Skip to main content
SpringerLink
Log in

Log-ratio approach in curve fitting for concentration-response experiments

  • Published:
Environmental and Ecological Statistics Aims and scope Submit manuscript

Abstract

The assessment of the ecological risk of chemical contamination by pollutants, pesticides or toxicants is of primary interest in environmental statistics. Concentration-response models play a fundamental role in computing the risk values connected with some exposure levels of a particular contaminant in living organisms. The present paper proposes a regression model called simplicial regression. This model is able to cope with the relative character of the explanatory and response parts via the logratio methodology of compositional data. Consequently, it allows performance of the corresponding statistical inference under the assumption of normality. Some real-world examples show that simplicial regression even outperforms the existing well-established methodologies on standard accuracy and quality-of-fit criteria. The better fit is due to the change of scale entailed by the new model.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  • Aitchison J (1986) The statistical analysis of compositional data. Chapman & Hall, London

    Book  Google Scholar 

  • Backhaus T, Altenburger R, Boedeker W, Faust M, Scholze M, Grimme LH (2000) Predictability of the toxicity of a multiple mixture of dissimilarly acting chemicals to Vibrio fischeri. Environ Toxicol Chem 19:2348–2356

    Article  CAS  Google Scholar 

  • Backhaus T, Froehner K, Altenburger R, Grimme LH (1997) Toxicity testing with Vibrio fischeri: a comparison between the long term (24 h) and the short term (30 min) bioassay. Chemosphere 35:2925–2938

    Article  CAS  Google Scholar 

  • Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York

    Google Scholar 

  • Casella G, Berger RL (2007) Statistical inference, 2nd edn. Duxbury Press (Thomson Learning Academic Resource Center), Pacific Grove

    Google Scholar 

  • Cribari-Neto F, Zeileis A (2010) Beta regression in R. J Stat Softw 34(2):1–24

    Google Scholar 

  • Davidian M, Carroll RJ, Smith W (1988) Variance functions and the minimum detectable concentration in assays. Biometrika 75:549–556

    Article  Google Scholar 

  • EFSA (2005) Opinion of the scientific panel on plant health, plant protection products and their residues on a request from EFSA related to the assessment of the acute and chronic risk to aquatic organisms with regard to the possibility of lowering the uncertainty factor if additional species were tested. EFSA J 301:1–45 (2005)

  • Egozcue JJ, Daunis-i-Estadella J, Pawlowsky-Glahn V, Hron K, Filzmoser P (2011) Simplicial regression, the normal model. J Appl Probab Stat 6:87–108

    Google Scholar 

  • Egozcue JJ, Pawlowsky-Glahn V (2006) Simplicial geometry for compositional data. In: Buccianti A, Mateu-Figueras G, Pawlowsky-Glahn V (eds) Compositional data analysis in the geosciences: from theory to practice. Geological Society, London, pp 145–160

    Google Scholar 

  • Egozcue JJ, Pawlowsky-Glahn V, Mateu-Figueras G, Barceló-Vidal C (2003) Isometric logratio transformations for compositional data analysis. Math Geol 35:279–300

    Article  Google Scholar 

  • Environment Canada. Guidance document on statistical methods for environmental toxicity tests. Report EPS /RM/46. Ottawa, ON (2005)

  • Ferrari S, Cribari-Neto F (2004) Beta regression for modelling rates and proportions. J Appl Stat 31:799–815

    Article  Google Scholar 

  • Filzmoser P, Hron K, Reimann C (2009) Univariate statistical analysis of environmental (compositional) data: Problems and possibilities. Sci Total Environ 407:6100–6108

    Article  CAS  PubMed  Google Scholar 

  • Finney DJ (1979) Bioassay and the practice of statistical inference. Int Stat Rev 47:1–12

    Article  Google Scholar 

  • Hron K, Templ M, Filzmoser P (2013) Estimation of a proportion in survey sampling using the logratio approach. Metrika 76:799–818

    Article  Google Scholar 

  • Kieschnick R, McCullough BD (2003) Regression analysis of variates observed on (0,1): percentages, proportions and fractions. Stat Model 3:193–213

    Article  Google Scholar 

  • Long JS (1997) Regression models for categorical and limited dependent variables. Sage, London

    Google Scholar 

  • Martín-Fernández JA, Palarea-Albaladejo J, Olea RA (2011) Dealing with zeros. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, Chichester, pp 43–58

    Chapter  Google Scholar 

  • Mateu-Figueras G, Pawlowsky-Glahn V (2008) A critical approach to probability laws in geochemistry. Math Geosci 40:489–502

    Article  Google Scholar 

  • Mateu-Figueras G, Pawlowsky-Glahn V, Egozcue JJ (2011) The principle of working on coordinates. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, Chichester, pp 31–42

    Google Scholar 

  • McCullagh P, Nelder JA (1989) Generalized linear models, 2nd edn. Chapman & Hall, London

    Book  Google Scholar 

  • Montgomery DC, Peck EA, Vining GG (2001) Introduction to linear regression analysis, 4th edn. Wiley, Hoboken

    Google Scholar 

  • Morgan BJT (1992) Analysis of quantal response data: monographs on statistics and applied probability. Chapman & Hall/CRC, london

