AoV-PLS: a new method for the analysis of multivariate data depending on several factors


Abstract


A new method for the analysis of a multivariate dataset depending on several factors is proposed. It is called AoV-PLS (Analysis of Variance-PLS). It is based on the decomposition of the dataset into the main effects, the interactions effects and possibly the residual matrix using a model akin to analysis of variance (ANOVA). Each effect is considered in turn and assessed through the use of a Partial Least Square regression (PLS-regression).
The connection of AoV-PLS to competing methods such as ANOVA-PCA and ANOVA-Simultaneous Component Analysis (ASCA) is emphasized and these methods are compared on the basis of a dataset pertaining to metabolomics field.

DOI Code: 10.1285/i20705948v8n2p214

Keywords: ANOVA; ANOVA-Simultaneous Component Analysis, ANOVA-PCA, PLS regression; PLS-DA; Metabolomics data

References


@article{Smilde105,

Author = {Smilde, A. K and Jansen, J. J. and Hoefsloot, H.C.J. and Lamers, R-J.A.N. and Greef, J. and Timmerman, M.E.},

Title = {ANOVA-simultaneous component analysis (ASCA): a new tool for analyzing designed metabolomics data},

Journal = {Bioinformatics},

Volume = {21},

Number = {13},

Pages = {3043-3048},

Year = {2005} }

@article{Barker03,

Author = {Barker, M. and Rayens, W.},

Title = {Partial least squares for discrimination},

Journal = {Journal of Chemometrics},

Volume = {17},

Number = {3},

Pages = {166-173},

Year = {2003} }

@article{Nocairi05,

Author = {Nocairi, H. and Qannari, E. M. and Vigneau, E. and Bertrand, D.},

Title = {Discrimination on latent components with respect to patterns. Application to multicollinear data},

Journal = {Computational Statistics and Data Analysis},

Volume = {48},

Number = {1},

Pages = {139-147},

Year = {2005} }

@Book{McLachlan04,

author = {Geoffrey J. McLachlan},

publisher = {Wiley Series in Probability and Statistics},

title = {Discriminant Analysis and Statistical Pattern Recognition},

year = {2004}

}

@article{Kemsley96,

Author = {Kemsley, E. K.},

Title = {Discriminant analysis of high-dimensional data: a comparison of principal components analysis and partial least squares data reduction methods},

Journal = {Chemometrics and Intelligent Laboratory Systems},

Volume = {33},

Number = {1},

Pages = {47-61},

Year = {1996} }

@article{Harrington05,

Author = {Harrington, Peter de B. and Vieira, Nancy E. and Espinoza, Jimmy and Nien, Jyh Kae and Romero, Roberto and Yergey, Alfred L.},

Title = {Analysis of variance-principal component analysis: A soft tool for proteomic discovery},

Journal = {Analytica Chimica Acta},

Volume = {544},

Number = {1-2},

Pages = {118-127},

Year = {2005} }

@article{Harrington06,

Author = {Harrington, Peter de B. and Vieira, Nancy E. and Chen, Ping and Espinoza, Jimmy and Nien, Jyh Kae and Romero, Roberto and Yergey, Alfred L.},

Title = {Proteomic analysis of amniotic fluids using analysis of variance-principal component analysis and fuzzy rule-building expert systems applied to matrix-assisted laser desorption/ionization mass spectrometry},

Journal = {Chemometrics and Intelligent Laboratory Systems},

Volume = {82},

Number = {1-2},

Pages = {283-293},

Year = {2006} }

@article{Sarembaud07,

Author = {Sarembaud, J. and Pinto, R. and Rutledge, D.N. and Feinberg, M.},

Title = {Application of the ANOVA-PCA method to stability studies of reference materials},

Journal = {Analytica Chimica Acta},

Volume = {603},

Number = {2},

Pages = {147-154},

Year = {2007} }

@Book{Tenenhaus98,

author = {Tenenhaus, Michel},

publisher = {Technip. Paris},

title = {La r'egression PLS, th'eorie et pratique},

year = {1998}

}

@article{Vis07,

Author = {Vis, Daniel and Westerhuis, Johan and Smilde, Age K and van der Greef, Jan},

Title = {Statistical validation of megavariate effects in ASCA},

Journal = {BMC Bioinformatics},

Volume = {8},

Number = {1},

Pages = {322},

Year = {2007} }

@article{Zwanenburg11,

Author = {Zwanenburg, Gooitzen and Hoefsloot, Huub C. J. and Westerhuis, Johan A. and Jansen, Jeroen J. and Smilde, Age K.},

Title = {ANOVA-principal component analysis and ANOVA-simultaneous component analysis: a comparison},

Journal = {Journal of Chemometrics},

Volume = {25},

Number = {10},

Pages = {561-567},

Year = {2011} }

@article{Pinto09,

Author = {Climaco-Pinto, R. and Barros, A. S. and Locquet, N. and Schmidtke, L. and Rutledge, D. N.},

Title = {Improving the detection of significant factors using ANOVA-PCA by selective reduction of residual variability},

Journal = {Analytica Chimica Acta},

Volume = {653},

Number = {2},

Pages = {131-142},

Year = {2009} }

@article {Marie14,

author = {Agnoux, Aurore Martin and Antignac, Jean-Philippe and Simard, Gilles and Poupeau, Guillaume and Darmaun, Dominique and Parnet, Patricia and Alexandre-Gouabau, Marie-C{'e}cile},

title = {Time window-dependent effect of perinatal maternal protein restriction on insulin sensitivity and energy substrate oxidation in adult male offspring},

volume = {307},

number = {2},

pages = {R184--R197},

year = {2014},

doi = {10.1152/ajpregu.00015.2014},

publisher = {American Physiological Society},

isbn = {1522-1490},

issn = {0363-6119},

journal = {American Journal of Physiology - Regulatory, Integrative and Comparative Physiology}

}

@article{Thissen09,

Author = {Thissen, Uwe and Wopereis, Suzan and van den Berg, Sjoerd and Bobeldijk, Ivana and Kleemann, Robert and Kooistra, Teake and Willems van Dijk, Ko and van Ommen, Ben and Smilde, Age},

Title = {Improving the analysis of designed studies by combining statistical modelling with study design information},

Journal = {BMC Bioinformatics},

Volume = {10},

Number = {1},

Pages = {52},

Year = {2009} }


Full Text: pdf
Bookmark and Share


Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.