present contribution focuses on three aspects of the generation, presentation and use of infrared (ir) spectroscopic data for maturity determination of sedimentary organic matter: (1) the use of diffuse reflectance Fourier-transformed infrared analysis to characterize maturity, (2) automated procedures for transfer and reduction of profiles obtained by the spectroscopic analysis; and (3) extraction of maturity information from the spectral profiles. A sample set consisting of 44 asphaltene samples from two wells in the North Sea is used to illustrate the potential of the combined spectroscopic and data-analytical approach. Multivariate regression with vitrinite reflectance as dependent variable is used to reveal the maturity information in the IR spectroscopic profiles. Eighteen samples covering the maturity range 0.29–0.83% ro were used for obtaining a joint multivariate regression model for the two wells. The maturity of the 44 samples was subsequently predicted from the ir profiles and the maturity trends for the two wells compared with trends obtained from vitrinite reflectance measurements.