Regression imputation with Q-mode clustering for rounded zero replacement in high-dimensional compositional data

References

• J. Aitchison, The Statistical Analysis of Compositional Data, Chapman & Hall, London, 1986.
   Google Scholar
• J. Chen, X. Zhang, and S. Li, Multiple linear regression with compositional response and covariates, J. Appl. Stat. 44 (2017), pp. 2270–2285. doi: 10.1080/02664763.2016.1157145
   Web of Science ®Google Scholar
• J.J. Egozcue, V. Pawlowsky-Glahn, G. Mateu-Figueras, and C. Barceló-Vidal, Isometric logratio transformations for compositional data analysis, Math. Geol. 35 (2003), pp. 279–300. doi: 10.1023/A:1023818214614
   Google Scholar
• P. Filzmoser, K. Hron, and C. Reimann, Univariate statistical analysis of environmental (compositional) data: Problems and possibilities, Sci. Total Environ. 407 (2009), pp. 6100–6108. doi: 10.1016/j.scitotenv.2009.08.008
   PubMed Web of Science ®Google Scholar
• G.B. Gloor, J.R. Wu, V. Pawlowsky-Glahn, and J.J. Egozcue, It's all relative: Analyzing microbiome data as compositions, Ann. Epidemiol. 26 (2016), pp. 322–329. doi: 10.1016/j.annepidem.2016.03.003
   PubMed Web of Science ®Google Scholar
• J. Hinkle and W. Rayens, Partial least squares and compositional data: Problems and alternatives, Chemometr. Intell. Lab. Syst. 30 (1995), pp. 159–172. doi: 10.1016/0169-7439(95)00062-3
   Web of Science ®Google Scholar
• H. Janečková, K. Hron, P. Wojtowicz, E. Hlídková, A. Barešová, D. Friedecký, L. Žídková, P. Hornik, D. Behúlová, D. Procházková, H. Vinohradská, K. Pešková, P. Bruheim, V. Smolka, S. Štastná, and T. Adam, Targeted metabolomic analysis of plasma samples for the diagnosis of inherited metabolic disorders, J. Chromatogr. A 1226 (2012), pp. 11–17. doi: 10.1016/j.chroma.2011.09.074
   PubMed Web of Science ®Google Scholar
• A. Kalivodová, K. Hron, P. Filzmoser, L. Najdekr, H. Janečková, and T. Adam, PLS-DA for compositional data with application to metabolomics, J. Chemom. 29 (2015), pp. 21–28. doi: 10.1002/cem.2657
   Web of Science ®Google Scholar
• J.A. Martín-Fernández, C. Barceló-Vidal, and V. Pawlowsky-Glahn, Dealing with zeros and missing values in compositional data sets using nonparametric imputation, Math. Geol. 35 (2003), pp. 253–278. doi: 10.1023/A:1023866030544
   Google Scholar
• J.A. Martín-Fernández, J. Palarea-Albaladejo, and R.A. Olea, Dealing with zeros, in Compositional Data Analysis: Theory and Applications, V. Pawlowsky-Glahn and A. Buccianti, eds., Wiley, Chichester, 2011, pp. 43–58.
   Google Scholar
• J.A. Martín-Fernández, K. Hron, M. Templ, P. Filzmoser, and J. Palarea-Albaladejo, Model-based replacement of rounded zeros in compositional data: Classical and robust approaches, Comput. Statist. Data Anal. 56 (2012), pp. 2688–2704. doi: 10.1016/j.csda.2012.02.012
   Web of Science ®Google Scholar
• J.M. McKinley, K. Hron, E.C. Grunsky, C. Reimann, P. de Caritat, P. Filzmoser, K.G. van den Boogaart, and R. Tolosana-Delgado, The single component geochemical map: Fact or fiction?, J. Geochem. Explor. 162 (2016), pp. 16–28. doi: 10.1016/j.gexplo.2015.12.005
   Web of Science ®Google Scholar
• J. Palarea-Albaladejo and J.A. Martín-Fernández, A modified EM alr-algorithm for replacing rounded zeros in compositional data sets, Comput. Geosci. 34 (2008), pp. 902–917. doi: 10.1016/j.cageo.2007.09.015
   Web of Science ®Google Scholar
• J. Palarea-Albaladejo and J.A. Martín-Fernández, Values below detection limit in compositional chemical data, Anal. Chim. Acta 764 (2013), pp. 32–43. doi: 10.1016/j.aca.2012.12.029
   PubMed Web of Science ®Google Scholar
• J. Palarea-Albaladejo and J.A. Martín-Fernández, zCompositions-R package for multivariate imputation of left-censored data under a compositional approach, Chemometr. Intell. Lab. Syst. 143 (2015), pp. 85–96. doi: 10.1016/j.chemolab.2015.02.019
   Web of Science ®Google Scholar
• J. Palarea-Albaladejo, J.A. Martín-Fernández, and J. Gómez-García, A parametric approach for dealing with compositional rounded zeros, Math. Geol. 39 (2007), pp. 625–645. doi: 10.1007/s11004-007-9100-1
   Google Scholar
• V. Pawlowsky-Glahn and A. Buccianti, Compositional Data Analysis: Theory and Applications, Wiley, Chichester, 2011.
   Google Scholar
• V. Pawlowsky-Glahn and J.J. Egozcue, Geometric approach to statistical analysis on the simplex, Stoch. Environ. Res. Risk Assess. 15 (2001), pp. 384–398. doi: 10.1007/s004770100077
   Web of Science ®Google Scholar
• V. Pawlowsky-Glahn, J.J. Egozcue, and R. Tolosana-Delgado, Modeling and Analysis of Compositional Data, Statistics in Practice, Wiley, Chichester, 2015.
   Google Scholar
• M. Templ, K. Hron, P. Filzmoser, and A. Gardlo, Imputation of rounded zeros for high-dimensional compositional data, Chemometr. Intell. Lab. Syst. 155 (2016), pp. 183–190. doi: 10.1016/j.chemolab.2016.04.011
   Web of Science ®Google Scholar
• M.C.B. Tsilimigras and A.A. Fodor, Compositional data analysis of the microbiome: Fundamentals, tools, and challenges, Ann. Epidemiol. 26 (2016), pp. 330–335. doi: 10.1016/j.annepidem.2016.03.002
   PubMed Web of Science ®Google Scholar
• K.G. van den Boogaart and R. Tolosana-Delgado, Analyzing Compositional Data with R, Springer, Heidelberg, 2013.
   Google Scholar
• K. Varmuza and P. Filzmoser, Introduction to Multivariate Statistical Analysis in Chemometrics, Taylor & Francis, New York, 2009.
   Google Scholar
• H. Wang, J. Meng, and M. Tenenhaus, Regression modelling analysis on compositional data, in Handbook of Partial Least Squares: Concepts, Methods and Applications, V.E. Vinzi, W.W. Chin, J. Henseler, and H. Wang, eds., Springer Berlin Heidelberg, 2010, pp. 381–406.
   Google Scholar