Chapter 4 – Regression

In this chapter, a survey of the theory behind the main chemometric methods used for multivariate calibration is presented. Ordinary least squares, multiple linear regression, principal component regression, partial least squares regression and principal covariate regression are discussed in detail. Tools for model diagnostics and model interpretation are presented, together with strategies for variable selection.

[1]  B. Kowalski,et al.  Partial least-squares regression: a tutorial , 1986 .

[2]  I. Jolliffe A Note on the Use of Principal Components in Regression , 1982 .

[3]  R. Leardi,et al.  Sequential application of backward interval partial least squares and genetic algorithms for the selection of relevant spectral regions , 2004 .

[4]  S. Wold,et al.  The multivariate calibration problem in chemistry solved by the PLS method , 1983 .

[5]  H. Lohninger,et al.  Validation of chemometric models for the determination of deoxynivalenol on maize by mid-infrared spectroscopy , 2008, Mycotoxin Research.

[6]  S. Engelsen,et al.  Interval Partial Least-Squares Regression (iPLS): A Comparative Chemometric Study with an Example from Near-Infrared Spectroscopy , 2000 .

[7]  S. Wold Cross-Validatory Estimation of the Number of Components in Factor and Principal Components Models , 1978 .

[8]  Wojtek J. Krzanowski,et al.  Principles of multivariate analysis : a user's perspective. oxford , 1988 .

[9]  S. Wold,et al.  PLS: Partial Least Squares Projections to Latent Structures , 1993 .

[10]  F. Galton Kinship and Correlation , 1989 .

[11]  H. Hotelling The Generalization of Student’s Ratio , 1931 .

[12]  Bruce R. Kowalski,et al.  Propagation of measurement errors for the validation of predictions obtained by principal component regression and partial least squares , 1997 .

[13]  Riccardo Leardi,et al.  Genetic algorithm-PLS as a tool for wavelength selection in spectral data sets , 2003 .

[14]  R. Bro PARAFAC. Tutorial and applications , 1997 .

[15]  Henk A. L. Kiers,et al.  Principal covariates regression: Part I. Theory , 1992 .

[16]  Bruce R. Kowalski,et al.  Qualitative Information from Multivariate Calibration Models , 1990 .

[17]  D. Massart,et al.  The Mahalanobis distance , 2000 .

[18]  B. Efron Bootstrap Methods: Another Look at the Jackknife , 1979 .

[19]  Ronald R. Coifman,et al.  Partial least squares, Beer's law and the net analyte signal: statistical modeling and analysis , 2005 .

[20]  Rasmus Bro,et al.  Some common misunderstandings in chemometrics , 2010 .

[21]  Gene H. Golub,et al.  An analysis of the total least squares problem , 1980, Milestones in Matrix Computation.

[22]  R. Penrose A Generalized inverse for matrices , 1955 .

[23]  J. E. Jackson A User's Guide to Principal Components , 1991 .

[24]  Rasmus Bro,et al.  Variable selection in regression—a tutorial , 2010 .

[25]  I. Jolliffe Principal Component Analysis , 2002 .

[26]  Paul Geladi,et al.  Principles of Proper Validation: use and abuse of re‐sampling for validation , 2010 .

[27]  Rasmus Bro,et al.  Finding relevant spectral regions between spectroscopic techniques by use of cross model validation and partial least squares regression. , 2007, Analytica chimica acta.

[28]  O. Kvalheim,et al.  Biomarker discovery in mass spectral profiles by means of selectivity ratio plot , 2009 .

[29]  N. M. Faber,et al.  Uncertainty estimation and figures of merit for multivariate calibration (IUPAC Technical Report) , 2006 .

[30]  H. Martens,et al.  Light scattering and light absorbance separated by extended multiplicative signal correction. application to near-infrared transmission analysis of powder mixtures. , 2003, Analytical chemistry.

[31]  B. Efron The jackknife, the bootstrap, and other resampling plans , 1987 .

[32]  N. M. Faber,et al.  Sample-specific standard error of prediction for partial least squares regression , 2003 .

[33]  K. F. Gauss,et al.  Theoria combinationis observationum erroribus minimis obnoxiae , 1823 .

[34]  M. Stone Cross‐Validatory Choice and Assessment of Statistical Predictions , 1976 .

[35]  Harald Martens,et al.  Reducing over-optimism in variable selection by cross-model validation , 2006 .

[36]  R. Tauler Multivariate curve resolution applied to second order data , 1995 .

[37]  Jian-hui Jiang,et al.  On estimating model complexity and prediction errors in multivariate calibration: generalized resampling by random sample weighting (RSW) , 2011 .

[38]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[39]  E. Oja,et al.  Independent Component Analysis , 2013 .

[40]  P. Rousseeuw,et al.  Unmasking Multivariate Outliers and Leverage Points , 1990 .

[41]  John C. Gower,et al.  A general theory of biplots , 1995 .

[42]  G. Udny Yule,et al.  On the Interpretation of Correlations between Indices or Ratios , 1910 .

[43]  R. L. Mason,et al.  Selecting principal components in regression , 1985 .

[44]  R Bro,et al.  Cross-validation of component models: A critical look at current methods , 2008, Analytical and bioanalytical chemistry.