    Book  Google Scholar 

  • Organization for Economic Cooperation and Development (2006) Current approaches in the statistical analysis of ecotoxicity data: a guidance to application. Chapter 6. Paris, France, pp 62–102

  • Pawlowsky-Glahn V, Buccianti A (2011) Compositional data analysis: theory and applications. Wiley, Chichester

    Book  Google Scholar 

  • R Core Team (2012) R: a language and environment for statistical computing. R Foundation for Statistical Computing, Vienna

  • Ripley BD (1996) Pattern recognition and neural networks. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Ritz Ch (2010) Toward a unified approach to dose-response modeling in ecotoxicology. Environ Toxicol Chem 29:220–229

    Article  CAS  PubMed  Google Scholar 

  • Scholze M, Boedeker W, Faust M, Backhaus T, Altenburger R, Grimme LH (2001) A general best-fit method for concentration-response curves and the estimation of low-effect concentrations. Environ Toxicol Chem 20:448–457

    Article  CAS  PubMed  Google Scholar 

  • Seber GAF, Wild CJ (2005) Nonlinear regression, Series in probability and statistics. Wiley, New York

    Google Scholar 

  • Stroup WW (2012) Generalized linear mixed models: modern concepts, methods and applications. CRC Press, Boca Raton

    Google Scholar 

  • Tolosana-Delgado R, van den Boogaart KG (2011) Linear models with compositions in R. In: Pawlowsky-Glahn V, Buccianti A (eds) Compositional data analysis: theory and applications. Wiley, Chichester, pp 356–371

    Chapter  Google Scholar 

  • van den Boogaart KG, Tolosana-Delgado R (2013) Analyzing compositional data with R. Springer, Heidelberg

    Book  Google Scholar 

  • Venables WN, Ripley BD (2002) Modern applied statistics with S. Springer, New York

    Book  Google Scholar 

  • Vighi M, Migliorati S, Monti GS (2009) Toxicity on the luminescent bacterium Vibrio fischeri (Beijerinck). I: QSAR equation for narcotics and polar narcotics. Ecotoxicol Environ Saf 72:154–161

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgments

Research partially financially supported by the Italian Ministry of University and Research, FAR (Fondi di Ateneo per la Ricerca) 2011. The authors also gratefully acknowledge the support of both the Operational Program Education for Competitiveness—European Social Fund (Project CZ.1.07/2.3.00/20.0170 of the Ministry of Education, Youth and Sports of the Czech Republic) and the grant IGA_PrF_2014_028 Mathematical Models of the Internal Grant Agency of the Palacký University in Olomouc. The authors are grateful to Professor Marco Vighi who has kindly permitted the elaboration of the Vibrio fischeri (Beijerinck) data set.

Author information

Authors and Affiliations

  1. Department of Economics, Management and Statistics, University of Milano-Bicocca, Milan, Italy

    Gianna S. Monti & Sonia Migliorati

  2. Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, Palacký University, Olomouc, Czech Republic

    Karel Hron, Klára Hrůzová & Eva Fišerová

  3. Department of Geoinformatics, Faculty of Science, Palacký University, Olomouc, Czech Republic

    Karel Hron, Klára Hrůzová & Eva Fišerová

Authors
  1. Gianna S. Monti
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sonia Migliorati
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Karel Hron
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Klára Hrůzová
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Eva Fišerová
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gianna S. Monti.

Additional information

Handling Editor: Bryan F. J. Manly.

Appendix: Supporting information

Appendix: Supporting information

Supplementary data associated with this article concern other non-polar and polar narcotics datasets.

See Figs. 3, 4, 5 and 6 and Tables 7, 8, 9, 10, 11 and 12.

Fig. 3
figure 3

Fitting comparison for Butylacetate compound

Full size image
Fig. 4
figure 4

Fitting comparison for the Diethylether compound

Full size image
Fig. 5
figure 5

Fitting comparison for the Metoxyaniline 4 compound

Full size image
Fig. 6
figure 6

Fitting comparison for the Phenylendiammine compound

Full size image
Table 7 Goodness of fit measures and DEV measure after CV for different regression models in the case of Butylacetate compound
Full size table
Table 8 Measures of accuracy after CV and goodness of fit measures for different regression models in the case of Diethylether compound
Full size table
Table 9 Effective log-concentrations resulting from the best-fit and simplicial regression models with the corresponding confidence intervals at 0.95 confidence level for non-polar narcotics
Full size table
Table 10 Measures of accuracy after CV and goodness of fit measures for different regression models in the case of Metoxyaniline 4 compound
Full size table
Table 11 Measures of accuracy after CV and goodness of fit measures for different regression models in the case of Phenylendiammine compound
Full size table
Table 12 Effective log-concentrations resulting from the best-fit and simplicial regression models with the corresponding confidence intervals at 0.95 confidence level for polar narcotics
Full size table

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Monti, G.S., Migliorati, S., Hron, K. et al. Log-ratio approach in curve fitting for concentration-response experiments. Environ Ecol Stat 22, 275–295 (2015). https://doi.org/10.1007/s10651-014-0298-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10651-014-0298-z

Keywords

Search

Navigation